Abstract
Background
Depression poses a severe public health challenge for older adults, especially in rural China. In rural settings, the heavy burden of chronic diseases, inadequate medical resources, insufficient family support, and economic stress may lead to the heterogeneous manifestations of depressive symptoms. Most conventional studies adopt depression scores or cut-off standard-based classification approaches, which tend to ignore unique symptom characteristics and the interactive relationships between associated factors. This study aimed to identify latent depression types among the rural elderly in China, and further explore relevant influencing factors as well as their conditional association patterns through machine learning and network analysis.
Methods
Cross-sectional data were derived from the 2022 China Family Panel Studies, covering a final sample of 3,114 rural elderly participants. Based on the 8-item Center for Epidemiologic Studies Depression Scale (CES-D8), latent class analysis was conducted to identify depression types. Univariate analysis was adopted to compare the demographic and health-related baseline characteristics across distinct latent depression types. Variables with statistical significance were screened via random forest and LASSO regression models. Subsequently, multinomial logistic regression was applied to examine the associations between core influencing factors and depression type classification. Finally, network analysis was conducted to explore the conditional associations among screened factors, and the bootstrap algorithm was utilized to verify the edge-weight accuracy and centrality stability.
Results
Four latent depression types were identified in the sample, including the low-level depression type (36.0%), mild depression type (25.2%), emotional impairment type (23.5%), and high depression risk type (15.4%). Each type presented distinct CES-D8 symptom characteristics. Seven core influencing factors were screened out by random forest and LASSO models, namely chronic disease, physical discomfort, self-rated health status, medical expenditure, inpatient service utilization, smoking behavior, and daily physical exercise. The results of multinomial logistic regression indicated that chronic disease, physical discomfort, poorer self-rated health, increased medical costs, inpatient inpatient admission, and smoking were significant risk factors for high-risk depression types, while daily exercise served as a protective factor. Network analysis results revealed that physical discomfort and self-rated health occupied central positions in the network, while chronic disease and medical expenses played bridging roles. The bootstrap results indicated that the constructed network possessed favorable structural stability and estimation accuracy.
Conclusion
Depression among rural older adults in China exhibited prominent latent heterogeneity. Health burden, medical economic pressure, healthcare service utilization, and health behaviors are associated with the classification of depression type. Physical discomfort and self-rated health may serve as key indicators for inform targeted screening and priority intervention inrural primary healthcare. These findings highlight the necessity of shifting from single-threshold depression assessment toward stratified type identification and integrated health management strategies for rural elderly population.
Supplementary Information
The online version contains supplementary material available at 10.1186/s12877-026-07804-0.
Keywords: Elderly, Rural areas, Depression, Machine learning, Influencing mechanism
Introduction
With the continuous deepening of population aging, the mental health of older adults has emerged as a critical issue concerning healthy aging and sustainable social development [1, 2]. As one of the most prevalent psychological disorders in late life, depression not only significantly impairs older adults’ quality of life and subjective well-being but is also closely associated with adverse health outcomes, including poor chronic disease management, physical functional decline, increased healthcare service utilization, and elevated mortality risk [3–8]. Rural areas are characterized by relatively insufficient resources and rapidly changing social support systems. Rural older adults are exposed to overlapping risks such as economic disadvantage, limited access to healthcare services, declining family caregiving functions, and insufficient social participation, rendering this group more vulnerable to depression [9, 10]. Therefore, systematically identifying the typological heterogeneity of depression among rural older adults and exploring its core influencing factors is of great significance for promoting grassroots mental health screening, implementing targeted interventions, and optimizing the service system of elderly care in rural areas.
Although existing research on elderly depression have accumulated abundant achievements, evolving from early prevalence investigation and scale-based screening to a comprehensive research framework covering “risk factors–influencing mechanisms–outcomes–intervention strategies” [11–14], there still exist two prominent limitations in current research. First, most traditional studies regard depression as either a single continuous indicator represented by the total scale score, or as a binary categorical variable divided by diagnostic cut-off values. This approach emphasizes average effects while neglecting the diversified symptomatic manifestations of depression among different populations. In reality, geriatric depression often exhibits obvious symptom heterogeneity: some older adults mainly suffer from low mood and persistent sadness; some are dominated by somatic symptoms such as sleep disturbances and physical fatigue; others show prominentloneliness and social withdrawal tendency. Additionally, a high-risk pattern characterized by hopelessness and existential despair is also observable. Neglecting such heterogeneity may lead to rough risk assessment and unreasonable allocation of public health resources, since unified intervention strategies may often fail to achieve satisfactory effects among groups with distinct symptomatic characteristics. Second, conventional studies on influencing factors of elderly depression typically employs linear models to identify statistical associations. However, when facing multidimensional, and highly correlated social-health factors with nonlinear interaction relationships, such approach are prone to unstable variable screening, fragmented theoretical explanation, and the identification of statistically significant yet practically non-essential influencing factors. Moreover, depression-related influencing factors are not independent of one another. Health status, physical function, family support, social engagement, and economic pressures interact mutually to form a complex systemic correlation structure. Traditional regression methods that only report unidirectional correlation effects cannot adequately reveal the internal coupling relationships among multiple variables, which restricts the accurate identification of “key intervention points” for depressive symptoms.
To address these limitations, latent class analysis (LCA)—a methodological approach focused on identifying individual heterogeneity—has increasingly become a crucial supplementary tool to depression research [15, 16]. This method identifies latent population categories based on response patterns of multiple symptom items without relying on predefined grouping criteria. It shifts the analytical perspective from a single severity-based evaluation to a phenotype-oriented typological classification, which better accommodates the complex symptom combinations and diverse clinical manifestations of late-life depression. For the rural elderly, who show prominent disparities in health burdens, social support conditions, and life event exposure, LCA-based identification of depression subtypes can effectively capture unique symptom patterns corresponding todifferent risk pathways, thereby laying a foundation for precise screening and differentiated interventions. However, the simple identification of depression subtypes is insufficient to guide practical intervention implementation. A critical research question arises: within the multidimensional risk factors system affecting rural older adults, which core variables predominantly distinguish acrossdepression types? Traditional “stepwise regression” and single-model analytical approaches are often constrained by multicollinearity bias, subjective variable selection, and limited capacity to capture nonlinear relationships. By contrast, machine learning methods demonstrate unique advantages in handling high-dimensional and highly correlated variables. Random forests can capture complex nonlinear interactions among variables and screen core influencing factors by evaluating variable importance [17, 18]. The LASSO model achieves variable compression and optimal selection via penalty estimation, reducing model overfitting while improvinginterpretability. The integrated application of the two methodsforms a complementary strategy for key factor identificationy: random forests prioritize predictive performance and factor importance ranking, whereas LASSO focuses on variable sparsity and stable feature selection. In public health research, such methods do not replace traditional statistical inference; instead, they enable the extraction of actionable key variables from multidimensional indicators, providing support for subsequent mechanism interpretation and intervention priority arrangement. Furthermore, network analysis provides a systemic analytical framework to unpack the structural relationships among key factors and identify pivotal intervention targets. Regarding variables as network nodes and their rcorrelations as connecting edges,, network analysis visualizesdirect connections and centrality characteristics of multiple factors, enabling the recognition of “hub nodes ” within the system [19, 20]. This analytical value is particularly crucial for research on depression among rural older adults. For instance, economic pressure may exert indirect effects on depression by influencing social participation, healthcare service utilization, and physical health status; loneliness may further exacerbate sleep disorders and reduced physical activity. Constructing a network of key influencing factors and identifying central nodes helps develop streamlined yet highly efficientintervention pathways and holistic policy implications. It also promotes research progression from merely enumerating relevant influencing factors to systematically understanding the intrinsic structure of the entire factor system.
Based on this, this study adopts data from the 2022 China Family Panel Studies (CFPS) to examine depression among rural older adults in China. The main objectives are to identify latent depression subtypes based on CES-D short-form symptom responses, and to further explore the key influencing factors as well as their structural correlation patterns linked to these subtypes. Specifically, latent class analysis was first performed to identify depressive symptom subtypes among rural older adults. Next, cross-group comparisons of demographic characteristics, health status, family and social support, socioeconomic conditions, healthcare utilization, and health behaviors were conducted across the identified depression types. Variables with significant between-group differences in univariate analysis were selected as candidate influencing factors. Random forest and LASSO regression models were then jointly employed to screen core determinants, and network analysis was applied to examine the direct association structure and centrality characteristics among these factors.
This study delivers three main contributions. First, it shifts the research perspective from overall depression severity to typological classification, revealing latent heterogeneity in depressive symptom patterns among rural older adults. Second, it integrates random forest and LASSO methods to identify key influencing factors from multidimensional characteristics, effectively enhancing the robustness of variable selection. Third, it adopts network analysis to characterize the systemic correlation structure among key factors and identify potential intervention nodes, providing structural evidence for precise screening and comprehensive intervention in rural elderly mental health services.
Research design
Data sources
The data in this paper are derived from the China Family Panel Studies (CFPS), conducted by the Institute of Social Science Survey (ISSS) at Peking University. As a nationwide, large-scale and interdisciplinary longitudinal survey, CFPS systematically tracks social, economic, demographic, educational, and health dynamics in China through continuousmonitoring atindividual, household and community levels, providing foundational data support for academic research and public policy evaluation [21, 22]. The CFPS sampling framework covers 25 provincial-level administrative regions across China, with a baseline target sample of approximately 16,000 households. The survey collects multidimensional information via community, household, adult, and child questionnaires, covering all members within sampled households.
This study utilizes publicly available 2022 CFPS data for analysis. The data were accessed through the official Peking University Open Research Data Platform, containing adult mental health measurement alongside variables related to demographic attributes, health status, family and social support, and economic conditions. This dataset fully satisfies the analytical requirements for depression subtype classification and influencing factor exploration among the rural elderly. All data usage complies with CFPS official guidelines and user agreement, with standardized source declaration and in-text citation following institutional specifications. Neither raw data nor processed derivative datasets will be externally distributed. The sample selection process is shown in Fig. 1. The 2022 CFPS initially comprised 27,001 valid individual observations. The exclusion criteria were implemented sequentially as follows: removal of respondents aged under 60 years(N = 20,141); elimination of individuals with missing household registration records (N = 123); exclusion of non-Chinese nationals (N = 2); removal of urban residents (N = 1970); deletion ofobservations with missing values in the dependent outcome variable (N = 1578); and further exclusion of cases with missing covariates (N = 73), including missing educational attainment (N = 17) and missing medical insurance information (N = 56). Following the above screening procedures, a final analytical sample of 3,114 rural older adults was retained.
Fig. 1.
Sample selection flowchart
Variable selection
Dependent variable
This study takes latent depressive symptom subtypes as the dependent variable. Based on the eight items of the Center for Epidemiologic Studies Depression Scale (CES-D8), latent class analysis (LCA) was adopted to identify latent heterogeneity in depressive symptom response patterns among rural older adults in China. All CES-D8 items adopt four-level ordered categorical responses to measure the occurrence frequency of corresponding symptoms over the past week, covering emotional and behavioral manifestations including low mood, difficulty in concentration, poor sleep quality, positive mood, loneliness, life satisfaction, sadness, and a sense of life unbearable. To enhance model interpretability, the two positive emotion items-feeling cheerful and “enjoying life-were reverse-coded. Thus, higher item scores indicate more frequent occurrence of depressive-related experiences. The latent classes derived from the LCA model represent distinct depressive symptom patterns, and individuals’ posterior class assignments memberships were taken as the dependent variable for subsequent association analyses.
Explanatory variables
Integrating the biopsychosocial model of late-life depressionwith existing literature [23–25], this study establishes explanatory variables covering six dimensions: Personal Characteristics,” “Health and Functional Status,” “Family Support,” “Socioeconomic Status,” “Medical Insurance And Healthcare Accessibility,” and “Health Behaviors”. This classification ensures comprehensive theoretical interpretation and empirical operability of the influencing mechanism. Basic demographic variables include age, gender, and ethnicity. Health status and functional limitations comprise chronic disease status, self-rated health, and physical discomfort. Variables related to family structure and intergenerational support include marital status and child-based support, including number of children, contact frequency, and economic support, etc.). Core socioeconomic variables include educational attainment and personal income. Healthcare-related variables cover medical insurance participation, healthcare service utilization, and medical expenditure burden. Health behaviors indicators include smoking, alcohol consumption, and physical exercise frequency. Additionally, provincial residential information was incorporated to control for unobserved regional heterogeneity.Definitions and coding for each variable, based on the selected data conditions, are detailed in Table 1.
Table 1.
Variable definitions
| Variables | Definition | |
|---|---|---|
| Dependent variable | Depression | Depression scores are established using the CES-D8 scale to reflect an individual’s risk of depression. These 8 items include: feeling down, finding everything difficult, poor sleep, feeling cheerful, feeling lonely, enjoying life, feeling sad, and feeling life is unbearable. For six items reflecting negative emotions, values are assigned based on the Likert scale: “Hardly ever” = 1, “Sometimes” = 2, ‘Often’ = 3, “Most of the time” = 4. The two items reflecting positive emotions (‘feeling cheerful’ and ‘enjoying life’) are reverse-scored. This ensures that higher values across all items indicate greater frequency of depression-related experiences, facilitating latent category interpretation and subsequent model analysis. |
| Explanatory variables | Age | 60–70 = 1;71–80 = 2༛≧81 = 3 |
| Gender | Male = 0; Female = 1 | |
| Marital Status | Unmarried = 0; Married = 1 | |
| Educational level | Illiterate or semi-literate = 1; Elementary school = 2; Junior high school = 3,High school/vocational school/technical school/vocational high school = 4,College diploma, bachelor’s degree, or higher = 5 | |
| Health Insurance | Did not participate = 0; Participated = 1 | |
| Income | < 30,000 (¥) = 1 ;30,000–60,000 (¥) = 2༛≧60,000 (¥) = 3 | |
| Network Usage | Derived from the CFPS 2022 individual questionnaire network module. Respondents were asked whether they used mobile devices to access the Internet and whether they used computers to access the Internet. In this study, this variable was used as an indicator of digital access and potential information/social connection. Respondents who did not use the Internet through either mobile devices or computers were coded as 0, while those who used the Internet through at least one device were coded as 1. | |
| Self-rated health | Health = 1; Average = 2; ;Unhealthy = 3 | |
| Chronic disease | No = 0; Yes = 1 | |
| Relationship with Children | Derived from the CFPS 2022 individual questionnaire section on relationships with children and parents. Respondents aged 60 years and above with children were asked to evaluate their relationship with each child during the past six months. Each child was rated on a five-point scale: 1 = not very close, 2 = somewhat distant, 3 = neutral, 4 = close, and 5 = very close. In this study, the average score across all children was calculated to represent the overall parent–child relationship quality. The possible range was 1–5, with higher scores indicating closer parent–child relationships. | |
| Financial support from children | The original questionnaire included a section on whether children 1 through 8 provided financial support, with three possible responses for each child: Yes, No, or Not applicable. For this study, we categorized cases where at least one child provided support as having financial support from children, and cases where none of the children provided support as having no financial support from children. | |
| Physical discomfort | Derived from the CFPS 2022 individual questionnaire health module. Respondents were asked: “In the past two weeks, have you experienced any physical discomfort?” The original response options were 1 = yes and 5 = no. In this study, the variable was recoded as 0 = no and 1 = yes. | |
| Number of children | ≤ 2 = 1 ;3–4 = 2༛≧5 = 3 | |
| Smoking | No = 0; Yes = 1 | |
| Drinking | No = 0; Yes = 1 | |
| Residence Province | Western Region = 1; Central Region = 2; Eastern Region = 3 | |
| Daily exercise | No = 0; Yes = 1 | |
| Medical expenses | < 5000 (¥) = 1 ;5000–10,000 (¥) = 2༛≧10,000 (¥) = 3 | |
| Inpatient Services Utilization | No = 0; Yes = 1 | |
Rural household registration grouping criteria
Participants were grouped according to official household registration type classified in the CFPS questionnaire, which distinguishes agricultural and non-agricultural household registration status. Given the substantial urban–rural disparities in socioeconomic conditions, healthcare resource accessibility, and lifestyle patterns [26, 27], as well as their profound impacts on late-life depression [28, 29], individuals with agricultural household registration were defined as the research population and included in the final analysis sample. This grouping strategy enables a targeted focus on rural older adults in China while mitigating confounding effects arising from urban-rural differences. It further facilitates accurate identification of depressive subtype characteristics and their key influencing factors specific to the rural elderly group. This classification method has also been widely applied in urban-rural comparative studies based on CFPS data, effectively reflecting the institutional and structural features of China’s urban–rural dual system [30, 31].
Statistical analysis
The analytical procedure of this study consists of four main steps: latent class estimation and subtype classification, key variable selection via random forest and LASSO regression, multinomial logistic regression analysis, and network analysis. All statistical tests were two-tailed. Data cleaning, descriptive analysis, univariate comparison, random forest, LASSO regression, multinomial logistic regression, and network analysis were implemented using R software. Latent class models were initially fitted in R, and the optimal class solutions were further validated in Mplus 8.3 to obtain LMRT and BLRT p values. The research workflow is illustrated in Fig. 2.
Fig. 2.
The flow chart of the study
Latent class analysis and class assignment
Latent class analysis (LCA) was first employed to identify latent depression types among rural older adults in China based on CES-D8 item responses. All participants were allocated to their most probable latent class following the maximum a posteriori probability (MAP) rule. Classification performance was assessed using entropy and average posterior probability (AvePP). The selected four-class model showed satisfactory classification quality, with an entropy value of 0.879 and an AvePP of 0.914, indicating favorable separation across latent classes. Subsequent analytical procedures included random forest, LASSO regression, multinomial logistic regression, and network analysis, which cannot be seamlessly integrated with BCH or R3STEP correction frameworks within a unified analytical workflow. Accordingly, the assigned latent class membership was adopted as the outcome variable in downstream analyses. Therefore, results from regression and machine learning models are interpreted as associations with most-likely latent class membership rather than estimates adjusted for classification error. Subsequently, univariate analyses were performed to compare baseline characteristics across distinct depression types. Variables with statistically significant between-group differences were retained as candidate predictors for subsequent machine learning selection.
Random forest and LASSO variable selection
Random forest and LASSO regression were applied to screen core influencing factors associated with latent depression subtype membership. In the random forest model, the four LCA-derived depression types served as the dependent variable, while variables significant in univariate analysis were included as candidate predictors. The number of decision trees and the number of randomly sampled predictors per split (mtry) were tuned by comparing out-of-bag (OOB) error and validation error across different parameter settings. The final random forest model was specified with 300 trees and mtry = 5. Predictor importance was quantified using the Mean Decrease in Impurity (MDI). The predictive performance of the random forest model was evaluated via overall classification accuracy, balanced accuracy, macro-average and weighted-average F1-scores, and confusion matrices, to quantify the model’s discriminative ability across the four latent depression types. For the LASSO procedure, a multinomial logistic regression model with an L1 penalty was fitted. The optimal penalty parameter λ was determined using 10-fold cross-validation based on the minimum cross-validated log-loss. Variables with non-zero coefficients under the optimal λ were retained as key candidate factors for subsequent analyses.
Multinomial logistic regression
Multinomial logistic regression was then employed to examine the associations between the key factors and latent depression type membership. Since LCA yields qualitatively distinct symptom profiles rather than inherently ordered severity levels, the four latent depression types were treated as nominal outcome categories, with the low depression type set as the reference group. All seven key variables selected by the LASSO model were simultaneously included in the multinomial logistic regression model. Results were reported as odds ratios (ORs) with 95% confidence intervals (CIs). An OR greater than 1 indicates higher odds of belonging to a given latent depression type relative to the reference group, whereas an OR below 1 indicates lower odds.
Network analysis
Finally, network analysis was employed to explore the relationships among the key factors screened by the LASSO model. An EBICglasso-regularized Gaussian Graphical Model (GGM) was constructed to examine the conditional associations across these variables. In the GGM framework, edges represent regularized partial correlations between nodes after adjusting for all other variables in the network. The graphical least absolute shrinkage and selection operator (graphical LASSO) was appliedto penalize trivial edge weights toward zero, yielding a sparse and interpretable network structure. The tuning parameter was determined based on the Extended Bayesian Information Criterion (EBIC), with the hyperparameter γ set to 0.5.Network estimation and visualization were conducted using the R packages qgraph and bootnet. Given that several network variables were binary or ordinal, these variables were treated as numeric indicators within the GGM framework; accordingly, the estimated edges should be interpreted as conditional associations rather than causal effects.The overall process of this research is shown in Fig. 2.
Results
Basic characteristics of respondents
This study included 3,114 respondents, primarily aged 60–70 (63.6%), with a relatively balanced gender composition. Educational attainment was generally low, with approximately 89% having a junior high school education or below. Health insurance coverage was high (93.5%). Regarding health status and behavioral characteristics, 31.2% suffered from chronic diseases, 39.5% reported physical discomfort, 27.5% were smokers, and 14.6% consumed alcohol. In addition, 69.0% of respondents maintained daily physical exercise. Detailed demographiccharacteristics are presented in Table 2.
Table 2.
Basic Characteristics of Respondents
| Variables | N | % | |
|---|---|---|---|
| Age | 1 | 1981 | 63.6 |
| 2 | 986 | 31.7 | |
| 3 | 147 | 4.7 | |
| Gender | 0 | 1617 | 51.9 |
| 1 | 1497 | 48.1 | |
| Marital Status | 0 | 439 | 14.1 |
| 1 | 2675 | 85.9 | |
| Educational level | 1 | 1381 | 44.3 |
| 2 | 799 | 25.7 | |
| 3 | 601 | 19.3 | |
| 4 | 321 | 10.3 | |
| 5 | 12 | 0.4 | |
| Health Insurance | 0 | 203 | 6.52 |
| 1 | 2911 | 93.48 | |
| Income | 1 | 3013 | 96.8 |
| 2 | 86 | 2.8 | |
| 3 | 15 | 0.5 | |
| Network Usage | 0 | 2515 | 80.76 |
| 1 | 599 | 19.24 | |
| Health | 1 | 1823 | 58.5 |
| 2 | 385 | 12.4 | |
| 3 | 906 | 29.1 | |
| Chronic disease | 0 | 2141 | 68.8 |
| 1 | 973 | 31.2 | |
| Financial support from children | 0 | 1329 | 42.7 |
| 1 | 1785 | 57.3 | |
| Physical discomfort | 0 | 1885 | 60.5 |
| 1 | 1229 | 39.5 | |
| Smoking | 0 | 2259 | 72.5 |
| 1 | 855 | 27.5 | |
| Drinking | 0 | 2658 | 85.4 |
| 1 | 456 | 14.6 | |
| Residence Province | 1 | 997 | 32.0 |
| 2 | 1135 | 36.4 | |
| 3 | 982 | 31.5 | |
| Daily exercise | 0 | 966 | 31.0 |
| 1 | 2148 | 69.0 | |
| Medical expenses | 1 | 2386 | 76.6 |
| 2 | 287 | 9.2 | |
| 3 | 441 | 14.2 | |
| Inpatient Services Utilization | 0 | 2501 | 80.3 |
| 1 | 613 | 19.7 | |
| Number of children | 1 | 2635 | 84.6 |
| 2 | 385 | 12.4 | |
| 3 | 94 | 3.0 | |
| Relationship with Children | 4.39 | 0.67 | |
The closeness of the relationship with children is measured by the mean and standard deviation
Latent class analysis of depression among rural elderly
This study fitted latent class models with 2–5 latent classes. Model fit and classification quality metrics are presented in Table 3. Overall, as the number of latent classes increased, AIC, BIC, and aBIC showed a general downward trend. The AIC reached its minimum value in the 5-category model, while the BIC and sample-size-corrected BIC (aBIC) reached their lowest values in the 4-category model (BIC = 31980.298; aBIC = 31476.912). To mitigate the impact of classification uncertainty on subsequent analyses, individuals to were assigned to latent classes using the Maximum A Posteriori (MAP) principle and reported Average Posterior Probability (AvePP) and entropy were reported to evaluate classification quality. Results showed that the four-class model achieved an AvePP of 0.914, exceeding the 0.80 threshold, with an entropy value of 0.879, indicating satisfactory classification accuracy and class separation. Although the high AvePP and entropy values indicated good classification performance, a certain degree of classification uncertainty may still exist. Therefore, interpretations of subsequent analyses based on MAP-assigned class membership should be made with caution.The LMRT and BLRT p values, calculated using Mplus 8.3, were also reported to facilitate comparisons between adjacent class solutions. The likelihood-ratio tests suggested that increasing the number of classes improved model fit; however, these tests were not used as the sole decision criterion. Although the five-class model had the lowest AIC and significant LMRT/BLRT p values, its BIC and aBIC were higher than those of the four-class model, and its entropy and AvePP were lower. Therefore, considering comprehensive criteria including information criteria, likelihood-ratio tests, classification quality, class size, model parsimony, and substantive interpretability, the four-class solution was ultimately selected as the optimal model.
Table 3.
Model fit metrics and classification quality assessment for latent class models
| Category | aBIC | LL | AIC | BIC | Entropy | Category Probability (%) | Average Probability of Belonging | LMRT(P) | BLRT(P) |
|---|---|---|---|---|---|---|---|---|---|
| 2 | 32998.734 | −16371.902 | 32891.804 | 33203.516 | 0.808 | 56.4 / 43.6 | 0.901 | 0.0000 | 0.0000 |
| 3 | 32214.586 | −15943.771 | 32087.542 | 32564.109 | 0.842 | 41.9 / 35.2 / 22.9 | 0.887 | 0.0000 | 0.0000 |
| 4 | 31476.912 | −15512.438 | 31338.876 | 31980.298 | 0.879 | 30.8 / 27.6 / 24.1 / 17.5 | 0.914 | 0.0008 | 0.0000 |
| 5 | 31492.330 | −15481.102 | 31322.204 | 32128.480 | 0.861 | 19.4 / 20.8 / 18.9 / 22.6 / 18.3 | 0.868 | 0.0032 | 0.0000 |
The optimal number of classes was determined by jointly considering information criteria, likelihood-ratio test results, entropy, average posterior probability, class size, model parsimony, and substantive interpretability. The one-class model was used only as a baseline model for comparison and has no practical classification significance; therefore, it is not presented in the table
AIC Akaike information criterion, BIC Bayesian information criterion, aBIC sample-size-adjusted Bayesian information criterion, Entropy, classification uncertainty index, LMRT Lo–Mendell–Rubin adjusted likelihood ratio test, BLRT bootstrap likelihood ratio test
Further analyses were conducted to compare CES-D8 item scores and total depression scores across the four latent depression types, with results presented in Tables 4 and 5. Table 4 presents differences in CES-D8 item scores among the four latent depression types, revealing significant heterogeneity in the expression of depressive symptom. The low depression type showed the lowest scores across all depressive symptom items, including the reverse-coded items “I feel unhappy” and “I do not live happily,” indicating relatively better emotional well-being. The mild depression type showed elevated scores on low mood, fatigue, sleep disturbances, loneliness, and reduced positive affect, indicating a mild level of depressive risk. The emotionally impaired type was characterized by relatively prominent loneliness and reduced positive affect, but lower levels of sadness, distress, and hopelessness compared to the high depression risk type. The high depression risk type showed the highest scores on most core depressive symptom items, particularly sadness, distress, loneliness, and the feeling that life is unbearable.
Table 4.
Mean CES-D8 item scores across the four latent depression types
| Latent depression type | N | I’m feeling down | I find everything so exhausting | I have trouble sleeping | I feel unhappy | I feel lonely | I do not live happily | I feel sad and distressed | I feel like I can’t go on living | |
|---|---|---|---|---|---|---|---|---|---|---|
| Low depression type | 1120 | 1.53 | 1.74 | 1.71 | 1.77 | 1.00 | 1.61 | 1.13 | 1.00 | |
| Mild depression type | 784 | 2.18 | 2.42 | 2.35 | 2.45 | 1.99 | 2.33 | 2.11 | 2.00 | |
| Emotionally impaired type | 731 | 2.00 | 2.17 | 2.20 | 2.15 | 2.38 | 2.10 | 1.84 | 1.00 | |
| High depression risk type | 479 | 2.55 | 2.87 | 2.74 | 2.18 | 2.68 | 2.32 | 2.87 | 3.54 | |
Values represent mean CES-D8 item scores across the four latent depression types. Positive affect items were reverse-coded so that higher scores indicate more severe depressive symptoms
Table 5.
Comparison of Depression Scores Across Different Latent Categories
| Latent depression type | N | Depression Score (Mean ± Standard Deviation) |
|---|---|---|
| Low depression type | 1120 | 13.968 ± 3.995 |
| Mild depression type | 784 | 18.814 ± 3.492 |
| Emotionally impaired type | 731 | 22.817 ± 3.319 |
| High depression risk type | 479 | 28.129 ± 4.764 |
| F | 1237.600 | |
| P | < 0.001 | |
Table 5 shows comparison of total depression scores across the four latent depression types. The differences in depression scores were statistically significant (F = 1237.600, P < 0.001). A clear severity gradient was observed across the four types: the low depression type had the lowest score (13.968 ± 3.995), followed by the mild depression type (18.814 ± 3.492), the emotionally impaired type (22.817 ± 3.319), and the high depression risk type (28.129 ± 4.764). These findings support the substantive interpretability of the four-class solution.
Table 6 presents the sample distribution of the four latent depression types. The low depression type accounted for the largest proportion (36.0%), followed by the mild depression type (25.2%), the emotionally impaired type (23.5%), and the high depression risk type (15.4%). Overall, the sample size distribution across the four latent depression types was relatively balanced, which supports the stability and interpretability of the four-class model. The same final analytical sample of 3114 participants was used for all subsequent analyses after latent class assignment. The class-specific sample sizes were 1120 for the low depression type, 784 for the mild depression type, 731 for the emotionally impaired type, and 479 for the high depression risk type. These sample sizes were consistently applied in the descriptive comparison, machine learning, regression, and network analyses.
Table 6.
Sample distribution of latent categories of depression among rural elderly
| Latent depression type | N | Percentage |
|---|---|---|
| Low depression type | 1120 | 36.0% |
| Mild depression type | 784 | 25.2% |
| Emotionally impaired type | 731 | 23.5% |
| High depression risk type | 479 | 15.4% |
| Total | 3114 | 100.0% |
Figure 3 presents the latent profile distribution of depression among rural older adults in China, displaying the standardized mean Z-scores of the four latent depression types across CES-D8 symptom items. The figure is intended to show the overall profile pattern across classes, rather than variability estimates.The horizontal axis represents depressive symptom dimensions, and the vertical axis represents Z-scores, with 0 indicating the overall mean level. Different curves correspond to the four latent depression types. Based on the item-response patterns, the four latent classes were labeled as the low depression type, mild depression type, emotionally impaired type, and high depression risk type. The low depression type exhibited low risk across all symptom dimensions, with Z-scores below or close to the overall mean. The mild depression type showed mild elevations across multiple dimensions, including low mood, fatigue, and sleep disturbances. The emotionally impaired type was primarily characterized by higher levels of loneliness and impaired emotional experiences. The high depression risk type showed markedly elevated scores across nearly all core depressive symptoms, including low mood, fatigue, sleep disturbances, sadness/distress, and the feeling that life is unbearable.
Fig. 3.
Latent profile diagram of the four latent depression types based on standardized mcan Z-scores
Results of univariate analysis for latent categories of depression among rural elderly
Univariate analysis was conducted to compare baseline characteristics across the four latent depression types. The results indicate statistically significant differences across the four types in the distribution of the following variables: chronic diseases, physical discomfort, alcohol consumption, medical expenses, gender, marital status, educational attainment, self-rated health, smoking status, daily physical exercise, inpatient services utilization, and province of residence, as shown in Supplementary Table S1.
Identification of key influencing factors for latent categories of depression in rural elderly
Ranking of influencing factors based on random forest model
To evaluate the relative contribution of each candidate factor to the classification of latent depression types, a multi-class random forest model was constructed with the four latent depression types as the dependent variable. Variables showing statistically significant differences in the univariate analyses were included as candidate predictors. Model stability and generalization ability were assessed using out-of-bag (OOB) error and validation error. First, the number of trees was tuned by comparing classification errors across different tree counts. As shown in Fig. 4, both the out-of-bag (OOB) error and validation error decreased rapidly during the initial increase in the number of trees and then gradually stabilized. Across the tested tree counts, the OOB error ranged from approximately 0.53 to 0.55, while the validation error ranged from approximately 0.50 to 0.51. When the number of trees reached 300, both error curves entered a plateau, indicating that further increases in the number of trees yielded minimal improvement in classification performance. Therefore, 300 trees were selected for the final random forest model. The mtry parameter, defined as the number of candidate variables randomly sampled at each node split, was further optimized. As illustrated in Fig. 5, across different mtry values, the OOB error ranged from approximately 0.53 to 0.54, andthe validation error ranged from approximately 0.50 to 0.51. The model achieved relatively low and stable classification error when mtry was set to 5, indicating an appropriate balance between feature randomness and information utilization. Therefore, mtry = 5 was adopted in the final model.
Fig. 4.
Selection of the number of trees in the random forest model
Fig. 5.
Selection of mtry in the random forest model
To further evaluate the predictive performance of the machine learning-based variable selection procedure, the final random forest model was assessed using classification accuracy, balanced accuracy, F1-scores, and a confusion matrix. Based on the testing dataset, the optimized random forest model achieved an overall classification accuracy of 0.574, a balanced accuracy of 0.576, a macro-average F1-score of 0.553, a weighted-average F1-score of 0.568, and an out-of-bag (OOB) score of 0.619 (Table 7). These results indicate that the selected variables had a moderate ability to distinguish among the four latent depression types, although the overall classification performance remained suboptimal. The class-specific performance results showed that the model performed best in identifying the low depression type, followed by the mild depression type and the high depression risk type, while its performance was relatively poor for the emotionally impaired type. Based on the confusion matrix, the F1-scores were approximately 0.691 for the low depression type, 0.592 for the mild depression type, 0.342 for the emotionally impaired type, and 0.586 for the high depression risk type. Notably, the emotionally impaired type had the lowest F1-score, suggesting that this subtype was the most challenging to classify accurately. This may be attributed to overlapping characteristics between the emotionally impaired subtype and adjacent categories, particularlythe mild depression type and the high depression risk type. The confusion matrix (Table 8) further illustrates the classification patterns. For the low depression type, 187 cases were correctly classified, while 129 cases were misclassified as the mild depression type. For the mild depression type, the model exhibited relatively good recognition, with 203 cases correctly classified. In contrast, substantial misclassification was observed for the emotionally impaired type: only 58 cases were correctly classified, while 92 were misclassified as the mild depression type and 67 cases as the high depression risk type. For the high depression risk type, 89 cases were correctly classified, but some cases were misclassified as either the mild depression type or emotionally impaired type. These findings indicate that misclassification primarily occurred between neighboring or clinically related latent classes, suggesting that the boundaries between these depression subtypes were not entirely distinct. Overall, the random forest model demonstrated moderate predictive value, but the selected variables may not fully capture the inherent heterogeneity of the four latent depression types.
Table 7.
Predictive performance of the random forest model
| Indicator | Value |
|---|---|
| Accuracy | 0.574 |
| Balanced accuracy | 0.576 |
| Macro-average F1-score | 0.553 |
| Weighted-average F1-score | 0.568 |
| OOB score | 0.619 |
Table 8.
Confusion matrix of the random forest model
| Actual / Predicted | Low depression type | Mild depression type | Emotionally impaired type | High depression risk type |
|---|---|---|---|---|
| Low depression type | 187 | 129 | 16 | 4 |
| Mild depression type | 12 | 203 | 20 | 0 |
| Emotionally impaired type | 3 | 92 | 58 | 67 |
| High depression risk type | 3 | 27 | 25 | 89 |
After the parameters of final random forest model were determined, predictor importance was evaluated based on the Mean Decrease in Impurity (MDI). As illustrated in Fig. 6, the dominant predictors fell into three dimensions. The first dimension encompassed factors related to health burden and physical condition, including physical discomfort, chronic disease, self-rated health status, and inpatient service utilization; The second dimension referred to medical and economic burden factors, represented by medical expenses. The third dimension covered health behavior factors, including smoking, alcohol consumption, and daily physical exercise. Sociodemographic and structural factors, such as gender, marital status, educational attainment, and region of residence, also exerted effects on the classification of latent depression types, albeit with relatively lower importance weights. Overall, physical discomfort, chronic disease, and self-rated health status were the top-ranked predictors, followed by medical expenses and inpatient service utilization. These findings suggest that latent depression types among rural older adults were associated with health burden, medical economic burden, and health-related behaviors.
Fig. 6.
Ranking of predictor importance in the random forest model. Predictor importance was quantified using the Mean Decrease in Impurity (MDI) from the final random forest model with 300 trees and mtry set to 5. Higher MDI values indicate a greater contribution of the predictor to the classification of latent depression types
Key factor selection based on LASSO regression models
To further further screen the stable key factors associated with latent depression type membership, the Least Absolute Shrinkage and Selection Operator (LASSO) regression model was applied. A multinomial logistic regression framework with an L1 penalty was used to mitigate multicollinearity and enhance model parsimony. As shown in Fig. 7, the coefficients of candidate variables gradually shrank to zero with the increase of the penalty parameter, reflecting the variable selection process of the LASSO model. The optimal penalty parameter λ was determined via 10-fold cross-validation, taking the minimum cross-validated log-loss as the selection criterion. As shown in Fig. 8; Table 9, the optimal value was λ = 10.000, corresponding to Log(λ) = 2.303. At this value, seven variables maintained non-zero coefficients, while the coefficients of other candidate variables were shrunk to zero.
Fig. 7.
Coefficient profiles of variables in the LASSO model
Fig. 8.
Ten-fold cross-validation for selecting the optimal λ in the LASSO model
Table 9.
Summary of LASSO variable selection
| Indicator | Result |
|---|---|
| Model type | Multinomial LASSO logistic regression |
| Cross-validation | 10-fold cross-validation |
| Selection criterion | Minimum cross-validated log-loss |
| Optimal λ | 10.000 |
| Log(λ) | 2.303 |
| Number of retained variables | 7 |
| Retained variables | Chronic disease; physical discomfort; self-rated health; medical expenses; inpatient service utilization; smoking; daily exercise |
The retained variables were chronic disease, physical discomfort, self-rated health status, medical expenses, inpatient service utilization, smoking, and daily physical exercise. The standardized coefficients of these variables at the optimal λ are presented in Table 10. These variables were categorized into three domains: health status, medical burden and service utilization, as well as health behaviors. Specifically, chronic disease, physical discomfort, medical expenses, and inpatient service utilization retained positive non-zero coefficients in the high latent depression risk group, suggesting that disease burden, physical symptoms, and medical economic burden were strongly associated with severe latent depression profiles. Physical discomfort also presented positive coefficients in the mild depression and emotionally impaired groups, indicating its universal association with depression risk across different severity levels. In contrast, self-rated health status and daily physical exercise yielded negative coefficients in the low and/or mild depression groups, suggesting that better subjective health perception and regular physical activity may be associated with lower depression severity. Smoking retained non-zero coefficients in partial latent depression groups, indicating that health behavior factors may also played a role in the differentiation of depression subtype. In summary, the LASSO model effectively reduced the number of candidate predictors while reserving the variables most closely related to latent depression type membership. The selected variables were consistent with the major factors identified by the random forest model, which further verified the robustness of the factor selection results.
Table 10.
LASSO regression results for depression latent category variable selection at optimal λ
| Variables | Low depression type | Mild depression type | Emotionally impaired type | High depression risk type |
|---|---|---|---|---|
| Chronic disease | 0.000 | 0.000 | 0.214 | 0.386 |
| Physical discomfort | 0.000 | 0.173 | 0.298 | 0.512 |
| Self-rated health | -0.241 | 0.000 | 0.000 | 0.329 |
| Medical expenses | 0.000 | 0.000 | 0.187 | 0.274 |
| Inpatient Services Utilization | 0.000 | 0.000 | 0.000 | 0.196 |
| Smoking | 0.000 | 0.118 | 0.000 | 0.164 |
| Daily exercise | -0.203 | -0.121 | 0.000 | 0.000 |
Values represent standardized coefficients from the multinomial LASSO logistic regression model at the optimal λ. A value of 0.000 indicates that the coefficient was shrunk to zero by the LASSO penalty. Positive coefficients indicate that higher levels of the corresponding variable were associated with a greater probability of membership in the corresponding latent depression type, whereas negative coefficients indicate a lower probability of membership. The optimal λ was selected using 10-fold cross-validation based on the minimum cross-validated log-loss
Multinomial logistic regression analysis of factors associated with latent depression type membership
To further examine the associations between key influencing factors and latent depression type membership, a multinomial logistic regression model was constructed with the low depression type set as the reference group, See Table 11 for the results. The regression results showed that chronic disease, physical discomfort, poor self-rated health, high medical expenses, inpatient service utilization, and smoking were significantly positively associated with the likelihood of belonging to high risk latent depression types. By contrast, daily regular physical exercise was significantly associated with a reduced likelihood of being categorized into the high depression risk type membership. These findings suggest that health status, medical burden, healthcare service utilization, and health-related behaviors are critical influencing factors associated with latent depression type membership.
Table 11.
Multinomial logistic regression results for factors associated with latent depression type membership
| Variables | Mild depression type OR (95% CI) | Emotionally impaired type OR (95% CI) | High depression risk type OR (95% CI) |
|---|---|---|---|
| Chronic disease | 1.18 (1.01, 1.39)* | 1.34 (1.12, 1.60)** | 1.62 (1.31, 2.01)*** |
| Physical discomfort | 1.25 (1.06, 1.48)* | 1.57 (1.30, 1.89)*** | 2.08 (1.66, 2.61)*** |
| Self-rated health | 1.31 (1.09, 1.58)** | 1.68 (1.36, 2.08)*** | 2.24 (1.75, 2.87)*** |
| Medical expenses | 1.21 (1.02, 1.44)* | 1.43 (1.17, 1.75)** | 1.76 (1.38, 2.25)*** |
| Inpatient Services Utilization | 1.39 (1.10, 1.76)** | 1.58 (1.22, 2.05)** | 1.91 (1.42, 2.56)*** |
| Smoking | 1.16 (0.98, 1.38) | 1.31 (1.08, 1.59)** | 1.55 (1.23, 1.95)*** |
| Daily exercise | 0.86 (0.73, 1.01) | 0.74 (0.61, 0.90)** | 0.62 (0.49, 0.78)*** |
OR odds ratio, CI confidence interval
* P < 0.05, ** P < 0.01, *** P < 0.001
Network analysis of key influencing factors for latent types of depression in rural elderly
Network structure diagram
To further clarify the interrelationships among key factors affecting different latent categories of depression, a network analysis model was developed based on the seven core variables screened by LASSO regression. Edge weights reflect partial correlations after controlling for other variables, while edge thickness indicates association strength. The network structure results are shown in Fig. 9. The estimated network was constructed based on an EBICglasso-regularized Gaussian Graphical Model and represents conditional associations among the seven key factors after controlling for all other variables. In Fig. 9, edge thickness represents the magnitude of partial correlation between nodes after controlling for other variables. For better result interpretability, major numerical edge weights are elaborated below. The strongest positive edges were observed between medical expenses and inpatient inpatient utilization (edge weight = 0.460), physical discomfort and self-rated health status (edge weight = 0.420), chronic disease and physical discomfort (edge weight = 0.350), and chronic disease and medical expenses (edge weight = 0.310). Significant negative correlations existed between daily exercise and self-rated health (edge weight = − 0.280) and between daily exercise and chronic disease (edge weight = − 0.180). These results indicate that healthcare expenditure and inpatient service utilization were closely connected, while physical discomfort and subjective health perception also formed a central association within the network. The full edge-weight matrix is summarized in Supplementary Table S2. The overall network exhibits a moderately dense structure, in which health status variables are closely interconnected with healthcare service utilization. Notably, the association between physical discomfort and self-rated health status is most significant, manifested as a strong positive edge weight. This suggests that higher levels of physical discomfort correlate with poorer subjective health evaluation. Additionally, medical expenses exhibit a strong positive correlation with inpatient service utilization, reflecting an intrinsic linkage between hospitalization behavior and economic healthcare burdens. Chronic diseases showed positive associations with both physical discomfort and medical expenses, suggesting that chronic disease burden may affect depression risk via its associations with physical symptoms and healthcare expenditure. Conversely, daily exercise exhibits negative correlations with both chronic diseases and self-rated health status, suggesting that regular physical activity is conducive to better health status and reduced health risks. Smoking status shows a weak-to-moderate positive correlation with physical discomfort, which implies that unhealthy lifestyles may aggravate physical symptom burden. Overall, the network structure takes “perceived physical health—disease burden” as its core, with lifestyle factors serving as peripheral regulatory nodes. Thus, these findings indicate that physical discomfort and self-rated health stautus serve as core nodes within the depression-related factor network, while chronic diseases and medical expenses act as crucial bridges connecting health status to healthcare utilization. This result reveals the complex systematic interactions between health status, lifestyle, and healthcare utilization factors, providing empirical evidence for clarifying the association patterns of latent depression types.
Fig. 9.
Overall network structure
Notably, network analysis revealed that physical discomfort and self-rated health status occupy central positions within the network simultaneously. While these two indicators present empirical correlation in measurement, this finding retains solid theoretical and methodological validity. They reflect hierarchical and distinct health connotations: physical discomfort corresponds to direct somatic symptom perception and functional impairment [30, 31], while self-rated health embodies an individual’s comprehensive cognitive evaluation of overall health status, integrating past health experiences, current functional conditions, and future health expectations [32, 33]. Their co-occurrence as core position in the network suggests that depression risk among rural older adultsis driven not merely by objective disease burden but also involves the dual-path interaction of “physical experience–health cognition”. Physical discomfort may be associated with negative emotional perceptions, while self-rated health may reflect the cumulative effect of multiple health-related risks through psychological mechanisms such as perceived control, aging cognition, and health self-efficacy. These results highlight that targeted prevention and intervention for populations at latent depression risk should focus not only on chronic diseases and medical burdens but also mitigating physical discomfort experiences and reconstructing health cognition. Such a systematic intervention strategy targets the critical hubs within the risk network to weaken its impact.
Centrality metrics diagram
The centrality metrics analysis results are shown in Fig. 10, with specific numerical values listed in Table 12. The results indicate that physical discomfort and self-rated health exhibit the highest strength centrality values, implying the most extensive direct connections with other network variables and confirming their roles as core nodes. Among them, self-rated health also exhibits high closeness centrality, placing it in a pivotal structural location and enabling rapid spillover effects on other network factors. Chronic diseases and medical expenses demonstrate relatively high betweenness centrality, indicating their function as critical bridging nodes that link health status to healthcare service utilization pathways. In contrast, smoking and daily exercise exhibit lower centrality levels and are located at the peripheral layer of the network structure.
Fig. 10.
Centrality metrics plot
Table 12.
Centrality indices of nodes in the depression-related network
| Variables | Strength | Closeness | Betweenness |
|---|---|---|---|
| Physical discomfort | 1.214 | 0.182 | 0.318 |
| Self-rated health | 1.167 | 0.201 | 0.274 |
| Chronic disease | 0.842 | 0.154 | 0.402 |
| Medical expenses | 0.793 | 0.148 | 0.356 |
| Inpatient utilization | 0.621 | 0.139 | 0.227 |
| Daily exercise | 0.588 | 0.146 | 0.118 |
| Smoking status | 0.412 | 0.131 | 0.064 |
Strength denotes the sum of connection weights between a node and other nodes; Closeness indicates the overall proximity of a node within the network; Betweenness reflects the frequency with which a node serves as an intermediary node in the network
Edge weight bootstrap accuracy
A nonparametric Bootstrap method with 1000 repeated samples was adopted to assess the accuracy of edge weight estimates, with results presented in Fig. 11; Table 12. Overall, the 95% confidence intervals for primary edge weights are relatively concentrated and do not cross zero, indicating the statistical stability and reliability of core network associations. Among these, the edge connections between physical discomfort to self-rated health, as well as between medical expenses to inpatient service utilization, exhibited the highest estimation stability. Robustness examination of centrality metrics via sample reduction bootstrap further verified that the correlation coefficient between strength centrality and the original sample consistently exceeded the recommended threshold (r = 0.70), even under high sample retention ratios. This indicates strong robustness in both the network structure and centrality results.
Fig. 11.
Bootstrap edge weight accuracy plot
Table 13.
Bootstrap edge-weight accuracy Results
| Edge | Sample Edge Weight | Bootstrap Mean | 95% CI | |
|---|---|---|---|---|
| Physical discomfort – Self-rated health | 0.420 | 0.413 | 0.281 | 0.552 |
| Medical expenses – Inpatient utilization | 0.460 | 0.451 | 0.319 | 0.587 |
| Chronic disease – Physical discomfort | 0.350 | 0.342 | 0.198 | 0.497 |
| Chronic disease – Medical expenses | 0.310 | 0.304 | 0.167 | 0.462 |
| Smoking – Physical discomfort | 0.220 | 0.215 | 0.083 | 0.356 |
| Daily exercise – Self-rated health | −0.280 | −0.271 | −0.421 | −0.118 |
| Daily exercise – Chronic disease | −0.180 | −0.173 | −0.331 | −0.041 |
Edge weights were estimated using a nonparametric bootstrap procedure (1,000 resamples). The 95% confidence intervals (CI) indicate acceptable accuracy for most edges, with no CI crossing zero for the strongest associations
Centrality stability test
Figure 12 presents the centrality stability plot (Case-dropping bootstrap). The Strength centrality curve maintains high stabilityacross progressive sample exclusion (retention rate: 30%–90%), with the average correlation coefficient consistently above 0.7. The results indicate that the network structure and node importance are independent of individual samples, demonstrating robust model stability.
Fig. 12.
Central stability diagram
Consistency with random forest and LASSO results
Different from traditional regression models that assume a single causal pathway, network analysis estimates conditional correlations across variables and simultaneously reveals both direct and indirect relationships among multiple influencing factors. This provides more comprehensive structural evidence for empirical findings. In this study, Random Forest results ranked self-rated health status, physical discomfort, chronic diseases, and medical expenses as the most influential variables. Likewise, the LASSO regression retained the same seven variables at the optimal λ threshold, while network analysis also identified physical discomfort, self-rated health, and chronic diseases as core nodes. The high consistency of key factor screening among the three methodssignificantly enhances the credibility of the findings, demonstrating good agreement among different statistical and machine learning approaches in pinpointing critical influencing factors. Furthermore, Bootstrap edge weight accuracy tests revealed that the confidence intervals for major associated edges were relatively concentrated and did not cross zero, indicating good accuracy in network structure estimation. Centrality stability analysis further demonstrated that the centrality ranking of key nodes remained stable after partial sample exclusion, indicating that network results are resilient to sample fluctuations. Thus, network analysis provides an independent validation pathway for research findings from the perspectives of variable interaction and system structure, effectively strengthening the methodological robustness and empirical credibility of the study conclusions.
Discussion
Heterogeneity of depressive symptoms: rural elderly are not a “Homogeneous Depressed Group”
Based on CFPS data, this study employed Latent Class Analysis (LCA) to identify four latent types of depression among Chinese rural elderly at the CES-D symptom item level: low depression type, mild depression type, emotionally impaired type, and high depression risk type. The findings indicate that depression among rural elderly does not follow a simple, continuous distribution of severity but presents symptomatic heterogeneity. This reveals fundamental differences in symptom patterns and psychological experience structures among these groups. This finding aligns with existing research that advocates the perspective of depressive “symptom spectra” and “subtyping” [34–36], and remedies limitations of previous studies, primarily grouping participants based on total depression scores. Compared with previous latent class studies on depression in older adults, the typology identified in the present study shows both consistency and contextual specificity. Veltman et al. identified three depressive subtypes among older adults with major depressive disorder, including a moderately severe class, a severe melancholic class, and a severe atypical class, with appetite and weight-related symptoms serving as important distinguishing indicators [15]. Pérez-Belmonte et al. also showed that depressive symptom profiles in older adults are heterogeneous rather than uniform, and that the number and characteristics of subtypes may vary across populations and research settings [16]. Consistent with these studies, our findings support the view that late-life depression cannot be fully captured by a single total score or threshold-based classification standard. However, differing from studies conducted in clinical or Western elderly populations, the four latent depression types identified among Chinese rural older adults were primarily characterized by graded symptom severity, as well as prominent loneliness, impaired emotional experience, physical discomfort, and poor self-perceived health status. This difference may reflect the specific social and health context of rural China, where out-migration of adult children, widowhood, limited access to mental health services, chronic disease burden, and medical expense pressure collectively shape depressive symptom expression. Therefore, the low depression type, mild depression type, emotionally impaired type, and high depression risk type identified in this study represent not only different symptom profiles but also context-specific manifestations of depression among rural older adults in China.
From a symptomatic perspective, the typological differences uggest that distinct latent depression types may vary in core distress dimensions, intervention priorities, and risk evolution pathways, which carry significant theoretical and practical implications. Among rural elderly populations, “depression” manifests not only as continuous gradient from low to high severity but also as differentiated structural patterns of depressive symptoms. Such heterogeneity may be related to the interplay of long-term social structural factors and individual life trajectories. In the rural Chinese context, older adults often experience role degradation, decreased labor capacity, and reduced social participation [37, 38], though these changes occur asynchronously across individuals. Some individuals maintain low depression levels despite physical functional decline and reduced social engagement, corresponding to the low depression type. Others, without the highest level of overall depressive symptoms, display concentrated impairment in loneliness, diminished positive affect, and emotional experience, forming the emotionally impaired type. The formation of the emotionally impaired type may be further interpreted based on socioemotional selectivity theory and psychological mechanisms associated with loneliness. According to socioemotional selectivity theory, older adults tend to place greater emphasis on emotionally meaningful relationships as they perceive a limited remaining lifespan. Therefore, the weakening or breakdown of close emotional bonds exerts a particularly pronouncedimpact on their psychological well-being. In rural China, this mechanism may be amplified by social and family structural changes, including the out-migration of adult children, widowhood, shrinking neighborhood networks, and reduced daily social interaction opportunities. Under such circumstances, certain older adults may not present the severe somatic or global depressive symptoms, yet suffer prominent emotional distress characterized by loneliness, reduced positive affect, and impaired emotional experience. This explains why the emotionally impaired type emerged as a distinct latent subtype rather than simply an intermediate category of symptom severity.This suggests that rural elderly depression is not solely determined by the “number of symptoms,” but is dominated by core psychological distress dimensions. The high depression risk type may reflect a pattern of multiple risk accumulation, in which physical illness, functional limitations, economic pressure, and negative health perceptions are highly clustered within the same population, and was associated with higher levels of depressive symptoms across multiple dimensions. This subgroup represents the most vulnerable population of rural older adultsof, whose mental health issues tend to be persistent and cumulative. This indicates that individuals with identical “total scores” may differ in their core distress characteristics. Therefore, targeted identification and individualized intervention strategies are required, rather than uniform intervention schemes formulated solely based on total score thresholds.
Baseline characteristic differences: health burden and healthcare accessibility characteristics underpin latent category differentiation
Univariate analyses y revealed significant differences across multiple sociodemographic characteristics, health conditions, health behaviors, and healthcare-related factors among different latent depression types. Overall, health burden and healthcare-related variables played a prominent role in latent category differentiation. Chronic diseases, physical discomfort, self-rated health status, hospitalization service utilization, and medical expenses were disproportionately concentrated in the high depression risk and emotional impairment categories, indicating a high co-occurrence of physical health problems and depressive symptoms among rural elderly populations. This finding aligns with existing research on the “co-morbidity of late-lifedepression and physical illness” [39–41], while bearing stronger practical significance in the rural settings. First, in rural areas, chronic diseases are often accompanied by persistent physicalpain, activity limitations, and impaired daily functioning. These conditions may be associated with reduced self-efficacy and independence. Second, limited access to healthcare services may trigger uncertainty and helplessness in chronic disease management, thereby exacerbating negative emotional experiences. Finally, self-rated health reflects not only objective health status but also individuals’ comprehensive evaluations of aging trajectories, social value, and future life prospects, rendering it highly sensitive in distinguishing latent depression types. From this perspective, the central positions of physical discomfort and self-rated health in both random forest and network analyses are not incidental. Instead, their prominence arises from inherent psychological linkages with multiple pathogenic pathways of depression, including physical functional decline, social role loss, and future life uncertainty.
This study further reveals that the burden of medical expenses and inpatient services utilization are significantly concentrated in the high-depression-risk group, exhibiting high mediating centrality in network analysis. This finding highlights the amplifying effect of economic pressure on depressive symptoms among rural older adults. In rural families, older adults often rely on their children or limited social security benefits for livelihood. Increased medical expenses may also induce feelings of guilt and self-blame, such as perceived over-reliance on children and excessive family burden. This emotional experience was more prominent in the high depression risk group and was associated with aggravated depressive symptoms. Inpatient service utilization itself does not directly cause depression. However, within the unique socioeconomic context of rural China, hospitalization may be associated with elevated depression risk. This explains why inpatient service utilization functions as a critical bridging node in the network, connecting health status, economic burden, and psychological outcomes.
Advantages and consistent evidence of machine learning methods in identifying key factors
The machine learning models in this study should be interpreted primarily as tools for robust variable screening rather than high-precision predictive models. The random forest model demonstrated moderate classification performance, suggesting that the included health, behavioral, medical, and sociodemographic variables could partially distinguish latent depression types but remained insufficient to achieve high predictive accuracy. This finding is theoretically reasonable because latent depression categories are defined by symptom response patterns and may also be influenced by unmeasured psychological, social, and contextual factors. Accordingly, observable variables alone cannot fully classify individuals into distinct latent categories using observable variables alone.
Nevertheless, the application of random forest and LASSO provideddistinct methodological advantages over conventional regression modeling. First, random forest can capture potential nonlinear relationships and interaction effects among multidimensional predictors, which are often undetectable in traditional regression models. Second, LASSO regression performs variable shrinkage and selection under multicollinearity, thereby improving model estimation stability. Third, the consistency between random forest importance ranking, LASSO-selected variables, and subsequent multivariable logistic regression results, further validates the robustness of the identified key influencing factors.The multinomial logistic regression results should be interpreted as associations with specific latent depression types membership relative to the low depression type. This approach is more consistent with the LCA framework, given that the identified classes represent heterogeneous symptom profiles rather than strictly ordered severity levels. This approach is consistent with the graded severity pattern observed across the four latent classes. Therefore, machine learning methods were used as complementary analytical tools for identifying key influencing factors and uncovering complex data structures, while logistic regression provides interpretable effect estimates for statistical inference.
Network analysis reveals structural association patterns among key factors
To further elucidate the structure association among key influencing factors, this study employed network analysis to characterize the topological relationships among the seven key variables, supplemented by Bootstrap stability testing. The results indicate that physical discomfort and self-rated health occupy the most central positions in the network, with the highest strength and proximity centrality, suggesting their pivotal role in the overall risk structure. Concurrently, chronic diseases and medical expenses demonstrate relatively high mediating centrality, implying their bridging function in linking health status and healthcare utilization/economic burden. This network architecture offers a novel perspective for understanding the association mechanisms related to latent depression subtypes: depressive symptoms in high-risk and emotionally impaired individuals may not be driven by a single factor alone, but rather by a multi-node interconnected risk pathway characterized by “physical discomfort → diminished health perception → chronic disease comorbidity → increased medical burden”. Bootstrap edge weight accuracy tests and centrality stability analyses confirmed that the network estimates have high accuracy and acceptable stability, further validating the reliability of structural interpretation. These findings not only provide empirical evidence for understanding high-risk depression subtypes but also identify key intervention targets for developing effective strategies.
Policy recommendations
Based on the above analyses, this study proposes the following policy recommendations. (1) Advance depression screening from “total score-based identification” to “type-specific stratified management”. Primary care and public health services can develop differentiated strategies according to four potential types: For the low depression type, routine follow-up and health promotion should be emphasized. For the mild depression type, mental health education and behavioral interventions should be strengthened. For the emotionally impaired type, emotional experiences and psychosocial support should be prioritized. For the high depression risk type, standardized referral pathways and priority follow-up should be established.(2) Take “physical discomfort–self-rated health” as a practical intervention entry point in rural primary care. Network analysis indicated that physical discomfort and self-rated health are core nodes in the risk network, suggesting that improving physical symptom experiences and health perception may serve as a feasible direction for mental health promotion in rural primary care settings. In rural China, these interventions can be implemented through village health stations and township health centers. First, village doctors should be trained to recognize common emotional problems among older adults during routine chronic disease follow-up, particularly loneliness, persistent low mood, sleep disturbances, and reduced interest in daily activities. Second, brief psychological screening tools can be incorporated into regular health management services for hypertension, diabetes, and other chronic diseases. Third, village health stations can provide low-intensity psychosocial interventions, such as health education, emotional support counseling, sleep and pain management guidance, relaxation training, and referral guidance for high-risk individuals. Fourth, township health centers can establish clear referral pathways for older adults with severe depressive symptoms or suicidal ideation. These measures would enhance the accessibility and feasibility of psychological supportwithin the existing rural primary healthcare system. (3) Alleviate medical burdens and optimize healthcare utilization pathways. The bridging role of chronic diseases and medical expenses suggests that economic burdens may be associated with elevated depression risk. Further measures include expanding outpatient medical insurance coverage for chronic diseases among rural older adults, improving the capacity of primary care institutions in initial diagnosis and continuous care, and optimizing medical insurance reimbursement structures and assistance mechanisms to alleviate psychological stress caused by high medical costs. (4) Enhance the accessibility of health behavior interventions. Health behavioral factors such as smoking, alcohol consumption, and daily exercise are correlated with latent depression subtypes. Low-cost, sustainable intervention measures—such as personalized exercise prescriptions, smoking cessation and alcohol reduction reduction programs, and healthy lifestyle promotion campaigns—should be widely implemented in rural communities to boost behavioral change and synergistically improve mental health. (5) Address regional disparities and optimizetargeted resource allocation. Provincial differences in residential regions suggest that socioeconomic development and healthcare resource difference distribution may influence depression risk. Mental health service capacity building and resource allocation should be tailored to regional characteristics.
Conclusion
Based on the CFPS rural elderly sample, this study adopted latent class analysis using CES-D item data to identify four latentdepressive symptoms types: low depression type, mild depression type, emotionally impaired type, and high depression risk type. Significant intergroup differences were observed in baseline characteristics across the four types. Health status, medical burden and healthcare utilization, health behaviors, and sociodemographic attributes were closely associated with differentiation of latent depression types. Random forest and LASSO methods were applied to screen core influencing factors, and multinomial logistic regression was further employed to examine their associative relationships with latent subtype membership. Network analysis revealed physical discomfort and self-rated health as core nodes, while chronic diseases and medical expenses functioned as critical bridging nodes within the network structure. Bootstrap tests confirmed high accuracy and stability of the network estimation results. Overall, this study constructed a comprehensive evidence chain for depression research among rural older adults in China, following a logical analytical sequence of “type identification—differential comparison—key factor screening—effect estimation—structural association exploration.” The findings provide empirical support for precise identification, stratified management, and comprehensive intervention strategies for depression among rural older adult populations.
Limitations
This study has several limitations. First, the cross-sectional design precludes rigorous causal inference. Although associations were detected between latent depression types and key influencing factors, the temporal sequence between depression patterns and related variables could not be determined. Future studies should use longitudinal data to examine the dynamic transitions of depression subtypes and their underlying determinants. Therefore, all identified relationships should be interpreted as associations rather than causal pathways or mechanistic effects. Second, depressive symptoms was measured using the CES-D scale, a widely adopted screening tool rather than a clinical diagnostic instrument. Therefore, the identified latent depression types reflect symptom patterns rather than clinically diagnosed depressive disorders. In addition, self-reported responses may introduce recall bias and reporting bias. Third, latent class analysis inevitably involves classification uncertainty.Although the four-class model exhibited satisfactory classification quality with high entropy and average posterior probability, participants were assigned to latent classes based on the maximum a posteriori probability rule. Neither BCH or R3STEP correction methods were not applied in the subsequent analyses. This may induce slight attenuation or bias in the estimated associations between influencing factors and latent depression types. Given the downstream analytical workflow integratingrandom forest, LASSO regression, multinomial logistic regression, and network analysis, a unified three-step correction procedure was difficult to implement across all models. Therefore, the findings should be interpreted as associations with the most probable latent class membership, rather than estimates adjusted for classification error. Future studies should apply BCH, R3STEP, or other classification-error correction approaches to verify the robustness of these associations. Fourth, the selection of analytical variables was constrained. The formation of latent depression types may also be shaped by unmeasured factors, such as major life events, functional limitations, community resources availability, social participation, and psychological resilience. Residual confounding may thus remain. Future research could enrich the analytical framework by incorporating multi-source observational data. Fifth, the employed machine learning models are better regarded as robust variable screening tools rather than high-precision predictive models. The random forest model yielded moderate and limited predictive performance, indicating that the included variables could only partially distinguish latent depression types. Future studies should incorporate more comprehensive psychological, social, environmental, and longitudinal indicators to improve predictive validity and external generalizability. Sixth, several methodological limitations regarding network analysis should be noted. Measures of physical discomfort and self-rated health may contain conceptual overlap, which could inflate their pairwise edge weight. Although the partial correlation network framework and bootstrap tests indicated acceptable robustness, future research should adopt more refined health measurement tools and redundancy testing strategies to better distinguish somatic symptom experience from subjective health evaluation. In addition, an EBICglasso-regularized Gaussian Graphical Model was used to estimate the network structure, and several binary or ordinal variables were treated as numeric indicators. Therefore, the derived edge weights should be interpreted as conditional associations rather than definite causal relationships or strictly distribution-specific parameters. Mixed graphical models or Ising models may be adopted in future studies to verify network structure robustness for mixed-type variables. Seventh, model selection in latent class analysis relied on comprehensive theoretical and statistical judgment. Although LMRT and BLRT p values were calculated using Mplus 8.3, the five-class model also showed significant likelihood-ratio test results and the lowest AIC. The four-class model was retained because it demonstrated the lowest BIC and aBIC, higher entropy and AvePP, more balanced class distribution, and clearer substantive interpretability. Independent samples or longitudinal data are suggested for future studies to further verify the stability and generalizability of the four-class solution. Finally, the generalizability of the findings is limited. The sample was restricted to rural registered older adults in China. Therefore, the results are more applicable to rural settings, Further investigation is needed to explore urban–rural disparities and cross-regional heterogeneity in depressive symptom subtypes and associated influencing factors.
Directions for further research
Future research can deepen the relevant studies through the following approaches: (1) Adopt longitudinal tracking data to implement latent transition analysis (LTA) or growth mixture models, exploring the dynamic transitions of depression subtypes among older adults and their predictive factors. (2) Incorporate richer mechanistic variables (e.g., functional limitations, major life events) to construct more comprehensive theoretical frameworks and examine the mediating and moderating effects of key influencing factors. (3) Conduct multi-group latent category comparisons across urban-rural or regional contexts to evaluate the typological consistency of depression subtypes and contextual differences in their influencing factors. (4) Enhance methodological integration: extend network analysis to explore the synergistic relationships between symptom-level and factor-level networks, or incorporate machine learning interpretability methods (e.g., SHAP) to enhance model transparency.
Supplementary Information
Acknowledgements
We would like to express our gratitude to the editors and reviewers for their hard work. Thank you.
Authors’ contributions
Bo Dong collected, cleaned and prepared the data. Bo Dong and Li Wang analyzed and interpreted the data. Bo Dong and Yifan Li drafted the manuscript and made subsequent revisions. Bo Dong read and approvedthe final manuscript.All authors read and approved the final manuscript.
Funding
The author(s) declare that no financial support was received for the research and/or publication of this article.
Data availability
Publicly available datasets were analyzed in this study. This data can be found here: http:/ /www.isss.pku.edu.cn/cfps/.
Declarations
Ethics approval and consent to participate
The data utilized in this study were obtained from the publicly available CFPS, administered by the Institute of Social Science Survey (ISSS) at Peking University. The CFPS project received ethical approval from the Biomedical Ethics Committee of Peking University (approval number: IRB00001052-14010), and written informed consent was obtained from all participants prior to their participation in the original survey. The present study was based on anonymized secondary data that are publicly available and did not involve direct interaction with human participants. Therefore, additional ethical approval and informed consent were not required. This study was conducted in accordance with the principles of the Declaration of Helsinki.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Bo Dong and Li Wang contributed equally to this work and should be considered co-first authors.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
Publicly available datasets were analyzed in this study. This data can be found here: http:/ /www.isss.pku.edu.cn/cfps/.