Identification and prediction of the degree of multidimensional returning to poverty risk for the household in China through the novel hybrid model: Based on the survey data of China Family Panel Studies (CFPS)

Abstract

In China, absolute poverty has been effectively eliminated, but this does not signify the complete eradication of poverty. Instead, poverty persists in the forms of relative and secondary poverty. More concerningly, regions or households lifted out of poverty continue to face numerous risks of returning to poverty. In this context, measuring poverty solely based on monetary metrics is no longer adequate. Furthermore, the primary focus of grassroots governance has shifted from merely assessing poverty to accurately predicting the multifaceted risks associated with falling back into poverty. A multidimensional poverty indicator system is constructed to measure and predict the risk of multidimensional returning to poverty in China. Then, the Alkire–Forster counting method is applied to measure the risk of multidimensional poverty return and demonstrate the contribution of various indicators to multidimensional poverty return using tracking survey data from the China Family Panel Studies (CFPS). The results show that the multidimensional poverty return in China is mainly caused by the factors in two or three dimensions, where the social development capability dimension has the highest contribution to the multidimensional poverty return index with 43.12 %, followed by the health and education dimensions. Moreover, according to the finding that the identification of multidimensional poverty varies with the values of the poverty cut-off, a novel and practicable method is proposed to classify the risk into three levels, noted as the high, medium and low levels. Consequently, a hybrid model is constructed to predict the risk of multidimensional poverty return by integrating the Archimedes optimization algorithm (AOA), variational mode decomposition (VMD) and Bi-directional long short-term memory (BiLSTM) neural networks. Finally, the performance of the constructed model is validated with an accuracy up to 99.81 %. The constructed model's efforts outperform the traditional BiLSTM and several prevalent machine learning algorithms through extensive comparative experiments. These results illustrate that the proposed model can accurately and stably predict the potential risk of poverty return for multidimensional poverty groups and regions. In conclusion, drawing from the analysis of factors contributing to the risk of relapsing into poverty in this study, policy suggestions have been formulated focusing on education, social capacity enhancement, and healthcare system advancement. In summary, this paper provides new insights into the factors contributing to multidimensional poverty recurrence and the methods for assessing its risk levels, while also introducing a more precise approach to predicting these levels.

1. Introduction

Poverty is still one of an urgent problem in human society and a common challenge faced by the international community. Even in developed countries like the United States, its extensive economic growth also has failed to lift many existing poor people out of poverty. In recent years, various emergencies and disasters, such as the COVID-19 pandemic, have had a significant impact on global economic development and resulted in larger areas of returning to poverty. Even though China's achievement of comprehensive poverty alleviation in 2020 is a remarkable milestone in its long-term effort on poverty governance, the problem of returning to poverty still persists in some areas or individuals out of poverty. According to the investigation of the registered poor households, the number of people who returned to poverty in China was 684,000, 208,000, and 58,000 in 2016–2018, respectively [1]. Apart from the general income-related factors, the pressure of returning to poverty remains significant due to illness, education, and natural disasters, where poverty or returning to poverty only caused by disease increased from 42.2 % in 2013 to 44.1 % in 2015 [2]. It is obvious that poverty isn't caused by income or monetary-based factors alone [3,4]. In the post-poverty era, multidimensional relative poverty has become a major task in China's anti-poverty struggle [5]. In 2020, General Secretary Xi Jinping pointed out that nearly 2 million people who have escaped from poverty are at risk of returning to poverty, and almost 3 million of the marginal population are at risk of poverty at the symposium on the decisive victory in poverty eradication. The unidimensional measurement of poverty related to the income factor is proven a conservative estimates as compared to the multidimensional measure [6,7]. The multidimensional poverty is more stable than the income poverty [7]. Under this situation, academic research on poverty has expanded from a single static dimension of income to multidimensional welfare poverty [8,9].

In China, scholars studying poverty issues are increasingly adopting multidimensional approaches to measure poverty, moving away from the exclusive reliance on income or monetary standards. Research conducted as early as 2010 compared four approaches to poverty identification: China's official method, participatory poverty assessment, the monetary approach, and the use of multidimensional poverty indicators (MPI), with the conclusion of minimal overlap among the poor households identified by each method [10]. Subsequently, a significant number of scholars have employed multidimensional poverty evaluation methods to study poverty. Their research can be categorized into three main areas. First, some researchers focus on regions as units of analysis to explore the development and disparities of multidimensional poverty across different areas. For instance, studies using Chinese provinces as evaluation units have examined the multidimensional measurement of poverty and its spatiotemporal characteristics from the perspective of development geography [11]. Qi et al. [12] established a multidimensional poverty indicator system using the poverty monitoring dataset to analyze regional poverty based on macro indicators of regional development, further examining regional imbalances in multidimensional poverty. He et al. [13] identified significant spatial and temporal heterogeneity in the incidence of multidimensional poverty in China by surveying 2,022 county-level regions, noting that poverty levels are higher in the western region compared to the lower levels in the eastern region, and that the intensity of poverty increases over time in nationally designated poor counties. Meanwhile, Wang and Qi [14] developed a county-level multidimensional poverty measurement model to examine developmental differences among 14 contiguous destitute areas, confirming the spatial heterogeneity of the Multidimensional Poverty Index (MPI), which varies from high in the west to lower in the east. In detail, In detail, the vulnerability to multidimensional poverty indexes (VMPI) assesses regional rankings and each region's contribution to the country's VMPI, listed from highest to lowest as western, central, eastern, and northeastern [15]. Dou et al. [16] investigated the factors influencing multidimensional poverty reduction and categorized poverty types in Gansu Province using the ArcGIS spatial analysis method. Additionally, nighttime light imagery has been utilized to determine the scale of multidimensional poverty at the county level [[17], [18], [19]].

Beyond studying the spatial characteristics of multidimensional poverty and accurately measuring it within regions, scholars have also explored key factors that alleviate multidimensional poverty. Wang et al. [20] investigated the impacts of tourism on poverty alleviation from the perspective of multidimensional poverty, demonstrating that tourism economic development has significantly contributed to poverty reduction in Fenghuang County. Shuai et al. [21] proposed an analytical framework to explore the relationship between ecosystem services and the multidimensional poverty index, revealing how ecosystem services contribute to poverty reduction in China's Three Gorges Reservoir region. Xiang et al. [22] demonstrated that the coupling level of multidimensional poverty and geological disasters is comparatively prominent through a study on this relationship. In addition, the development of solar photovoltaic projects is viewed as an innovative approach to poverty alleviation in China, effectively reducing poverty levels related to economic, social, and human capital [23]. Further research suggests that the largest contributors to the MPI in these photovoltaic poverty alleviation project pilots are financial and socio-generative factors [24]. Huang et al. [25] provide a systematic review of the impacts of solar photovoltaic projects on poverty alleviation, pointing out that excessive investment inhibits the promotion efficiency of poverty alleviation instead. This research on multidimensional poverty across regions focuses on the development characteristics and heterogeneity of multidimensional poverty between regions, offering recommendations and a foundation for the formulation of more rational poverty alleviation policies in diverse areas.

The other aspect focuses on multidimensional poverty measurement at the household or individual level based on survey data. The primary focus of this research is to develop an assessment indicator system that includes dimensions such as economic factors (income), health, education, and living conditions, aimed at measuring multidimensional poverty indices for individuals or households [[26], [27], [28], [29]]. However, the specific indicators selected vary across studies. Wang et al. measured the Multidimensional Poverty Index (MPI) at the household level, finding significant regional, topographical, and geographical disparities in multidimensional poverty [27]. Zhai et al. [30] developed an index system to assess the Multidimensional Poverty Index (MPI) and the sustainable poverty alleviation capacity of farmers in Yunnan province, demonstrating that ability poverty is the predominant form of poverty among farmers. Overall, the alleviation of multidimensional poverty among Chinese residents is primarily due to a reduction in the incidence of multidimensional poverty, rather than a decrease in its intensity [26,29]. Additionally, a decomposition analysis of multidimensional poverty factors indicates that education, health, chronic illness, and disability are the predominant contributors to multidimensional poverty in Chinese households [26,29,31]. Zhou et al. [32] also confirmed that per capita net income and medical insurance have contributed a lot to the overall chronic multidimensional poverty alleviation of China's rural residents through an investigation on the China's multidimensional poverty reduction effectiveness.

Notably, research on multidimensional poverty in China has increasingly focused on the poverty status of key demographics, including women, children, the middle-aged, the elderly, rural migrant workers, and the migrant population. Peng presented an analytical framework for the multidimensional relative poverty to measure and compare the relative poverty of women and men in rural households in China, clearly illustrating that women experience significantly higher relative poverty than men [33]. Wang et al. examined the levels of multidimensional poverty among persons with disabilities and concluded that enhancing employment services is crucial for reducing their poverty, with an additional emphasis on improving their education and social participation [34]. Similarly, research on multidimensional poverty among children has revealed significant spatial heterogeneity in this demographic's poverty levels [35]. Meanwhile, potential child multidimensional poverty varies by age, gender, and geographic region [6]. Xu et al. [36] built a multidimensional poverty index to capture rural children's poverty and found that the experience of being left-behind significantly increases the probability of falling into multidimensional poverty. Gao et al. [37]examined the effects of rural Dibao receipt on severe child multidimensional poverty. Shen and Alkire [6] constructed a multidimensional poverty indicator system that incorporates various factors contributing to a child's development and well-being. Likewise, Li and Zhang [38] demonstrated that multidimensional poverty also had a direct effect on psychological well-being and distress of left-behind children. Regarding middle-aged and older people, although the incidence of multidimensional poverty has generally decreased, the average intensity of poverty remains stable [39]. Multidimensional poverty among the elderly in China is generally severe, but intergenerational support, particularly emotional support from children, significantly influences poverty alleviation among the elderly [40]. Additionally, good physical and mental health significantly reduces the likelihood of poverty among middle-aged and elderly individuals [41]. Li et al. [42] examined the impact of public long-term care insurance in China on multidimensional poverty among the middle-aged and older populations, focusing on specific indicators such as consumption, material well-being, and social participation. Yu et al. [43] explored the effect of China's New Rural Pension Scheme on reducing multidimensional poverty among the rural elderly. Migrant workers, as a distinct group in China, attracted much attention in this field. The situation of their multidimensional poverty was gradually improving, but the long-term negative impact remains increasingly prominent [44,45]. Correspondingly, the main factors contributing to the multidimensional poverty of the floating population are in the social security and education dimensions [46].

Furthermore, scholars have focused on the mechanisms of multidimensional poverty alleviation and the factors influencing it. Good governance positively impacts the convergence of multidimensional poverty, with the multidimensional headcount ratio declining more rapidly in provinces that have stronger promotional incentives and higher fiscal expenditures [47]. However, in nature conservation areas, increased environmental regulation intensity has significantly heightened multidimensional poverty among farmers by restricting their freedom in production decisions [48]. As to the multidimensional poverty in rural area, agricultural green development [49] and agricultural commercialization [50] have effectively reduced household multidimensional poverty, especially in health and living standards. Additionally, land transfer can significantly reduce the incidence of relative poverty but land lease out and land lease in have asymmetrical effects on multidimensional poverty alleviation [47,48]. Moreover, public-private partnership model of rural land consolidation models can significantly alleviate poverty status of rural households [51]. Particularly, the proliferation of electronic products during rural revitalization has also impacted the multidimensional poverty status of rural households. The mobile internet plays a crucial role in reducing poverty across all dimensions in rural areas, though its impact varies by region [52]. The use of digital information technology has varying effects on poverty reduction across different income groups, demonstrating a significantly higher impact on low-income groups [53].

Further to the above, scholars have investigated the impact of government-led public programs on rural multidimensional poverty, focusing on aspects such as infrastructure development [54], public transfer payments [55], financial inclusion [[56], [57], [58]], digital financial inclusion [59], relocation projects [60], public health services [61], and public pension programs [62]. For instance, Ge et al. illustrated how the introduction of large-scale high-speed railways has improved regional accessibility, enhances local tourism, increases labor mobility, and promotes human capital accumulation, thereby alleviating multidimensional poverty [54]. These studies underscore the necessity of strengthening infrastructure, enhancing rural information technology, intensifying fiscal policy, broadening public services, innovating rural development models, and fortifying grassroots capabilities for poverty governance to effectively alleviate poverty.

What's more, in practical poverty governance, the current criteria for the poor in China are household-based and take into consideration monetary and non-monetary factors. The monetary criteria are related to the household income and the poverty line while the importance of non-income indicators is also emphasized by the fact that the income exceeds the national poverty alleviation standards while satisfying the "two no worries and three guarantees", which refer to assurances of adequate food and clothing, and guarantees of access to compulsory education, essential medical services and safe housing for impoverished rural residents [12]. Meanwhile, to better deal with the return to poverty, China has established affiliated institutions to monitor the status of areas and individuals out of poverty and to detect potential risks of returning to poverty promptly; however, due to the diversity of the identification index and the broad coverage of monitored populations, the existing manual recognition and evaluation methods cannot precisely predict the potential target with the risk in advance. They can only make judgments after the return to poverty has occurred, resulting in the loss of the best time to stop the spread of the risk of returning to poverty, leading to the emergence of repeated poverty and increasing the cost of poverty management.

Therefore, not only is it necessary to conduct an in-depth analysis of the risks of falling back into poverty, understand the specific causes and influencing factors that lead to poverty-stricken populations falling back into poverty, including economic, social, and policy factors, but also to pay attention to the possibility and potential trends of falling back into poverty. Predictive research on the risks of poverty returning helps in formulating more scientific and practical poverty alleviation policies and projects. Based on the prediction results, it is essential to focus on groups and regions with a higher risk of poverty returning and develop targeted assistance plans to help them escape poverty continuously and stably, providing more reliable protection for the sustainable development of poverty-stricken populations and regions. What's more, sustainable poverty alleviation and permanent eradication of poverty can only be achieved by fully predicting and reducing the risks of poverty returning.

In summary, existing research on multidimensional poverty in China has primarily focused on measuring poverty, analyzing influencing factors, and examining temporal and spatial dynamics, as well as exploring mechanisms for poverty reduction. However, there is a critical gap in the theoretical research concerning the prevention of poverty relapse, particularly on a large scale, following the elimination of absolute poverty. Therefore, this study aims to extend the scope of research on multidimensional poverty to include not only measurement but also early warning systems for potential relapses. First, this study builds a comprehensive indicator system for the risk of multidimensional poverty relapse based on the existing multidimensional poverty index (MPI) framework, assessing the contribution of various factors to the risk of relapse. Second, rather than merely confirming the presence of risk, it categorizes relapses into different severity levels to offer a more precise assessment of associated risks. Third, the study develops a hybrid prediction model to forecast the risk of multidimensional poverty relapse. A bidirectional long short-term memory (BiLSTM) neural network model is established, enhanced by the variational mode decomposition (VMD) technique. This approach decomposes the multidimensional poverty indicators to improve the model's prediction accuracy. Theoretically, this study comprehensively analyses the risk factors associated with multifaceted poverty and enhances prediction accuracy by integrating substantial information. Practically, it provides alternative advanced technology for global poverty governance and early warnings, enabling policymakers to implement proactive measures to mitigate the risks of poverty returning.

2. Literature review

This section primarily reviews existing research on multidimensional poverty, covering measurement of multidimensional poverty, the application of the Alkire-Foster (A-F) method in multidimensional poverty measurement, and predictive studies on multidimensional poverty and then offers a brief commentary on these studies.

2.1. The measurement of multidimensional poverty

Poverty is a complex social problem worldwide, and poverty eradication is a common goal for human beings. With the development of society and the deep research, our comprehension of poverty and eradication has shifted from a narrow focus on income-based poverty to a broader perspective encompassing income, health, education, and social advancement. Poverty should be viewed as a multidimensional issue from a long-term and sustainable perspective. The research on multi-dimension poverty can be traced back to the capacity approach theory introduced by Sen [63,64], which argues that the essence of poverty is the deprivation of capacity approach and emphasizes the improvement of quality of life from a multidimensional perspective, containing psychology, basic need theory, participatory and sustainable development theory. The development of human society is multifaceted, resulting in a complex process of eradicating poverty, so we have to conduct a study on poverty from a multidimensional perspective [65].

For the measurement of multidimensional poverty, Hagenaars [66] constructed the multi-dimension poverty index based on two dimensions of income and leisure and conducted the first quantitative measurement of multidimensional poverty. And then, Alkire and Foster proposed the A-F method for measuring the multidimensional poverty index (MPI), which has been widely used in many domains [67]. Using the A-F method, Alkire's team measured the MPI for 104 developing countries, and the in-depth investigation was declared in the United Nations Human Development Report [68]. The contribution of the indicator to multidimensional poverty can be decomposed using the A-F method. Wang et al. [27] improved the multidimensional poverty index to calculate and compare the dynamics of multidimensional poverty among 3009 rural households and draw a conclusion that the targeted poverty alleviation policy and education have a significant impact on multidimensional poverty eradication. Moreover, the indicators contributing to multidimensional poverty are decomposed using the A-F method to illustrate that adult education, health, and chronic diseases have the most significant impact on the incidence of multidimensional poverty [69]. Xiao et al. [70] measured the household's multidimensional poverty in terms of health, education, income, living standard, and social relations and explored the effects of land lease and labor migration on rural households' multidimensional poverty reduction. Chen et al. [71] evaluated the multidimensional poverty in 4 districts of Taiwan, and the results indicated that the levels of multifaceted poverty are disparate for various districts and vary across cities and counties. Yang et al. [72] estimated the multidimensional poverty for Ethnic Tibetan farm and herder households in Gansu Province, illustrating education status, labor availability, self-health assessment, and home toilet type, occupied the top positions.

In addition, different types of households have distinct factors resulting in multidimensional poverty. The main factors of multidimensional poverty for farmers were the income source, housing, and health care expenditure, although a large proportion of multidimensionally poor farm households were non-income poor [73]. Comparatively, as for the workers, the educational level of adults and the availability of facilities such as water and electricity have essential effects on their multidimensional poverty. It is proven that there is gender inequality in multidimensional poverty through a study on an individual-based multidimensional poverty measure [74]. Permanyer [75] and Lekobane [76] presented a concept for individual-level multidimensional poverty measurement and evaluated the context-specific multidimensional poverty index based on individual data, revealing multidimensional poverty incidence is higher than the estimated monetary measure. Rogan [77] applied the A-F method to propose a multidimensional approach, measuring the gender poverty gap in post-apartheid South Africa. Mohanty et al. [78] and Xiang et al. [22] assessed the multidimensional poverty in remote mountainous areas. Mushongera et al. [79] estimated a multidimensional poverty index for Gauteng province, suggesting that the index for various municipalities and wards is of apparent distinction.

2.2. The application of the A-F counting method

Except for the usage in the static analysis of multidimensional poverty, the A-F counting method is also adopted to disclose its feature of dynamics and temporal trends, particularly for chronic poverty. Zhang et al. [29] also found the durations of deprivation regarding education contributed the most to a dramatic reduction in overall multidimensional poverty after investigating the multidimensional poverty in rural China from a longitudinal perspective. Dhongde and Haveman [80] analyzed the spatial and temporal trends in multidimensional poverty in the United States and found more than a quarter of individuals with incomes above the poverty threshold remained multidimensional poor. Khan et al. [4]conducted a multidimensional estimate of poverty in the Punjab province for two periods, demonstrating that the relative proportion of educational and health poverty is higher; the evolution of multidimensional poverty in Mozambique is comprehensively investigated using the A-F counting method [81]. The Watts multidimensional poverty index was selected to measure multidimensional poverty in China during the transition period considering three dimensions: income, knowledge and health [82]. The United Nations Human Development Report-Multidimensional Poverty Index (UNDP-MPI) was created to measure multidimensional poverty for farm households in ecologically sensitive areas [73]. Besides, the scholar also do much effort on explaining the impact of specific factor on the multidimensional poverty, such as the impact of mobile Internet use on multidimensional poverty [52], the coupling relationship between multidimensional poverty and geological disaster risk [22], and the influence of the mechanism of financial inclusion [56,58]. Li et al. [83] and Bao & Yang [84] explored the influencing factors of poverty returning based on accident chain theory and found that poor natural environment, insufficient policy protection, lack of inner development motivation and low quality of labor force jointly contribute to the occurrence of poverty return, and categorized the causal factors of poverty return into four types: institutional poverty return, resource and environment poverty return, disaster risk poverty return and capacity poverty return. Moreover, Klimovsky et al. [85], Brunn et al. [86] and Kóti [87] highlight the problems of measuring multidimensional poverty through a survey of the Roma population in Hungary and Slovakia, emphasizing the quality of the existing human capital and lack of education have a significant impact on the occurrence of multidimensional poverty. It's apparent that the relevance of poverty measurement indicators may vary by geographical area. In practice, the President of Colombia has taken the lead in promoting the application of the method in the domestic anti-poverty field by constructing the Colombian National Multidimensional Poverty Index [88].

The scholars have also extended the A-F method to specific areas, such as energy poverty [[89], [90], [91], [92], [93]], child poverty [3,35,36], older adult [39,94,95], as well as people with disability [34,96,97]. Sokolowski et al. [89] created a multidimensional index accounting for energy deprivation and measure it in Polish. Nussbaumer et al. [98] constructed the multidimensional energy poverty index (MEPI) to measure energy poverty in African countries to accurately measure the incidence and intensity of energy poverty. Abbas et al. [99] adopted the MEPI integrating ordinary least squares (OLS) regression models and Tobit models to examine the multidimensional energy poverty for South Asian countries, showing that household size, household wealth, educational attainment, occupation, and gender of the household principal were significant negative socioeconomic determinants of multidimensional energy poverty, while the residence, home ownership status, and breadwinner's age played an important positive role in multidimensional energy poverty. Otherwise, the Alkire-Foster approach was applied to construct a multidimensional poverty indicator system that analyzed multiple factors contributing to a child's development and well-being and estimated multidimensional poverty experienced by children [6]. Ortiz et al. [100] emphasized child poverty should be measured from multidimensional poverty perspective. Xu et al. [36] captured rural children's poverty by building a multidimensional poverty index system of five dimensions (right to subsistence, health, protection, development, and participation). What's more, the poverty rate of households with disability is always higher than that of non-disabled households [96], and the monetary poverty isn't consistent with the evaluation of non-monetary, so the multidimensional poverty assessment is suitable for this kind of household [97]. Wang et al. [34] stated that multidimensional poverty is generally in the group of people with disability, and education and social participation had more impact than other factors by means of investigating disabilities in China.

2.3. The prediction of multidimensional poverty

In the previous study on poverty governance and prevention of relapse into poverty, researchers are becoming increasingly interested in predicting the risk of relapse into poverty since they have realized that relying solely on multidimensional poverty analysis is not enough to tackle these complex issues. Moreover, grassroots government departments are also paying more and more attention to predictive research on the risk of relapse into poverty because predicting the risk of relapse into poverty can provide direct evidence that allows the government to address potential risks of relapse into poverty in practical management issues. By predicting the risk of relapse into poverty, the government can take targeted measures to consolidate the achievements of poverty alleviation and promote the sustainable development of the poverty-stricken population. In this way, the government can more effectively help impoverished people to stably overcome poverty and avoid the risk of falling back into poverty, thereby achieving sustainable poverty governance. Therefore, to prevent the occurrence of poverty returning, accurate prediction methods are needed to predict the risk of poverty returning. The current literature also focuses on a certain dimension or the identification of the existing poverty status of households, and there is a lack of research on the prediction of the risk of poverty returning. Chen [101] used an exposure-sensitivity-adaptability analysis framework to measure the risk of returning to poverty index of farm households that escaped from poverty and found that financial capital and human resource are the main factors of preventing them from returning to poverty. Cluster Analysis is also used to assess the threats of poverty returning [102]. Christiaensen [103] verified the small area estimation approach in predicting poverty based on data related to consumption. Puurbalanta [104] proposed a Clipped Gaussian Geo-Classification model to classify household poverty whose classification and prediction accuracy of the model was better than that of the existing classification models such as the Cumulative Probit model.

In addition, many general prediction methods have been used in predicting the risk of poverty returning, such as logistic regression [105], decision trees [106], and deep learning techniques [107,108]. A decision tree and logistic regression model were used to assess the risk of returning to poverty in Karst ecologically fragile areas [106]. Zhang et al. [109] constructed a poverty-returning risk monitoring based on back propagation (BP) neural network to analysis the risk for the registered poor households in China. Meanwhile, Du and Zhao [110] utilized the BP neural network to verify the performance of the analytic hierarchy process in evaluating the early warning of returning to poverty for farmers. Tang [111] used remote sensing data for the first time to predict the poverty status of communities in developing countries through convolutional neural networks (CNNs). Alsharkawi et al. [107] conducted a study on the forecasting of poverty returning based on the LightGBM algorithm and achieved the best performance with 81 % F1-Score.

2.4. Commentary on the reviewed literature

In general, the existing research on multidimensional poverty primarily focuses on identifying the factors contributing to poverty, analyzing the mechanisms behind poverty occurrence, and developing frameworks for poverty governance. However, compared with the study on the analysis of multidimensional poverty, there is currently much less quantitative research exploring how to predict the potential risks of falling back into poverty under multidimensional poverty risk, although many prediction methods are applied to forecast the risk of returning to poverty, particular for the risk prediction incorporating the analysis on multidimensional poverty. What's more, the existing research is more prone to forecast whether there is a potential risk of multidimensional returning to poverty while neglecting to identify its degree. Meanwhile, the accuracy of prediction models also needs to be further improved. As to the practice, in order to more accurately predict the multidimensional return to poverty risk to improve the efficiency and effectiveness of the grassroots government in poverty governance, there is an urgent need for more accurate prediction models capable of predicting the degree of multidimensional return to poverty risk.

3. Methodology

This section aims to develop a predictive model by taking into account the measurement and analysis of multidimensional poverty. To achieve this, various methods are utilized in this research paper, including the A-F method, Archimedes optimization algorithm, variational mode decomposition technique and bi-directional long and short-term memory neural network model. This section begins with a brief description of these methods.

3.1. Alkire-Foster method

The Alkire-Foster method, also known as the A-F method, is a comprehensive measure of deprivation initially presented by Alkire and Foster in 2011 [67]. This method focuses on the theory of capacity deprivation, which suggests that poverty should be evaluated not only based on income level but also various dimensions of well-being. The A-F method has gained significant recognition and prominence in the field of poverty measurement due to its ability to capture the multidimensional nature of poverty. It goes beyond solely relying on income or monetary indicators and takes into account a range of factors that contribute to deprivation. According to the previous literature review, it can be found that the A-F method provides a comprehensive understanding of poverty by integrating multi-dimensional factors and is widely used in previous studies to assess poverty levels and identify its multiple dimensions. The A-F method is a robust approach and allows us to categorize and prioritize different factors inducing poverty based on their relative importance. Therefore, in this paper, the A-F method is adopted to assess and analyze multidimensional poverty using the data from CFPS. Specifically, as for this method, the individual deprivation in each dimension is evaluated by deprivation identification, dimension summation and dimension decomposition. The specific process is demonstrated below.

This method starts to identify whether the deprivation for every individual on each indicator is obvious or not. The matrix $X_{ij}^t$ represents the data of an individual under various dimensions which construct a specifical index system, where $t$ denotes the time dimension, $i$ indicates the number of total individuals, and $j$ means the number of indicators. The deprivation cutoffs for all indicators form a vector $Z_j$. The determination of whether an individual $i$ is deprived on an indicator $j$ or not is denoted by $g_{ij}^t$, calculated as Equation (1).

$$g_{ij}^t=\{\begin{array}{l}1,x_{ij}^t<Z_j\\ 0,x_{ij}^t\ge Z_j\end{array}$$ (1)

The deprivation matrix $g_{ij}^0$ is obtained by combining the data matrix according to the critical values in the indicator system. The deprivation matrix is used to store the deprivation of every individual, and the corresponding value in the matrix is 1 if the individual is deprived under the indicator; otherwise, the value is assigned to 0. The average deprivation rate of individuals in indicator $j$ at moment $t$, denoted by $p_j^t$, and the formula is expressed as Equation (2):

$$p_j^t=\frac{\sum _{i=1}^n{g}_{ij}^t}{n}$$ (2)

where $n$ is the total number of the individuals. Meanwhile, $h_{ij}^t$ and $q_{ij}^t$ indicate the status of returning to poverty and the rate of returning to poverty for the $i$ individual under the $j$ dimension at the $t$ moment, respectively, and the formula is shown as Equations (3), (4):

$$h_{ij}^{t+1}=\{\begin{array}{l}\begin{array}{l}1,if{g}_{ij}^{t+1}=1\text{and}{\mathrm{g}}_{ij}^t=0\end{array}\\ 0,otherwise\end{array}$$ (3)

$$q_{ij}^t=\frac{\sum _{1=1}^n{h}_{ij}^t}{\sum _{1=1}^n\left(1-g_{ij}^{t-1}\right)}$$ (4)

After the identification of the deprivation of each individual on each indicator, the number of impoverished people is yielded, and then the incidence of multidimensional poverty $\left(H\right)$, the average share of deprivation $\left(A\right)$, and the multidimensional poverty index $\left(MPI\right)$ are calculated by Equations (5), (6), (7), which represent the number of multidimensionally poor people, the average number of deprived indicators, and the poverty level of the overall region, respectively,.

$$H=\frac{q}{n}$$ (5)

$$A=\frac{{\sum }_{i=1}^n{c}_i\left(k\right)}{q}$$ (6)

$$MPI=H\times A$$ (7)

where $q$ is the number of multidimensionally poor people, $n$ denotes the total population, and $c_i\left(k\right)$ is the number of deprived indicators for the $i$ individual at the selected threshold value of $K$.

Finally, the overall multidimensional poverty index can be decomposed in term of different indicators to achieve the contribution of each indicator to the overall multidimensional poverty index, which demonstrates the impact of each indicator on the overall poverty level. The contribution degree of the $j$ indicator to the $MPI$, denoted as $MP{I}_j$, can also be computed as shown in Equation (8). This process is utilized to assess the significance of each indicator and determine its relative importance in shaping multidimensional poverty.

$$MP{I}_j=\frac{w_{j}C{H}_j}{MPI}\times 100\%$$ (8)

where $w_j$ is the selected weight of the $j$ indicator.

3.2. Archimedes optimization algorithm

The Archimedes Optimization Algorithm (AOA), inspired by Archimedes' principle in physics, is a heuristic optimization algorithm proposed by Hashim et al. in 2020 [112]. In the context of AOA, this principle is applied to the search for an optimal solution. The core process of AOA is to find the global optimal solution by considering the solution in each search space as an object floating under buoyancy and dynamically adjusting its status according to environmental pressure and gravity. By utilizing this approach, AOA possesses a superior global exploration capability compared to traditional optimization algorithms. In addition, AOA stands out from other optimization algorithms due to its simple structure, robust adaptability, easy implementation with only a few parameters, and the ability to escape from local optima. These features make AOA a powerful tool for solving complex optimization problems. To provide a clearer and simpler understanding of the algorithm, the specific procedures of AOA are as follows:

Initialization and update operations: randomly initialize the original position ($x$), density $\left(den\right)$, volume $\left(vol\right)$ and acceleration $\left(acc\right)$ of each individuals and set the rules for updating these parameters, referring to Equations (9), (10), (11), (12).

$$TF=\exp \left(\frac{t-t_{\max }}{t_{\max }}\right)$$ (9)

$$d^{t+1}=\exp \left(\frac{t_{\max }-t}{t_{\max }}\right)-\left(\frac{t}{t_{\max }}\right)$$ (10)

$$de{n}_i^{t+1}=de{n}_i^t+rand\times \left(de{n}_{best}-de{n}_i^t\right)$$ (11)

$$vo{l}_i^{t+1}=vo{l}_i^t+rand\times \left(vo{l}_{best}-vo{l}_i^t\right)$$ (12)

where $TF$ is the transfer operator conducting the transform of search pattern, and $d^{t+1}$ represents the density decreasing factor. Correspondingly, $de{n}_i^t$ and $vo{l}_i^t$ note the density and volume of the $i$ individual at generation $t$, respectively. Here $t$ is the current iteration number, $t_{\max }$ denotes the maximum number of iterations, and $rand$ is a random number generated in the range of [0, 1].

Global exploration: when $TF\le 0.5$, the algorithm performs the global exploration function. Perform the acceleration update of individuals using Equation (13). To ensure numerical stability, the acceleration is normalized using Equation (14). Then, update the position of the individuals according to Equation (15).

$$ac{c}_i^{t+1}=\frac{de{n}_{mr}+vo{l}_{mr}+ac{c}_{mr}}{de{n}_i^{t+1}\ast vo{l}_i^{t+1}}$$ (13)

$$ac{c}_{i-norm}^{t+1}=u\times \frac{ac{c}_i^{t+1}\min \left(acc\right)}{\max \left(acc\right)\times \min \left(acc\right)}+l$$ (14)

$$x_i^{t+1}=x_i^t+c_1\times rand\times ac{c}_{i-norm}^{t+1}\times d\times \left(x_{rand}-x_i^t\right)$$ (15)

where $ac{c}_i^{t+1}$ is the acceleration of the $i$ individual at the next generation, $de{n}_{mr}$, $vo{l}_{mr}$, and $ac{c}_{mr}$ are the density, volume, and acceleration of the randomly selected individuals, respectively, $x_i^t$ denotes the position vector of the $i$ individual at the $t$ iteration, and $c_1$ is a constant.

Local search: when $TF>0.5$, the algorithm is in the local search phase. The individual's acceleration is updated by Equation (16).

$$ac{c}_i^{t+1}=\frac{de{n}_{best}+vo{l}_{best}+ac{c}_{best}}{de{n}_i^{t+1}\times vo{l}_i^{t+1}}$$ (16)

$$x_i^{t+1}=x_{best}^t+F\times c_2\times rand\times ac{c}_{i-norm}^{t+1}\times d\times \left(T\times x_{best}-x_i^t\right)$$ (17)

where $x_{best}$ denotes the position of the global optimal individual, and $ac{c}_{best}$ implies the acceleration of the corresponding individual. Here $c_2$ is a constant, $T=c_3\times TF$ and $c_3$ is a constant.

$F$ is a parameter used to determine the direction of the individual position update, defined as Equation (18).

$$F=\{\begin{array}{l}+1ifp\le 0.5\\ -1ifp>0.5\end{array}$$ (18)

where $p=2\times rand-c_4,c_4$ is a constant. The more details regarding the configuration of the relevant parameters can be found in Ref. [112].

3.3. Variational mode decomposition

The variational mode decomposition (VMD) is a novel and adaptive signal decomposition method for processing non-stationary and nonlinear signals [113]. The raw signal or series can be decomposed into a set of intrinsic modes with limited bandwidth and a center frequency [114]. VMD can overcome the shortcomings of empirical modal decomposition and its improved version so that it has been widely used to solve various engineering problems, such as fault feature extraction of rolling bearing [115,116], fault diagnosis [117], feature extraction [118,119], identification of electromechanical oscillatory modes [120], stock price forecast [121], load forecast [122,123], wind power forecast [124], and so on. The basic process is illustrated as follows:

The raw signal or series is decomposed into $K$ components, which have a finite bandwidth with the center frequency. These components are then demodulated to the baseband frequency mixed with the center frequency using the Hilbert transform. To estimate the signal bandwidth of each component, the function for the variational problem is constructed as shown in Equation (19). The objective is to minimize the summation of the estimated bandwidth of each component while the constraints demonstrate the amount of information synthesized in each component is guaranteed to be the same as the original signal.

$$\begin{array}{l}{\min }_{\left\{u_k\right\},\left\{{\omega }_k\right\}}\left\{\sum _{k-1}^K{\Vert {\partial }_t\left[\left(\delta \left(t\right)+j{\pi }^{-1}{t}^{-1}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}\Vert }_2^2\right\}\\ s.t.{\sum }_{k=1}^K{u}_k=f\left(t\right)\end{array}$$ (19)

where $u_k$ and ${\omega }_k$ are the $K-th$ modal component and the corresponding central frequency after decomposition, respectively. Here ${\partial }_t$ is the partial derivative of time $t$, $\delta \left(t\right)$ is the Dirac function, $j$ is the imaginary unit, and $u_k\left(t\right)$ is the modal function.

Next stage is to solve the optimal solution of the variational problem. Utilizing the Lagrange multiplier operator $\left(t\right)$ , the Lagrange parameter $\lambda$ and the quadratic penalty parameter $\alpha$, Equation (19) is transformed into an incremental Lagrange function as shown in Equation (20).

$$L\left(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda \right)=\alpha {\sum }_{k=1}^K{\Vert {\partial }_t\left[\left(\delta \left(t\right)+j{\pi }^{-1}{t}^{-1}\right)u_k\left(t\right)\right]e^{-j{\omega }_{k}t}\Vert }_2^2+{\Vert f\left(t\right)-{\sum }_{k=1}^K{u}_k\left(t\right)\Vert }_2^2+⟨\lambda \left(t\right),f\left(t\right)-{\sum }_{k=1}^K{u}_k\left(t\right)⟩$$ (20)

After iterative calculation, the $K-th$ modal component is obtained as shown in Equation (21).

$${\hat{u}}_k^{n+1}\left(\omega \right)=\frac{\hat{f}\left(\omega \right)-{\sum }_{i<k}{\hat{u}}_i^{n+1}\left(\omega \right)-{\sum }_{i>k}{\hat{u}}_i^n\left(\omega \right)+\frac{\hat{\lambda }\left(\omega \right)}{2}}{1+2\alpha {\left(\omega -{\omega }_m\right)}^2}$$ (21)

where $\hat{f}\left(\omega \right)$, ${\hat{u}}_k\left(\omega \right)$, and $\hat{\lambda }\left(\omega \right)$ are the Fourier transforms of $f\left(t\right)、u_k\left(t\right)、\lambda \left(t\right)$, respectively; ${\omega }_n$ is the center of gravity of the power spectrum of the current modal function; and $\omega$ is the modal frequency.

The superior performance of VMD has been extensively examined and proven effective in solving numerous engineering and prediction problems. However, it is essential to note that in practical applications, the researcher's experience plays a critical role in determining two core parameters for VMD - the component number and the penalty factor in the construction of the variational problem. The selection of these parameters is crucial as it directly impacts the effectiveness of the VMD decomposition results. While there are existing practical experiences that can provide guidance in determining the number of components, choosing the appropriate parameters still remains a complex challenge. This paper aims to address this issue and provide a methodology to ensure the accurate and proper utilization of VMD. Additionally, the application of VMD is introduced to the study of multidimensional poverty. By incorporating VMD into the predictive model, the efficiency of utilizing the available data is improved, enabling a more effective prediction of poverty dynamics.

3.4. Bidirectional long and short-term memory neural network

In 1997, Hochreiter and Schmidhuber introduced the concept of the long and short-term memory network (LSTM) model as an innovative solution to two major issues encountered in traditional recurrent neural networks (RNNs): the gradient disappearance and gradient explosion problems [125]. The LSTM model overcomes these challenges by incorporating a gate structure that enables the addition or removal of information to or from cell states. By introducing this gate structure, LSTM effectively regulates the flow of information, allowing for better preservation and utilization of essential information for a more extended period. This gate structure can be visualized in Fig. 1.

Fig. 1.

LSTM network structure.

The calculation of the four gates in each LSTM cell is illustrated as follows:

Forget gate: determines whether the cell retains or forgets certain information at a specific time step to help optimize the performance of the network by dynamically adjusting the relevance of past information based on the current input, calculated by Equation (22).

$$f_t=\sigma \left({W_f}^{\ast }\left[h_{t-1},x_t\right]+b_f\right)$$ (22)

Input gate: receives the information entered at the current time and updates the relevant information stored in the corresponding cells, as shown in Equation (23).

$$i_t=\sigma \left({W_i}^{\ast }\left[h_{t-1},x_t\right]+b_i\right)$$ (23)

Cell state: The cell state refers to the accumulated internal information within a cell at a particular time. The state information of this moment is obtained by calculating the state information that this cell acquired from previous moments and the input information received by the cell at the current moment, using Equation (24).

$$C_t={f_t}^{\ast }{C}_{t-1}+{i_t}^{\ast }\check{C_t}$$ (24)

where $\check{C_t}=\tanh \left(W\left[h_{t-1},x_t\right]+b\right)$ is the candidate value of the cell state.

Output gate: the output of the cell is computed by Equation (26). Here the hidden state of the cell is produced in Equation (27).

$$O_t=\sigma \left(W_o\left[h_{t-1},x_t\right]+b_o\right)$$ (26)

$$h_t={O_t}^{\ast }\tanh \left(C_t\right)$$ (27)

where $W_{\ast }$ and $b_{\ast }$ denote the weight and bias of the corresponding gates, respectively. Similarly, $f_t$, $i_t$, and $O_t$ is the output of the gates, respectively. $x_t$ is the input, $h_t$ is the hidden state, and $\sigma$ and $\tanh$ are the activation functions.

Although LSTM is proper to deal with time series data, it can only process input sequences in a single direction and also has some limitations when processing series data to some extent, especially for the complex relationship existing between the data with a relatively large time step. As a consequence, a bi-directional long short-term memory neural network (BiLSTM) is proposed as a variant of LSTM to surmount its drawbacks [126]. For the BiLSTM network, the input sequences were processed from two directions (forward and backward) separately as shown in Fig. 2, making BiLSTM able to capture the before and after information so that the network can better learn and exploit the dependencies and relationship in the sequences.

Fig. 2.

Bidirectional LSTM network structure.

3.5. The hybrid model

The hybrid prediction model is designed and constructed to eradicate the potential risk of returning to poverty from a multidimensional perspective. To this end, firstly, an evaluation indicator system is urgent to be built, synthesizing more comprehensive indicators. Meanwhile, the A-F counting method, a sophisticated and commonly used methodology in the field of poverty research, is selected to measure and analyze multidimensional poverty. The analysis results are valuable in exposing the complicated mechanism for poverty incidence, as well as in recognizing the return of poverty and formulating targeted measures to prevent poverty from returning. Secondly, the variational mode decomposition technique is selected to extract more effective information from the multidimensional indicators, which aims to help improve the model's prediction accuracy. Moreover, in order to tackle the issue arising from the mode number and the penalty factors, the AOA method is adopted to optimize the selection of the core hyperparameters of VMD. Finally, a BiLSTM neural network is constructed to predict the risk of poverty returning, the input data of which is the decomposed data yielded by the AOA-VMD method. The process of the hybrid model is further explained as follows, and the framework is demonstrated in Fig. 3 in detail.

Step 1

Based on the survey data from CFPS, establish a system of evaluation indicators and then assess multidimensional poverty from a household's perspective through the A-F methodology. Meanwhile, there is a need to focus on the overall incidence of multidimensional poverty and the contribution of each indicator to multidimensional poverty occurrence.

Step 2

The evaluation results of the multidimensional poverty produced by the A-F method are adopted as a criterion for assessing the risk of poverty reoccurrence.

Step 3

Optimize the selection of parameters for the VMD method using the AOA method.

Step 3.1

Set the parameters of the AOA method, including the maximum number of generations, the number of populations, as well as the initial density, volume, and acceleration of the individuals;

Step 3.2

Referring to information entropy, Use the envelope entropy of each component as the criterion for evaluating the merit of individuals in the AOA method;

Step 3.3

Implement the AOA method according to the abovementioned process until meeting the termination condition and output the optimal number of modal components and penalty factors.

Step 4

According to the optimal parameter combinations, the original data are decomposed into the corresponding modal components by VMD. The decomposed components are input into the prediction model.

Step 5

Divide the data into training, validation, and test sets.

Step 6

Set the parameters of BiLSTM such as the number of network layers, the number of neurons, the maximum training times, the initial learning rate, the learning weight adjustment method, and the training accuracy requirement.

Step 7

Train the neural network with the training set and validation set and input the optimal neural network model;

Step 8

Verify the model's performance based on the test set.

Fig. 3.

The framework of the hybrid prediction model.

3.6. Data sources

The data for this study are derived from the China Family Panel Studies (CFPS), which examine both the economic and non-economic welfare of Chinese households. The CFPS addresses a range of topics including economic activities, education, living conditions, population migration, and health. Initiated in 2010, this biennial project draws samples from 29 provinces, municipalities, and autonomous regions across six major regions of China (as illustrated in Fig. 4). The sample includes provinces from the northeastern, northern, eastern, central-southern, northwestern, and southwestern regions, thus representing the diverse household situations and reflecting the broader context of the risk of multidimensional poverty recurrence in Chinese households. Upon acquiring the data, our initial step involved aggregating all samples based on household codes to compile the data for each household. After basic data processing, including the removal of vacancies and outliers, we finally obtained 4176 household datasets available for analysis. In Fig. 4, circles indicate the geographic distribution of these households, with the size of each circle corresponding to the number of households from the respective provinces.

Fig. 4.

Geographical distribution of data sources.

3.7. Socioeconomic and geographical features

Fig. 4 illustrates that the dataset utilized in this study is predominantly sourced from the Northeast, East, Central-South, and select provinces in the Southwest regions. Henan, Liaoning, and Guangdong emerge as the provinces with the highest data sources. This is primarily due to their status as populous provinces at the survey's inception and their relatively higher economic development compared to the Northwest region, which facilitated data accessibility. Fig. 5 presents the household net income statistics for all families in 2020. It reveals that household net income predominantly falls within the range of 6,000 to 20,000, with no households falling below the national poverty line. Household expenditures primarily encompass education investments, medical expenses, and food consumption. Notably, 8 % of households allocate over 30 % of their total expenses to education, 9 % allocate 30 % to medical services, and 18 % allocate over 50 % to food consumption.

Fig. 5.

Statistics of household net income per capita.

Similarly, a deeper analysis of the educational attainment of each family's members reveals that 68 % of households have adults with less than 9 years of education, indicating they have not completed the mandatory education required in China (as depicted in Fig. 6). Regarding healthcare services, only 15.8 % of households have opted for additional commercial medical insurance services alongside rural cooperative medical care. However, in 2020, 27.7 % of households had members hospitalized for significant illnesses, and 36.9 % of households had members in an unhealthy condition. Furthermore, 6.4 % of households experienced unemployment, while 29 % lacked unemployment insurance. These basic statistical insights reveal that households lifted out of poverty still encounter various threats. Despite compulsory education being enforced in China, many individuals still drop out during this phase, rendering them more vulnerable during unforeseen public events. While many households faced health issues in 2020, the implementation of cooperative medical care projects ensured that medical expenses did not become their primary expenditure. Nonetheless, the limited adoption of commercial medical insurance among these households underscores the importance of promoting and implementing such insurance to bolster their resilience against future risks.

Fig. 6.

Statistics on average years of education for adults.

4. Analysis of multidimensional poverty return

4.1. Evaluation system

Drawing on the previous research on multidimensional poverty and considering the availability and accessibility of the data, the comprehensive evaluation system is constructed utilizing 12 indicators which are organized into five dimensions, including economy, health, education, living standard and social development capacity in line with their role in society governance, as shown in Table 1. Furthermore, as to the A-F method, it's worth noting that the weights of the indicators also affect the analysis results to some extent, which are generally determined according to their relative importance in the system. In order to more objectively reflect the formation mechanism of multidimensional poverty, the weight of each indicator in this study is considered equal importance. The corresponding weights are also illustrated in Table 1. Meanwhile, another essential issue related to the A-F method is to predetermine the deprivation cut-offs for each indicator. The deprivation cut-off is used to identify whether the household is viewed relatively poor in the corresponding indicator or not, which is demonstrated in Table 1.

Table 1.

Indicators, deprivation cut-offs and weights for the A-F method.

Dimension	Indicator	Deprivation cut-off	Weights
Economy	Net income per capita (X1)	The annual per capita net income of the family is lower than the national poverty line	1/5
Health	Health status (X2)	At least one member's health status is considered unhealthy	1/15
	Medical insurance (X3)	All members do not have any commercial insurance or social security	1/15
	Family medical expenditures (X4)	The proportion of household medical expenditure to total household consumption expenditure exceeds 0.6	1/15
Education	Education expenditures (X5)	The proportion of household education expenditure to total household consumption expenditure is more than 0.6	1/15
	Children's education (X6)	At least one child aged 15 or below is out-of-school	1/15
	Adult education states (X7)	At least one adult has 9 or less years of education	1/15
Living standard	Housing (X8)	Housing area per capita is equal to or less than 15 square meters	1/20
	Fuel (X9)	The main fuel resource is firewood	1/20
	Water (X10)	Have no access to healthy water source, such as well water, tap water, mountain water, mineral water, pure water, and filtered water.	1/20
	Electricity (X11)	The average household electricity bill per month is less than 20 RMB.	1/20
Social development capacity	Labor force (X12)	The household has no healthy young labor	1/5

4.2. Poverty incidence and returning to poverty rate of all indicators

Before presenting the results of the multidimensional poverty analysis, it is possible to observe the direct differences in the measurement of poverty under the situation of only considering unidimensional factors through the measure of poverty incidence in a single indicator. Details are shown in Table 2. Firstly, as China's poverty alleviation efforts continue to advance, the overall poverty incidence and the returning-to-poverty rate of all indicators have a general downward trend to some extent, with a most significant decrease of 7.5 percentage point of the poverty incidence in net income per capita indicator from 2014 to 2018. Meanwhile, the returning-to-poverty rate in net income per capita decline from 8.63 % in 2014 to 2.31 % in 2018, but it rebounded to the level seen in 2016 by 2020. Secondly, as to the indicators in living-standard dimension, the returning-to-poverty rate in the housing indicator is always at a lower level with the effort of implementing the rural dangerous housing rehabilitation project and new rural construction project conducted by the central and local government. Similarly, the poverty incidence in the water indicator also remains low and no household falls back into poverty under this factor except in 2020. The incidence of poverty in the fuel indicator decreased by 7.4 percentage points. However, the returning to poverty generally continued to decline, but there was an increase in 2020. In contrast, as to the access to electricity also contained in the dimension of living standard, the poverty incidence increased by almost 6 percentage points, with an upward trend in returning to poverty rate. Thirdly, as for the health dimension, the poverty incidence stays at a high level of over 50 percentage points in the health status and medical insurance indicators. Conversely, the incidence of poverty in the indicator of household medical expenditure remained consistently low, at less than 1 percentage point from 2014 to 2018, but experienced a slight increase in 2020. The rate of returning to poverty in the health status indicator decreased significantly by nearly 49 percentage points, from 52.28 % in 2014 to 3.75 % in 2018, and also dropped by almost 8 percentage points in the commercial medical indicator. However, the health status indicator increased to 10.54 % in 2020. What's more, as to the education dimension, the incidence of poverty and the rate of return to poverty under the education expenditure indicator have been at a low level. However, the incidence of poverty and the rate of return to poverty in children and adult education status are at a high level mainly due to the relatively stringent criteria for these two indicators and the fact that it is difficult to improve these two indicators within a short period of time.

Table 2.

Poverty incidence and return-to-poverty rates during 2014–2020.

Indicators	Poverty incidence				Returning to poverty rate				Proportion of the returning to poverty rate to poverty incidence
	2014	2016	2018	2020	2014	2016	2018	2020	2014	2016	2018	2020
X1	13.32 %	8.33 %	5.87 %	5.17 %	8.63 %	3.86 %	2.31 %	3.86 %	64.80 %	46.32 %	39.26 %	74.54 %
X2	55.87 %	95.97 %	52.31 %	50.20 %	52.28 %	48.76 %	3.75 %	10.54 %	93.57 %	50.80 %	7.16 %	34.89 %
X3	96.49 %	95.35 %	96.12 %	82.09 %	17.37 %	10.49 %	9.73 %	9.67 %	18.00 %	11.00 %	10.13 %	11.79 %
X4	0.33 %	0.17 %	0.58 %	3.11 %	0.30 %	0.15 %	0.50 %	2.75 %	91.30 %	87.50 %	86.42 %	88.46 %
X5	0.17 %	0.01 %	0.48 %	1.96 %	0.15 %	0.01 %	0.38 %	1.77 %	87.50 %	82.30 %	79.10 %	90.24 %
X6	94.80 %	95.17 %	93.80 %	97.82 %	13.08 %	9.35 %	8.04 %	1.60 %	13.79 %	9.83 %	8.57 %	1.64 %
X7	71.62 %	71.92 %	66.86 %	48.85 %	59.51 %	14.11 %	8.99 %	3.76 %	78.94 %	74.18 %	76.52 %	7.70 %
X8	3.27 %	2.65 %	2.85 %	2.90 %	2.58 %	1.97 %	2.18 %	2.20 %	83.10 %	19.62 %	13.45 %	20.22 %
X9	29.76 %	26.39 %	22.36 %	17.74 %	7.92 %	4.22 %	2.67 %	4.12 %	26.61 %	15.98 %	11.96 %	23.21 %
X10	9.86 %	5.22 %	5.45 %	18.80 %	0.00 %	0.00 %	0.00 %	4.84 %	0.00 %	0.00 %	0.00 %	25.73 %
X11	2.67 %	10.25 %	8.44 %	29.00 %	1.97 %	9.76 %	5.53 %	8.99 %	73.91 %	95.22 %	65.53 %	37.90 %
X12	50.77 %	52.26 %	53.96 %	48.23 %	40.74 %	21.96 %	16.51 %	15.06 %	80.24 %	42.02 %	30.60 %	31.23 %

4.3. Results of multidimensional poverty returning

The results of the multidimensional poverty returning measure are shown in Table 3. During 2014–2018, China's multidimensional poverty returning rate decreased by 18.2 %, the proportion of household suffering from multidimensional poverty returning decreased by 27.7 %, and the poverty returning index decreased from 20 % in 2014 to 6.4 % in 2018, which indicates that China has achieved great success in poverty eradication. Nevertheless, it is particularly noteworthy that all these indicators experienced a certain degree of increase in 2020, especially the multidimensional poverty incidence.

Table 3.

Results of multidimensional poverty returning.

	2014	2016	2018	2020
Proportion of household experiencing multidimensional returning to poverty	40.00 %	17.40 %	12.30 %	16.76 %
Multidimensional poverty incidence	64.40 %	67.40 %	61.50 %	97.99 %
Multidimensional poverty index	0.2000	0.1150	0.0640	0.0624
Multidimensional return to poverty rate	25.80 %	11.70 %	7.60 %	16.43 %

Meanwhile, Table 4 shows the contribution of each indicator on the multidimensional return to poverty when the cut-off value is set 4. The contributions of health insurance, children education, adult education status, and labor force level are comparatively significant, where the most significant contribution is from the labor force indicator in the social development capital dimension with a contribution rate of 48.3 % in 2018. The contributions of medical insurance and children education increased during 2014–2018, with an increase of 8 % and 7 %, respectively, while the contributions of net income per capita and health status showed significant decreases with a decline of 9.2 % and 8.1 %, respectively. Furthermore, 2020 represents a unique time period. Key contributing indicators during this year include health status, electricity, per capita income, medical insurance, and household medical expenses, with relatively minor disparities in their contributions.

Table 4.

Contribution of the indicators on multidimensional poverty returning (K = 4).

Contribution rate	2014	2016	2018	2020
Net income per capita	12.00 %	4.70 %	2.80 %	11.10 %
Health	11.70 %	15.10 %	3.60 %	16.16 %
Medical Insurance	7.10 %	10.80 %	15.10 %	9.10 %
Family Medical Expenditures	0.10 %	0.00 %	0.30 %	10.07 %
Education Expenditures	0.00 %	0.00 %	0.30 %	3.00 %
Children's Education	6.10 %	9.70 %	13.10 %	4.04 %
Adult education level	13.80 %	11.80 %	10.10 %	5.10 %
Housing	0.90 %	1.00 %	1.70 %	2.10 %
Fuel	2.00 %	1.60 %	1.60 %	1.60 %
Water	0.00 %	0.00 %	0.00 %	7.00 %
Electricity	0.50 %	2.20 %	2.90 %	15.15 %
Labor force	45.80 %	43.10 %	48.30 %	14.14 %

4.4. Grade of the risk of multidimensional poverty returning

Furthermore, in order to verify the impact of the poverty cut-off value on the multidimensional poverty returning, the MPI with different cut-off values is assessed and illustrated in Table 5 and Fig. 7. When the cut-off value is 1, the multidimensional poverty incidence is 0.995, which indicates that the probability of poverty in at least one dimension for the households is up to 99.5 %. While the K value is greater than or equal to 9, the multidimensional poverty incidence declines to 0, indicating that there are no households with 9 and more indicators poor. With the increase of the cut-off, the incidence of poverty and the multidimensional poverty index gradually decreased. In contrast, the average deprivation intensity showed a gradually increasing trend, which indicated that while the incidence of multidimensional poverty decreased with the increase of the influencing factors, the depth of deprivation of farmers gradually increased. These multidimensional deprived farmers had more incredible difficulty shaking off poverty and faced more risk of returning to poverty, which should be paid attention to in the anti-poverty effort. The results provide a helpful insight into the indication of the grade for the multidimensional poverty returning. According to the value of poverty cut-off value, the households viewed as multidimensional poor with the corresponding cut-off of 6 are identified as a high risk of returning to poverty while the cut-offs of 3 are considered as a low risk, otherwise, the households are noted as recognized as medium risk. This guideline can effectively deal with the problem of identifying the grade of the risk in the actual monitoring and early warning of the risk of returning to poverty.

Table 5.

Multidimensional poverty returning with different cut-offs.

Cut-off	Poverty Incidence: H	Average deprivation intensity: A	Multidimensional Poverty Index: MPI
1	0.995	0.347	0.346
2	0.919	0.336	0.334
3	0.629	0.429	0.264
4	0.455	0.466	0.206
5	0.116	0.565	0.063
6	0.029	0.677	0.020
7	0.012	0.733	0.008
8	0.001	0.824	0.001
9	0.000	0	0
10	0.000	0	0

Note: MPI indicates a composite indicator of local poverty status.

Fig. 7.

Variation of multidimensional poverty returning.

4.5. Multidimensional poverty index decomposition with different cut-offs

The contribution of the five dimensions of economy, health, education, living standard and social development capacity to the multidimensional poverty index with different cut-off values was calculated using the A-F method (in Table 6) and visualized in Fig. 8. The contribution of the health and education dimensions gradually decreases as the cut-off value increases, which reveals that the health and education dimensions are less important than the economic and social development capability dimensions for farmers with deep deprivation. This finding is consistent with the experience from the long period of poverty governance, where the deep poverty-stricken regions need to be addressed first and foremost in terms of economic development, including building economic infrastructure and improving human resources. Meanwhile, the contribution of the economic dimension is low when the cut-off value is small, and the contribution increases gradually with the value. The lack of economic capital will directly enhance the difficulty of getting out of poverty and amplify the risk of returning to poverty. Multidimensionally poor households often lack the opportunity to expand reproduction and improve the current living conditions. The living standard dimension fluctuates less with the cut-off values due to the endogenous and inherent nature of these factors for multidimensionally poor households. Overall, the contribution of social development capacity is the highest and fluctuates with the cut-off value, with 40.18 % at the value of 4 and 24.23 % at the value of 8. However, the overall deprivation rate is still at a high level, with 24.23 % at the value of 8.

Table 6.

Multidimensional poverty with different poverty cut-offs.

Poverty cut-off	Economy	Health	Education	Living standard	Social development capacity
1	3.40 %	28.67 %	31.06 %	5.66 %	31.22 %
2	3.51 %	28.05 %	30.51 %	5.63 %	32.29 %
3	4.45 %	23.79 %	26.96 %	6.21 %	38.59 %
4	5.50 %	22.83 %	26.72 %	4.77 %	40.18 %
5	13.32 %	21.67 %	22.92 %	10.70 %	31.38 %
6	27.98 %	16.91 %	18.97 %	7.20 %	28.94 %
7	27.30 %	17.29 %	18.43 %	9.68 %	27.30 %
8	24.28 %	17.94 %	17.93 %	15.54 %	24.23 %
9	0.00 %	0.00 %	0.00 %	0.00 %	0.00 %
10	0.00 %	0.00 %	0.00 %	0.00 %	0.00 %

Fig. 8.

Multidimensional poverty with different cut-offs.

4.6. Discussion

The results of the poverty incidence and return-to-poverty rate for all indicators suggest that the targeted poverty alleviation program has been effective in reducing income poverty and achieving its expected goals. The poverty incidence and return-to-poverty rate for the electricity indicator within the living standards dimension are particularly noteworthy. The main reason is the frequent occurrence of extreme weather in recent years, which leads to tensions in electricity consumption, while the stability of power supply in remote rural areas deteriorates. However, to deal with this urgent issue, the government has implemented a variety of power projects to improve residents' access to electricity, including the development of clean energy, the promotion of rooftop solar installation, the improvement of rural transmission line and other measures. Similarly, the health status and medical insurance indicators have a high-level poverty incidence, which is mainly due to the decline in the number of newborns and the aging of the rural population, which has led to a deterioration in the health status of rural households. Meanwhile, individuals in rural areas still depend on traditional agriculture and migrant labor as their primary income source and do not have the financial resources to pay for commercial medical insurance for their entire family. This result also shows a need for more attention to commercial medical insurance in rural regions. Commercial medical insurance, as a significant complement to rural cooperative medical care, effectively prevents impoverished households from falling back into poverty due to sudden illnesses that can cause labor shortages, reduced economic income, increased medical expenses, and other risks. Its role in preventing a relapse into multidimensional poverty is gradually becoming apparent, particularly in rural areas. However, due to inadequate understanding of commercial medical insurance and constraints on rural income sources, its adoption among rural households remains uncommon. To address this, the government can enhance public financial support for rural cooperative medical care and poverty alleviation funds. These funds can be utilized to promote commercial medical insurance in rural regions, with subsidies offered to specific demographic groups for insurance purchases. Tailored commercial health insurance options can be introduced to meet the diverse needs of different groups, such as maternity insurance for women, critical illness coverage for migrant workers, and major illness protection for the elderly and children. It is equally crucial to regulate the sales and claims processes of commercial medical insurance in rural areas. Government intervention, as a third-party oversight entity, can ensure transparency and fairness. Establishing uniform bidding procedures and stringent qualifications for insurance providers are vital steps in this regard. Additionally, government involvement in the claims process, including the initiation of emergency payment procedures, can safeguard households from significant economic hardships arising from major medical events. In conclusion, to mitigate the risk of falling back into poverty due to illness, it is imperative to establish a government-led framework for commercial medical insurance in collaboration with private insurers. This framework should encompass policies supporting the promotion, scope delineation, subsidy mechanisms for insurance purchases, and claims processing of commercial health insurance.

On the contrary, the poverty incidence of the household medical expenditure keeps a low level, mainly due to the Chinese government's vigorous implementation of the rural cooperative medical scheme, which has helped to defray the high costs of medical care for people with severe illnesses and hospitalizations with the consequence of significantly reducing the risk of returning to poverty for the individuals because of illness. The decline of return-to-poverty rate in the health status indicator and the low level of household medical expenditures also prove that the rural cooperative medical scheme can mitigate the risk of households returning to poverty caused by deteriorating health status. Meanwhile, the poverty incidence and the return-to-poverty in the indicator of education expenditures indicator are at low level, which shows that increasing public financial support for compulsory education can effectively reduce the burden of education on households. In conclusion, due to factors such as development concepts and living habits, other non-income dimensions are more stable than income dimensions, and most of them are persistent poverty, which makes it challenging to achieve poverty reduction within a short period of time, implying that China should pay more attention to the non-monetary factors than the income factors. Meanwhile, these results show the percentage of households deprived per indicator and highlight the importance of adopting multidimensional indicators in the measure of poverty. Moreover, it is important to note that these patterns occurred between 2012 and 2018. The analysis indicates that the poverty incidence and return-to-poverty rate for all previously well-performing indicators increased in 2020. The primary reason for this increase is the impact of COVID-19 in 2020, which led to significant income reductions or loss of income for many households. Additionally, COVID-19 infections resulted in increased medical expenses, deteriorated health conditions, and worsened living conditions for many families. These anomalies further demonstrate the fragility of poverty alleviation and underscore the importance of long-term monitoring and accurate prediction of multidimensional poverty.

Considering the assessment of relapse into multidimensional poverty, the results suggest that as society and economy advance, the quantity and quality of human resources become more and more important in influencing multidimensional poverty, while the influence of economic factors decreases. In 2020, China historically eliminated absolute poverty, but relative poverty still exists across the rural households, especially in the remote mountainous region. As to the solution of relative poverty, it is necessary to focus on the multi-dimensional measure of poverty to overcome the shortcomings associated with unidimensional poverty measurement. Meanwhile, the significant increase in multidimensional poverty incidence in 2020 further highlights the severe negative impact of public emergency on poverty alleviation efforts. Furthermore, the results of multidimensional poverty index decomposition demonstrate that the social network tied by blood and local relationships makes it difficult to change the self-sufficient lifestyle formed over a long period of time for multi-dimensional poor households. What's more, the households with deeper multi-dimensional poverty are primarily old or disabled groups, and most of them are intensely dependent on social assistance and national underwriting policy to achieve poverty alleviation and avoid falling back into poverty.

In summary, based on CFPS data, poverty incidence and poverty return rates are assessed from both unidimensional and multidimensional perspectives using 12 indicators across five dimensions: economy, health, education, living standards, and social development capacity. The multidimensional poverty index is further decomposed into each indicator to assess the contribution of each factor to the overall poverty index. Considering single indicators, the poverty return rate in China has dropped significantly in recent years. However, the risk of poverty return still exists, particularly in non-income factors such as health and education, which are heavily influenced by internal and external environments and are challenging to improve completely in the short term. According to the analysis of multidimensional poverty, poverty return is mainly induced by two- or three-dimensional factors, with the social development capacity dimension contributing the most to the multidimensional poverty return index, followed by the health and education dimensions. Moreover, it is crucial to pay more attention to the impact of unexpected public emergency on households that have already escaped poverty. To achieve sustainable poverty alleviation, it is essential to strengthen the monitoring and prediction of multidimensional poverty return risks. Additionally, the identification of multidimensional poverty varies with different poverty cut-offs, which can be used to recognize the grade of multidimensional poverty return risk and further provide a foundation for predicting potential multidimensional poverty risk.

5. Prediction of the risk of multidimensional poverty return

5.1. Data selection

This section tests the performance of the proposed prediction model based on CFPS 2012–2020 data after the identification of the grade of multidimensional poverty returning risk according to the finding in subsection 4.4. In order to consider more comprehensive factors in the prediction model and verify the adaption of the prediction model, the indicators used for the prediction can be extended to other dimensions not contained in the A-F method. Therefore, 14 indicators are selected as input data for predicting poverty returning risk and described in detail in Table 7. To eliminate the influence of indicators, the positive indicators data are normalized by formula $x^{\prime }=\raisebox{1ex}{$x-x_{\mathit{min}}$}\!\left/ \!\raisebox{-1ex}{$x_{\mathit{max}}-x_{\mathit{min}}$}\right.$, while the negative indicators are normalized using the function $x^{\prime }=\raisebox{1ex}{$x_{\max }-x$}\!\left/ \!\raisebox{-1ex}{$x_{\mathit{max}}-x_{\mathit{min}}$}\right.$, where $x,x^{\prime },x_{\min },x_{\max }$ is the original data, the normalized data, and the minimum and maximum of the original data, respectively.

Table 7.

Poverty returning risk evaluation indicators.

Dimension	Indicator	Assignment
Economy	net income per capita (X1)	more than 30000 = 1; 10001–30000 = 2; less than or equal to 10000 = 3
Health	Health status (X2)	very healthy = 1; quite healthy = 2; comparatively healthy = 3; general = 4; unhealthy = 5
	Medical insurance (X3)	the number of family medical insurance per capita, greater than 1 = 1; 0.51–1 item = 2; less than 0.5 = 3
	Medical expenditure (X4)	household medical expenditure accounted for total household expenditure, less than 20 % = 1; 21 %–60 % = 2; 61 %–100 % = 3; more than 100 % = 4
Education	Education expenditure (X5)	family education expenditure accounted for the total household expenditure, less than 20 % = 1; 21 %–60 % = 2; 61 %–100 % = 3; more than 100 % = 4
	Children education (X6)	children under 15 years old and out of school, no = 1; families with out-of-school children aged 15 years and under = 2
	Adult education (X7)	family population with the highest education, junior college/university and above = 1; high school/technical secondary school degree = 2; junior high school education = 3; primary school education = 4, illiteracy = 5
Living standards	Housing (X8)	more than 100m2 = 1; 81m 2–100m 2 = 2; 61 m 2–80 m 2 = 3; 41m2–60m2 = 4; less than or equal to 40m2 = 5
	Car (X9)	Yes = 1; No = 2
	Fuel (X10)	cooking fuel, natural gas/pipeline gas, solar energy/biogas = 1; canned gas/liquefied gas = 2; electricity = 3; coal = 4; chaicao = 5
	Drinking water (X11)	cooking water, barreled water/purified water/filtered water = 1; tap water = 2; well water = 3; pond water/spring water = 4; rainwater/cellar water/river and lake water = 5
	Electricity (X12)	monthly electricity, more than 100 yuan = 1; 81–100 yuan = 2; 61–80 yuan = 3; 41–60 yuan = 4; less than or equal to 40 yuan = 5
Social development capacity	Social network (X13)	humanity expenditure, more than 4000 yuan = 1; 2001–4000 yuan = 2; 1001–2000 yuan = 3; less than 1000 yuan = 4
	Labor force (X14)	family health young and middle-aged labor force, yes = 0; no = 1

5.2. Initial analysis of the performance of the proposed model

To begin with, in the prediction model constructed in this paper, the VMD model is used to decompose the multidimensional features. To gain the optimal results of the decomposition, it is necessary to optimize the core parameters of the VMD model using the AOA algorithm for each indicator. Therefore, for the AOA algorithm, the population number is set 10, the maximum iteration is 20, and the densities, volumes, and accelerations of the individuals are randomly initialized. Finally, the optimal parameter combinations for 14 indicators in VMD mode are yielded separately and shown in Table 8.

Table 8.

Optimal parameters of VMD for all indicators.

	X1	X2	X3	X4	X5	X6	X7
penalty factor $\left(\alpha \right)$	3182	3500	2137	200	238.51	200	200
decomposition number $\left(K\right)$	10	6	10	6	5	2	4
	X8	X9	X10	X11	X12	X13	X14
penalty factor $\left(\alpha \right)$	200	200	200	829.11	200	3500	200
decomposition number $\left(K\right)$	4	4	2	4	2	10	2

Consequently, the VMD algorithm with the corresponding optimal parameters is implemented on each indicator to decompose and extract the potential effective components from the normalized data. Moreover, the decomposed data of each indicator are used as input data for the BiLSTM neural network and further the data set need to be divided into the training and test sets in the ratio of 9:1, which means that 90 % of the data is applied to train the prediction model and the remaining data is reserved in the test set. The test set is used to verify the performance and generalization ability of the finally obtained AOA-VMD-BiLSTM and the common BiLSTM neural network. Furthermore, the main parameters of the BiLSTM neural network are listed in Table 9 and the training process of both networks are illustrated in Fig. 9.

Table 9.

Main structural parameters of the BiLSTM neural network model.

parameter	value
Number of classifications	3
BiLSTM units	20
Epochs	100
Initial learning rate	0.03
Learning rate schedule	piecewise

Fig. 9.

Training process of BiLSTM and AOA-VMD-BiLSTM.

Considering the convergence curves of the prediction accuracy of the two models (the upper figure in Fig. 9), it can be seen that the AOA-VMD-BiLSTM model converges faster compared with the traditional BiLSTM neural network model. In the second round of training, the network starts to be stable, and the prediction accuracy curve does not fluctuate significantly with an accuracy of up to 100 % nearly. In contrast, the traditional BiLSTM neural network has a significant fluctuation in accuracy in each round of training, where the accuracy consistently fluctuates below 90 %. These results indicate that the performance of the traditional BiLSTM model in predicting multidimensional poverty returning risk on the training set is unstable and less accurate. Besides, the loss function curves in Fig. 9 also reconfirm this conclusion. The constructed model in this paper produces less loss in the training stage and gets to the steady state more quickly with a final loss of almost 0, while the traditional BiLSTM model fluctuates significantly around 0.6. Hence, it is verified that the constructed model is proper to deal with the prediction of multidimensional returning to poverty risk and outperforms the traditional BiLSTM model.

Furthermore, the training-process results respond to the accuracy and stability of the model. Still, its generalization ability needs to be verified on the test set, which directly demonstrates its ability to be applied to the new data in the practical scene. Meanwhile, the confusion matrix in the classification problem is more intuitive to depict the prediction effect of the model. As a result, the confusion matrices of the AOA-VMD-BiLSTM model and BiLSTM model on the test set are illustrated in Fig. 10, Fig. 11, where H indicates the high risk of multidimensional return to poverty, and M and L denote the medium and low risk, respectively.

Fig. 10.

Confusion matrix of BiLSTM.

Fig. 11.

Confusion matrix of AOA-VMD-BiLSTM.

As to Fig. 10, it can be seen that the traditional BiLSTM model has an overall accuracy of 80 % on the test set, where the prediction accuracy for the households with a high and medium grade of multidimensional returning to poverty risk is 94 % and 82.9 %, respectively. What's more, it's worth noting that the accuracy of the household of low-level risk is 0, implying this method isn't able to distinguish this specific risk from other forms. In contrast, the results in Fig. 11 show that the accuracy of the presented model on the whole test set is up to 99.8 %, with the prediction accuracies for the households at various levels of risk being over 98 %. Generally, it's important to highlight that the traditional BiLSTM model may have serious misjudgment of the potential risk of multidimensional poverty returning; in other words, the proposed model has an outstanding performance through the initial analysis.

5.3. Comparison experiments

To provide a deeper insight into the performance and effectiveness of the presented model, the comparison experiments are conducted to verify the efforts of the novel model by comparing its results with that of other popular machine learning algorithms, such as support vector machine, decision tree, boosting tree, logistic regression and cosine nearest neighbor. Furthermore, in addition to the confusion matrix, commonly employed metrics, such as accuracy, precision, recall and F1-Score [62] (referring to Equations (28), (29), (30), (31)), are selected to evaluate and compare the effectiveness of different classification models. The detailed comparison results are listed in Table 10.

$$Accuracy=\frac{TP+TN}{P+N}$$ (28)

$$Precision=\frac{TP}{TP+FP}$$ (29)

$$Recall=\frac{TP}{TP+FN}$$ (30)

$$F1-Score=\frac{TP}{TP+\frac{1}{2}\left(FP+FN\right)}=\frac{2\times Precision\times \mathrm{R}ecall}{Precision+\mathrm{R}ecall}$$ (31)

Table 10.

Evaluation of model prediction.

Model	Accuracy	Precision	Recall	F1-score
Support Vector Machine	81.20 %	84.21 %	93.96 %	88.81 %
Decision Tree	81.59 %	85.17 %	92.63 %	88.75 %
Boosting Tree	81.82 %	84.61 %	94.01 %	89.07 %
Logistic Regression	81.23 %	85.00 %	92.63 %	88.65 %
Cosine nearest neighbor	80.09 %	85.53 %	89.18 %	87.31 %
BiLSTM	80.43 %	84.21 %	93.95 %	88.81 %
AOA-VMD-BiLSTM	99.85 %	99.94 %	99.59 %	99.94 %

From the data in Table 10, it is apparent that all the metrics of the proposed model are over 99.5 %, significantly superior to the comparative models with an average F1-Score of about 88 %.

Furthermore, the stability of the proposed predictive models was further analyzed through 20 independent experiments for each model, with performance metrics recorded for each experiment, as shown in Fig. 12. Additionally, the performance metrics and execution times of the proposed models were compared with benchmark models. Table 11 presents the median performance metrics and execution times for each model, along with the results of the Mann-Whitney U test (denoted by H). The value of H indicates whether the constructed model significantly outperforms the comparison model at a 5 % significance level. $h=0$ tends to imply that the corresponding performance of the proposed model don't statically differ from that of the benchmark models, while $h$ with a value identical to 1 or -1 is likely to suggest the performance of the proposed model is better or worse than the corresponding compared algorithms.

Fig. 12.

Stability of the predictive models.

Table 11.

The stability and computational complexity the predictive models.

		Support Vector Machine	Decision Tree	Boosting Tree	Logistic Regression	Cosine nearest neighbor	BiLSTM	AOA-VMD-BiLSTM
Accuracy	Median	0.8178	0.8160	0.8222	0.8169	0.8083	0.8105	0.9982
	$h$	1	1	1	1	1	1	–
Precision	Median	0.8458	0.8582	0.8544	0.8568	0.8442	0.8443	0.9991
	$h$	1	1	1	1	1	1
Recall	Median	0.9342	0.9105	0.9310	0.9213	0.9171	0.9338	0.9994
	$h$	1	1	1	1	1	1	–
F1-score	Median	0.8875	0.8839	0.8890	0.8870	0.8797	0.8872	0.9988
	$h$	1	1	1	1	1	1	–
Execution Times (s)	Median	0.8574	0.0434	0.6003	0.3139	0.1270	84.8872	83.2174
	$h$	−1	−1	−1	−1	−1	0	–

Fig. 12 shows that the performance of all models is relatively stable, without significant fluctuations, indicating that the sample size in this study meets the requirements for model training and allows the models to reach a stable state. Additionally, Table 11 demonstrates that the performance metrics of the predictive models constructed in this study are superior to those of the comparison models. However, in terms of execution time, the models constructed in this study require more time compared to the comparison models. Unlike traditional machine learning models, neural network models have more parameters to learn during the training process, making computations more complex and time-consuming. This limitation applies to all predictive models based on neural networks. It should also be noted that the models in this study require additional time for parameter optimization using AOA to optimize the VMD, but this time is not included in Table 11. This exclusion is mainly because the decomposition of poverty data can be completed independently of the predictive models in practical poverty governance, which does not affect the models' performance in actual application.

The outstanding performance indicates that the constructed model can accurately forecast the potential risk of returning to poverty in multidimensional poverty groups and even provide reliable support for decision-making processes with high precision to help identify the trends of multidimensional poverty risk. What is striking about poverty alleviation is that accurately predicting the risk of returning to poverty can effectively help intervene in the transmission of returning to poverty risk and timely interrupt its spread. At the same time, the proposed model can not only predict whether the potential risk of returning to poverty exists or not but also forecast its level, which can further help optimize poverty alleviation policy and formulate more proper and targeted poverty alleviation measures, thereby improving the efficiency of grassroots poverty governance.

6. Conclusions and policy recommendations

6.1. Conclusions

To effectively address the issue of poverty, it is crucial to conduct a comprehensive analysis of the root causes of poverty, such as lack of access to education, inadequate healthcare, limited job opportunities, and socio-economic inequalities that perpetuate poverty. Moreover, what is another equally important work is to accurately predict the potential risk of households falling back into poverty, which also requires a thorough understanding of the factors that contribute to poverty recurrence. Eventually, an integrated model is constructed in this paper. As for this model, firstly, The A-F method is applied to comprehensively measure multidimensional poverty in China using the data from CFPS in line with the multifaceted nature of poverty instead of a single perspective of income or monetary. On average, the overall multidimensional return to poverty has a significant downward trend during the research period due to the targeted poverty alleviation policy in 2013. The results show that the multidimensional poverty return of observed households is concentrated in two or three dimensions. Therefore, it is necessary to improve the dynamic monitoring and support mechanism so that the individuals prone to return to poverty can be identified in a timely manner to prevent the its incidence.

Secondly, the contribution of all factors in 5 dimensions to the overall MPI is decomposed to offer a deeper understanding of multidimensional poverty. The social development capability dimension contributed the most to the MPI, followed by the health and education dimensions. The current causes of multidimensional poverty returning in rural China are mainly due to the lack of labor in terms of quantity and quality. Meanwhile, the current high cost of medical and education expenditures and the unstable source of rural income have become the main factors for multidimensional poverty.

Thirdly, a practicable method for the recognition of multidimensional poverty return is present for the rule of the identification of multidimensional poverty varying with the value of poverty cut-off in the A-F method. Consequently, the predictive model is finally proposed by combining AOA, VMD and BiLSTM neural networks. Moreover, the experimental results based on the survey data also prove that the proposed model is superior to the traditional BiLSTM but other existing machine learning algorithms with an accuracy of 99.8 %. Therefore, the effectiveness of the model is verified and the model can also be applied to the actual poverty governance work to improve the accuracy of forecasting poverty returning risk in poverty governance and further ensure the realization of rural revitalization.

In summary, the main contribution of this study lies in extending existing research on multidimensional poverty to the investigation into the risks of multidimensional poverty recurrence. It verifies the significant impact of social development capacity, education, healthcare, and public infrastructure on the risk of household poverty recurrence. These factors will be crucial for future academic research and for grassroots management departments to focus on poverty governance. Additionally, the analysis of factors influencing poverty recurrence risks indicates that measures such as renovating dilapidated housing, strengthening cooperative medical care, increasing investment in compulsory education, and improving the rural safe drinking water supply can effectively alleviate the risk of poverty recurrence. These measures can also provide valuable insights into poverty governance in other underdeveloped regions. Furthermore, this study proposes a method for classifying the levels of multidimensional poverty recurrence risk based on the measurement of multidimensional poverty and recurrence risk, facilitating more refined research. Combined with the predictive models for poverty recurrence risk proposed in this study, this method can serve as a practical tool for poverty management, enabling the tracking and early warning of households transitioning out of poverty and preventing the spread of poverty recurrence risk.

6.2. Policy recommendations

Based on the research conclusions, policy recommendations are proposed to enhance the capacity for preventing poverty recurrence from the perspectives of multidimensional poverty recurrence monitoring, early warning, and prevention measures.

Initially, it is essential to improve the monitoring of poverty-stricken areas and households. The government should establish an official data collection system to regularly monitor key indicators for poverty-stricken areas and households. This system will provide timely insights into the living conditions of impoverished families and support data-driven predictions of poverty recurrence risks. Additionally, the government should increase funding for data monitoring by providing additional financial support to third-party research institutions. This will enable detailed surveys of these areas and households, with results promptly reported to management departments and made publicly available to support further research on poverty recurrence. Local governments should also foster collaboration between official agencies and research institutions to ensure that the data collected is authoritative, reliable, and timely. After improving the indicator monitoring and data release mechanisms, in poverty governance, monitoring indicators for poverty recurrence risk need to be dynamically adjusted based on their contributions, promptly removing indicators with low contribution rates and incorporating new indicators according to the actual situation. Meanwhile, there is a need to strengthen the delicate management of multidimensional poverty recurrence risks, transitioning from precision poverty alleviation to precise monitoring of poverty recurrence risks. When assessing poverty recurrence risks, it is crucial not only to determine the existence of these risks but also to specify their severity. Additionally, it is necessary to establish a more accurate early warning system for poverty recurrence risk, utilizing big data and neural network models to achieve precise predictions.

Furthermore, based on the research results of this study, specific measures for preventing poverty recurrence include: (1) Education: This study reaffirms the crucial impact of education on poverty and its recurrence. In order to break the intergenerational transmission of poverty, there is a need to increase investment in compulsory education and ensure access to primary educational resources for all individuals. Additionally, enhancing investment in adult education and skills training can improve the quality of the labor force within families, thereby strengthening their sustainable poverty alleviation capacity. (2) Healthcare: Increasing investment in rural medical insurance is necessary, particularly focusing on providing services for children, women, the elderly, and disabled individuals in rural areas. Incorporating more forms of commercial insurance into public healthcare services can reduce the likelihood of rural households falling into poverty due to illness. (3) Enhancing household's sustainable poverty alleviation capacity: Strengthening the sustainable poverty alleviation capacity of households requires continuously improving their social development capacity. Timely monitoring of the labor force development within households out of poverty and providing a comprehensive social security system can ensure fairer employment opportunities for households in remote areas. In addition, grassroots management departments should increase vocational skills training to enable the rural labor force to adapt to the requirements of particular jobs with social development. (4) Public infrastructure construction: Government departments should continue expanding investment in public infrastructure to provide a safer and more stable living environment for poverty-stricken areas and households out of poverty. Utilizing government-led housing renovation projects can provide safer housing for these households. Additionally, central government-regulated water resources projects ensure a clean water supply for all residents. Furthermore, small-scale distributed clean energy projects, jointly implemented by central and local governments, promote a stable energy supply for households in remote areas.

In conclusion, in the face of multidimensional poverty recurrence risks, poverty governance needs to transition from alleviation to prevention and resolution of multidimensional poverty risks through a comprehensive monitoring mechanism for multidimensional poverty and the establishment of a precise early warning system. What's more, the provision of a combination of long-term and robust multidimensional policies, rather than isolated measures, plays a vital role in preventing the spread and recurrence of poverty risks.

7. Limitations and future research direction

The limitations of this study lie in the analysis of multidimensional poverty relapse at the national level, which may overlook the uneven development among different provinces or regions. Additionally, all indicators were given equal weight in the analysis process, failing to reflect the unique factors affecting households in different regions. Moreover, the dataset was collected from households, posing certain difficulties in data acquisition and potentially limiting the applicability of the constructed predictive models. Therefore, future research will explore multidimensional poverty relapse in the following directions: Firstly, the study will expand to different regions and assign indicator weights based on the specific circumstances of households in those regions within the same indicator system. This approach will better align with regional development and highlight the main risks of poverty recurrence faced by different areas. Secondly, to capture regional characteristics of multidimensional poverty, an indicator system will be constructed from the perspective of regional development. This system will measure regional multidimensional poverty risks, enhancing the monitoring of such risks from a regional development viewpoint. Thirdly, the performance of the predictive models constructed in this study will be validated using data from other countries or regions to improve their applicability. Additionally, predictive models based on regional development data will be created to provide grassroots management departments with more effective multidimensional poverty early warning tools.

Funding

We acknowledge the financial support by the National Social Science Foundation of China (Grant No. 19AGL029).

Ethical approval

Not required.

Data availability statement

China Family Panel Studies (CFPS) is a nationally representative, biennual longitudinal survey of Chinese communities, families, and individuals launched in 2010 by the Institute of Social Science Survey (ISSS) of Peking University, China. If you want to obtain the data used in this paper, first visit website http://www.isss.pku.edu.cn/cfps/, register with your own email, and then apply to obtain the data.

CRediT authorship contribution statement

Jinsong Zhang: Project administration, Conceptualization. Tonggen Ding: Writing – original draft, Methodology, Data curation. Linmao Ma: Writing – review & editing, Writing – original draft, Software, Methodology, Formal analysis.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:Jinsong Zhang reports financial support and article publishing charges were provided by the National Social Science Foundation of China (Grant No. 19AGL029). If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.