Bayesian semi-parametric inference for joint modelling of childhood growth and appetite phenotypes

Abstract

Purpose

Early eating behaviours have been associated with later weight outcomes, yet their longitudinal development and relationship with growth trajectories remain insufficiently understood. This study aims to investigate how appetite-related behaviours in early childhood co-evolve with growth patterns and contribute to obesity risk.

Methods

We develop a Bayesian semi-parametric joint modelling framework to analyse repeated measures of growth indicators, such as body mass index, alongside questionnaire-based eating behaviour scores collected at multiple time points in children from the Singaporean GUSTO cohort (“Growing Up in Singapore Towards Healthy Outcomes”). The approach extends established models for ordinal questionnaire data to accommodate longitudinal observations and covariate effects, while growth trajectories are flexibly represented using spline-based regressions. Subject-specific demographic and clinical covariates are incorporated into both components of the model, allowing their effects on growth and eating behaviour to be assessed simultaneously. The two components are linked through a Bayesian nonparametric prior, specifically a Normalised Generalised Gamma Process, that enables data-driven identification of subgroups of children with similar developmental profiles.

Results

The proposed framework captures the dynamic interplay between appetite phenotypes and growth trajectories over time, allowing the identification of clinically meaningful clusters characterised by distinct behavioural and growth patterns.

Conclusion

The proposed integrated modelling strategy provides a nuanced understanding of how eating behaviours and growth co-develop in early life, offering new insights into mechanisms underlying childhood obesity risk and supporting the design of targeted early interventions.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12874-026-02950-w.

Introduction

The study of growth patterns in children commonly involves monitoring biomarkers such as body mass index (BMI) over time. In recent years, however, increasing attention has been directed toward early-life phenotypic characteristics, particularly eating behaviours. Eating behaviours established during the first years of life are of critical importance, as they lay the foundation for future dietary habits and health trajectories [1]. Early childhood eating behaviours have been associated with concurrent weight status [2] and with later risk of overweight, obesity, and related metabolic comorbidities [3]. Most existing evidence on early childhood eating behaviours arises from cross-sectional studies or prospective designs that rely on single time-point measures, typically using validated questionnaires [4]. Consequently, relatively little is known about how eating behaviour patterns evolve during the first years of life or how they co-develop with growth trajectories. Evidence on the stability of specific eating behaviours across early childhood is also mixed and likely behaviour-dependent [5]. For instance, picky eating appears to be transient, peaking around three years of age and gradually declining by about six years [6, 7]. Many previous studies have examined only a limited number of time points, constraining their ability to capture the dynamic nature of eating behaviour development. Recent work from the ALSPAC cohort, which assessed eating behaviours at multiple time points between 15 months and 10 years of age, has identified distinct developmental trajectories for over-eating, under-eating, and fussy eating. These trajectories were differentially associated with child weight at age 11 years, suggesting varying stability across behaviours and emphasizing their predictive value for later weight outcomes [6]. Nonetheless, earlier research has often been restricted by sparse longitudinal data and reliance on mean scores at discrete ages rather than on the continuous modelling of developmental trajectories, an approach that requires denser time-series data and larger samples.

Advances in the analysis of longitudinal questionnaire data now enable more detailed investigation of behavioural changes over time. The Child Eating Behaviour Questionnaire (CEBQ; [8]) remains one of the most widely used and well-validated instruments for assessing a broad range of eating behaviours from early infancy onward. The analysis of questionnaire data is usually carried out by first summing the answers to individual questions into summary scores, often by grouping the questions into sub-categories of relevance, and then modelling these scores directly as continuous observations (possibly after square root transformation to improve normality [9]). While this approach facilitates the implementation, it involves a loss of information due to the aggregation of the questionnaire answers, as well as the assumption made on the support of the data. Alternatively, widely used approaches that do not rely on summary scores are those from Item Response Theory (IRT). IRT is a class of statistical methods belonging to the wider class of latent trait models and employed for modelling questionnaire data, with the aim of capturing a specific construct of interest in the survey process. The questions within a questionnaire are commonly referred to as items, and can be answered by the respondents with values on a likert scale, i.e. an ordinal scale in which the differences in magnitude between two values are not explicitly known. For instance, the scale is often associated to the values , but the differences between consecutive categories do not necessarily represent the same increments in the underlying construct (e.g., depressive symptoms, anxiety traits, appetite phenotypes). In IRT models, the probability of answering within each of the possible categories is modelled via a link function parameterised by question- and subject-specific parameters, thus capturing both the characteristics of the questions (difficulties) as well as the aptitude of the respondent (traits). Two main classes of IRT models are widely used in the literature, based on the way the probabilities of answering within each available category are modelled. A widely used approach models such probabilities via a logistic function, while a second one models the cumulative probabilities first and then defines the likelihood by taking the differences between two adjacent categories. An example of the first one is the Generalised Partial Credit model (GPCM) [10, 11], which is used in this work, while the second class includes the Graded Response model (GRM) by [12]. The GPCM is an extension of the Partial Credit Model that introduces item-specific discrimination parameters.

In this work, we opt for the Generalised Partial Credit Model, as item-specific discrimination parameters lead to additional flexibility allowing for different questionnaire items to contribute unequally to the measurement of the underlying latent trait. This reflects the fact that some items are more informative than others in distinguishing between subjects with different appetite profiles. Compared with cumulative-link formulations such as the Graded Response Model, the GPCM directly models the probability of each response category and provides an intuitive interpretation of category transitions through item-specific threshold parameters. These features make the GPCM particularly suitable for the analysis of the CEBQ questionnaire and its extension to the longitudinal and covariate-adjusted framework considered in this study.

In many clinical and research settings, including the one analysed in this work, questionnaires are administered repeatedly across visits, introducing a longitudinal dimension to the data. In such cases, modelling individual item responses, rather than relying on aggregated summary scores, is generally preferred, as it prevents information loss and allows a more nuanced representation of the underlying constructs [13]. This approach is particularly relevant to the present study, as it enables the investigation of appetite phenotype evolution through the estimation of trajectories of latent traits over time. Extending standard IRT models to longitudinal settings requires specifying an appropriate distribution for the latent traits and estimating common item-specific parameters across measurement occasions [see, among others, 14, 15, 16, 17, 18]. Temporal dynamics within IRT frameworks can be modelled in several ways. For instance, Fischer [19] and Spiel and Gluck [20] incorporate time-specific constant effects in the latent trait formulation—a strategy also implemented in the R package eRm [21]. A more flexible Bayesian extension was proposed by Verhagen and Fox [22], who adopted a latent growth model with identifiability constraints. Similarly, Cremaschi et al. [23] modelled the temporal evolution of latent traits using an autoregressive (AR(1)) process, again enforcing appropriate constraints to ensure identifiability. Typically, repeated questionnaires consist of the same items across time points, allowing item-specific parameters to be shared over time. However, this assumption can be relaxed when only a subset of items remains consistent throughout the observation window, as illustrated by Cremaschi et al. [23].

In this work, we develop a joint modelling approach for longitudinal (BMI trajectories) and questionnaire (CEBQ) data, with the aim of investigating their interdependence and the relationship with child development. We focus on BMI because it is a widely used clinical indicator of growth and adiposity, derived from routinely collected height and weight measurements, making it readily measurable and consistently available across follow-up visits. In particular, we model the longitudinal outcomes via a flexible B-splines regression, while the answers to questionnaires at different time points are modelled using an extension of the Partial Credit model in Eq. (1) by [10] to allow for answers recorded at different time points and inclusion of covariates. The two components of the model, the BMI trajectories and the CEBQ questionnaires over time, are then connected by the specification of a flexible joint prior distribution over the response-specific parameters. In particular, we use Normalised Generalised Gamma process prior [24, 25] to induce clustering of the subjects and aid the identification of clinically-relevant subgroups. Finally, the proposed framework also accommodates subject-specific demographic and clinical covariates, allowing their effects on both growth trajectories and appetite-related behaviours to be quantified within a unified modelling framework.

The paper is structured as follows. Data and model section introduces the GUSTO data and the model, composed of longitudinal, IRT and Bayesian nonparametric (BNP) parts; Application to the GUSTO data section presents the results when the proposed method is applied to the GUSTO dataset and Discussion section concludes with a discussion. Additional information regarding the dataset, MCMC algorithm and results is provided in Supplementary Materials.

Data and model

The application motivating the proposed approach is the joint study of growth development and the evolution of appetite phenotypes in children. We use data from the Growing Up in Singapore Towards healthy Outcomes (GUSTO) cohort study, a Singaporean prospective birth cohort started in 2009 and still ongoing [26]. GUSTO is a richly phenotyped cohort, containing a large amount of information on mother-child pairs across various clinical domains. Information is available on children’s growth trajectories, eating behaviour and mental health; maternal pre- and post-partum characteristics such as physical and mental well-being, socio-demographic variables and medical history. Full details on the GUSTO cohort can be found in [26].

The primary outcomes of this study are the standardised BMI trajectories (Z-BMI) and caregiver-reported child eating behaviours assessed using the CEBQ. The Z-BMI values were derived from children’s height and weight, measured during routine clinical visits at multiple time points as described in detail by Soh et al. [26]. Height and weight were recorded at 14 unequally spaced occasions between ages one and nine years, while eating behaviours were assessed at one, three, five, and seven years of age using the CEBQ questionnaire. We adopted the WHO criteria to define overweight (BMI Z-score > 1 SD), obesity (BMI Z-score > 2 SD), and underweight (BMI Z-score < -2 SD). For simplicity, children classified as overweight or obese are collectively referred to as having overweight. The CEBQ comprises individual items grouped into eight subscales representing distinct dimensions of eating behaviour. Four subscales capture Food Approach (FAp) tendencies, while the remaining four reflect Food Avoidance (FAv) tendencies. Food approach behaviours reflect a heightened interest in food, such as increased appetite and responsiveness to food cues (e.g., sight or smell of food), and include subscales such as enjoyment of food, food responsiveness, and emotional overeating, all of which may predispose to overeating and weight gain. Conversely, food avoidance behaviours reflect a reduced interest in eating, selective or picky eating, and slower eating pace, as captured by subscales such as satiety responsiveness, food fussiness, and emotional undereating. These behaviours are often associated with lower energy intake or undernutrition. All questionnaire items and subscales are detailed in Supplementary Table 1. The questionnaires were completed by primary caregivers to capture children’s habitual eating behaviours. In addition, time-invariant covariates included in the analysis are listed in Supplementary Table 2.

First we describe the main properties of the GPCM and then introduce some notation and describe how BMI trajectories and the questionnaire data are modelled. Under the Generalised Partial Credit model, the probability of subject i answering question j with category h is given by:

1

where N is the number of respondents, J is the number of questions in the questionnaire, and m> 1 is the number of possible answering categories, assumed to be the same for all questions. The subject-specific parameter represents the latent trait, and captures the answering profile of the i-th subject. Within the range of estimated latent trait parameters, higher values of indicate a higher propensity of the respondent towards answering with higher values within the answering categories. As such, a higher corresponds to a higher intensity of the construct for subject i. Eq. (1) also contains the item-specific parameters and , for j = 1, … , J. The first one is a discrimination parameter, indicating the ability of the j-th question to differentiate between respondent profiles, while is a m-dimensional vector of difficulty parameters for the j-th question. In particular, the value indicates the increment in construct level required to answer question j with category l rather than l-1. As in standard IRT models, responses to individual items are assumed to be conditionally independent given the corresponding latent trait and the observed covariates, with the latent traits accounting for the dependence induced by the underlying appetite constructs. We now describe how the GPCM is used to jointly model the questionnaire responses and BMI trajectories.

Let us start with the IRT component in the model. Let be the three-dimensional array containing the questionnaire data, i.e, J questions answered by the N participants at time points, so that , for i = 1, … , N and j = 1, … , J. The number of mother-child pairs used for the analysis is N = 282. Answers are given by the mothers at one, three, five and seven years of age of the child, so that . The CEBQ questionnaire is composed of J = 35 questions with m = 5 answer categories ranging from 1 (Never) to 5 (Always) [8]. As reported in Supplementary Table 1, the questions are grouped into subscales reflecting the construct to be measured (e.g., EF = Enjoyment of Food, FF = Food Fussiness). Moreover, the subscales are further grouped into main domains (FAp and FAv), introduced earlier, see also Supplementary Table 1. We include this information in the model by using suitable indices indicating to which subscale and domain each question belongs. We indicate this by the indices and , where denotes the subscale and indicates the domain to which each item belongs to, for j=1,… ,J. We use the subscale information to model a different latent trait for each main domain, thus improving the interpretability of the model. As such, latent traits relative to FAp and FAv, respectively, are included in the model for each subject. We point out that this is not a multiple-latent trait model, where diverse latent traits are included in the specification of the link function and are estimated using all the questions. Here, each latent trait corresponds to a different set of questions. Finally, we include covariates into the IRT component of the model directly in the specification of the probability of answering in a certain category. The covariate values for each subject i = 1,… , N are collected into the -dimensional vector .

For i = 1, … , N, the longitudinal IRT part of the model is specified as follows:

2

where is the sub-scale specific prior mean of the and is the d-dimensional Gaussian distribution with mean and covariance matrix , is a d-dimensional vector of zeros and is the d-dimensional identity matrix.

To ensure the identifiability of the proposed model, we impose some constraints on the prior specification. Specifically, we fix the variances of regression coefficients and IRT parameters , and to one. This constraint is necessary to establish the scale of the latent traits in the model [27]. We also constrain the difficulty parameters , for j = 1, … , J, leaving the remaining m-1 terms unconstrained. From a structural equation modelling perspective, this corresponds to fixing one of the loadings to a constant [27].

Let us now move the the modelling of the BMI trajectories. We denote the longitudinal observations by for i = 1, … , N and . As before N = 282, while the number of unequally spaced time points of observation for the Z-BMI score is , ranging from one to nine years of age and shared across subjects. The time component is modelled via a cubic B-spline constructed using the R package splines [28], where the knots are fixed to the extremes and median values of the observed time points. In this setting, the time evolution of the data is described by a linear combination of polynomial basis terms, with subject-specific coefficients . More details on the specification of the B-spline basis functions for the GUSTO application are given in Application to the GUSTO data section. Additionally, fixed covariates are included in the analysis. A comprehensive list of such covariates is reported in Supplementary Table 2. Thus, for each i = 1, … , N, the vectors of longitudinal observations are modelled as multivariate Gaussian with mean vector and diagonal covariance matrix with entries equal to , with a vector of regression coefficients and a vector of ones, see Eq. (3). For i = 1, … , N, the longitudinal part of the model is given by:

3

where , and are defined as before and IG(a, b) indicates the inverse-gamma distribution with mean b/(a-1). The inverse-gamma prior (IG(3,2)) is a standard weakly informative prior for variance parameters in hierarchical Bayesian models. Under this specification, both the prior mean and variance are equal to one, providing a reasonable scale for the standardised BMI measurements while allowing substantial uncertainty and ensuring that inference is primarily driven by the observed data.

Finally, note that different sets of covariates can be included in the two parts of the model, indicated by and . Specifically, is included in the IRT component of the model, set outside the standard IRT contribution to the probability, to avoid being affected by the question-specific discrimination parameters. It is, however, scaled by the factor h for identifiability. Furthermore, note that in the IRT model, the regression coefficients are item-specific, allowing to capture question-specific covariate effects.

A desirable feature of our modelling strategy is the ability to identify risk sub-groups in the population by estimating the clustering structure of the subjects. Specifically, we jointly model the subject-specific parameters in the growth (Z-BMI) and eating behaviours (CEBQ) parts of the model via a nonparametric prior distribution. In the Bayesian framework, this is often achieved by specifying a Dirichlet process [DP, 29] prior on the parameters of interest. The DP is a prior distribution defined on the space of probability distributions. An appealing feature of the DP is that it induces a random partition of the subjects. For this reason, and for its analytical tractability, the DP is arguably the most popular prior distribution used in Bayesian nonparametric applications. However, it favours partitions composed of a few large clusters and several small clusters (or singletons), a feature usually referred to as the “rich-gets-richer” property. To mitigate such effect, alternative prior distributions can be specified, which allow for more flexible partition estimation. In this work, we employ the Normalised Generalised Gamma (NGG) process [24, 25], a generalisation of the DP which favours coarser partitions and fewer singletons, mitigating the“rich-gets-richer” effect of the DP. In particular, the NGG is characterised by two parameters, denoted here by κ> 0 and , and a centring distribution . In particular if a random measure P is distributed according to a NGG, then it can be represented as

where the are the jump sizes, almost surely and is a non-atomic probability measure. The parameter κ plays an analogous role as the mass parameter in the DP, controlling the distribution of the number of clusters, while σ controls the sizes of the originated clusters. Specifically, values of σ close to 1 increase the number of clusters, while keeping the cluster sizes small. Conversely, when σ approaches 0, clusters containing more elements are favoured. These features have been shown to be very useful in mixture modelling and clustering [25, 30]. When , the DP is recovered. We provide below the nonparametric part of the model:

4

A schematic representation of the full model is depicted in Fig. 1.

Fig. 1.

Summary of the proposed model. Circles represent random variables, while squares correspond to observations or fixed hyper-parameters

Application to the GUSTO data

We present the results obtained by analysing the GUSTO dataset. We fit the proposed model by fixing the hyperparameters as in Eqs. (3) - (4). The hyperparameters of the NGG prior are fixed to κ =1 and σ =0.75. The value κ =1 corresponds to a standard choice that induces a moderate prior tendency towards clustering, while σ =0.75 was selected to introduce a substantial degree of reinforcement and therefore depart from the Dirichlet Process case (σ =0). This specification favours a richer partition structure and has been found useful in Bayesian Nonparametric clustering applications where the objective is to identify both dominant and less prevalent subgroups.

The time component of the longitudinal model is represented using a cubic B-spline basis. Boundary knots are fixed at the minimum and maximum observed ages, while a single interior knot is placed at the median observation time, yielding knot locations at (1, 4.75, 9). Cubic splines (degree 3) are employed, as they provide a flexible yet smooth representation of non-linear trajectories and are widely used in statistical modelling [31, 32]. Under this specification, the spline basis consists of four functions (excluding the intercept term). The number and placement of knots are chosen to balance model flexibility and parsimony, consistent with common recommendations for spline modelling when only a limited number of distinct observation times are available [33]. This specification is sufficiently flexible to capture the main non-linear features of the BMI trajectories while avoiding unnecessary model complexity. In Section 3 of Supplementary Material, we investigate the sensitivity of the proposed methodology to the prior specification and modelling choices, demonstrating its robustness and flexibility.

In the application presented in this work, we use different sets of covariates for the longitudinal and IRT parts of the model. In particular, as Z-BMI is computed standardizing for sex, we exclude the covariate Sex from . Therefore, after expressing the categorical variables using dummies, the number of covariates is equal to for the Z-BMI and for the CEBQ, respectively. The missing rate in the Z-BMI observations is below 20% for all time points and overall equal to 6.51%, while for the CEBQ questionnaire, it is equal to 0.6%, 3.51%, 5.38% and 0.71% at each time point, respectively. Missing longitudinal outcomes (Z-BMI) and missing questionnaire responses (CEBQ items) are accommodated directly within the Bayesian model. Rather than discarding incomplete observations or performing a separate imputation step, missing values are treated as unknown variables and jointly estimated with all model parameters. During MCMC sampling, missing observations are updated from their full conditional posterior distributions given the observed data and current parameter values, allowing uncertainty due to missingness to be fully propagated through the posterior inference under the assumption that the data are missing at random (MAR). In contrast, missing values in the fixed covariate maternal education are imputed before model fitting using multiple imputation via the mice package [34], as these covariates enter the model as fixed design variables. The only covariate presenting missing information is the maternal level of education (6.38% missing values). Imputation of missing responses is carried out naturally in the Bayesian framework by considering them as additional parameters in the model. As such, they are sampled from the model at each iteration of the MCMC algorithm.

We devise an adaptive MCMC Metropolis-within-Gibbs algorithm for the update of the parameters of the proposed model, which is reported in detail in Supplementary Materials Section 2. We first run a short burn-in of 100 iterations to initialise the quantities needed in the adaptive MCMC steps. Then, we run 25000 iterations, of which 15000 are discarded as additional burn-in, and the remaining ones are thinned every two yielding a final sample of size 5000.

Clustering

Part (4) of the full model allows the estimate of a partition of the subjects, thanks to the choice of the nonparametric NGG prior used to link subject-specific parameters in the longitudinal and IRT parts. We use the posterior chain of partition samples to estimate the clustering configuration of the subjects. We estimate a single representative partition by minimising the posterior expected Binder loss [35, 36], where the expectation is taken over the posterior distribution of partitions obtained from the MCMC algorithm. This criterion does not require knowledge of a true clustering. Rather, it identifies the partition that best summarises the posterior clustering uncertainty. The estimated partition is closely related to the expected Rand Index [37, 38], a measure of similarity between partitions. In particular, minimising Binder’s loss is equivalent to maximising the posterior Expected Rand Index, so both criteria target the same optimal partition and differ mainly in their mathematical formulation rather than in their practical objective. The estimated Binder partition yields clusters of sizes (Cluster 1 : 105, Cluster 2 : 71, Cluster 3 : 69, Cluster 4 : 26, Cluster 5 : 7, Cluster 6 : 4), where we assign the cluster labels according to decreasing cluster size. We show in Fig. 2 the posterior co-clustering probabilities ordered according to the estimated Binder partition. We observe a clear pattern in the clustering distribution with little uncertainty.

Fig. 2.

GUSTO data. Pairwise posterior co-clustering probabilities. Subjects are ordered according to the estimated Binder partition, with cluster labels assigned in decreasing order of cluster size. The (i, j)-th entry of the matrix represents the posterior probability that subjects i and j belong to the same cluster, estimated as the proportion of MCMC iterations in which they are co-clustered

To characterise the clustering of the subjects, we show in Fig. 3 (bottom row) the longitudinal observations (i.e., Z-BMI trajectories) coloured according to the estimated clustering assignment. Note that discontinued lines correspond to missing patterns in the data. The partition of these trajectories suggests a grouping based on different growth patterns, characterised by different magnitudes of Z-BMI trajectories. Additionally, we report in Fig. 3 the sample mean trajectories within each cluster and the summary scores (sum of individual answers) obtained within each of the two main subscales of the CEBQ questionnaire, i.e. Food Approach and Food Avoidance.

Fig. 3.

GUSTO data. Z-BMI and CEBQ trajectories computed as sample mean and average sum scores, respectively. Shaded regions represent the 95% empirical quantile range. The first two rows refer to the CEBQ latent traits (Food Approach and Food Avoidance), while the last row reports the average Z-BMI trajectories within each cluster. Dotted lines in the Z-BMI panels indicate the values ± 1 and ± 2. Each column refers to a different cluster in the Binder partition. The average trajectories are computed from the raw data discarding the missing values in the dataset

Figure 3 highlights some interesting correspondence between Z-BMI trends and patterns of eating behaviour within the clusters. The trajectories presented in Fig. 3 are intended as descriptive summaries of the estimated clusters; importantly, the clustering itself is based on the joint posterior distribution of the subject-specific spline coefficients and latent appetite traits, rather than on visual inspection of the growth curves. The three biggest clusters are characterised by stable Z-BMI trajectories, with a slight decrease/increase in later years (approximately after year 3) for Clusters 2 and 3, respectively. These clusters are paired with complementary eating behaviour trajectories, where Cluster 2 has an overall increased Food Approach trajectory compared to Cluster 1, while the opposite can be observed for Cluster 3. Cluster 4 shows a sharp increase in the Food Approach trajectory starting around 2.5 years, accompanied by large values of Z-BMI starting also around the same time point (and plateauing at the end of the time window). This suggests that Cluster 4 groups children who developed overweight/obesity at an early stage, which corresponds to obesogenic eating behaviour patterns at the same time point. It is worth noting that Clusters 5 and 6 contain relatively few individuals (composed of less than 10 subjects). This is not unexpected in Bayesian nonparametric models based on random probability measures such as the Normalised Generalised Gamma (NGG) process, which are specifically designed to identify both common population-level patterns and rarer subgroups with atypical profiles. Rather than representing overfitting, these small clusters correspond to subjects located at the extremes of the joint distribution of appetite behaviours and growth trajectories. In particular, Cluster 5 is characterised by persistently low BMI values combined with high levels of food avoidance and declining food approach behaviours, while Cluster 6 displays the opposite pattern, i.e. elevated BMI trajectories associated with low food avoidance and increasing food approach tendencies. These findings are consistent with clinically meaningful phenotypes related to underweight and obesity risk. Nevertheless, given their small size, the precise characteristics of these clusters may be more sensitive to individual observations than those of the larger groups, and their interpretation should therefore be considered exploratory.

Longitudinal and IRT parameters

Model (2) involves some additional parameters which are of interest for this application. In particular, we consider the discriminatory parameters for j = 1, … , J, characterising the importance of individual questions in differentiating among different response profiles. To highlight this, we show in Fig. 4 the posterior mean and 95% credible intervals of these parameters for each question in the CEBQ questionnaire, grouped by subscale. We consider highly discriminatory a question for which the corresponding parameter has a posterior distribution concentrated on values higher than one. From Fig. 4, we identify which questions discriminate the most and the least, respectively. We report the five most/least discriminatory questions in Table 1, obtained by ranking the values of the posterior median of the corresponding discriminatory parameters . We observe how the least discriminatory questions have a more extreme construction (“My child always...”) which could encompass a wider variety of situations, or reflect an exaggeration in the maternal response, thus leading to outliers in the type of answers and ultimately to more variability in the estimates. Posterior item characteristic curves, i.e. the probability of answering the given question as a function of the latent trait θ, relative to these questions are shown in Supplementary Figs. 3 and 4. We can observe how the item characteristic curves relative to more discriminatory questions are more peaked, and the curves relative to answers in the middle (i.e., different from “Never” and “Always”) place mass on a smaller portion of the support of θ.

Fig. 4.

GUSTO data. Posterior distribution of the discriminatory parameters , for j = 1, … , J, grouped into subscales

Table 1.

GUSTO data. Most and least discriminatory questions, identified by the posterior distribution of the parameters , for j = 1, … , J. The top half of the Table refers to the five most discriminatory questions, while the lowest half to the least discriminatory ones. The corresponding posterior item-characteristic curves are reported in Supplementary Figs. 3 and 4

Question #	Main subscale	Subscale	Question text
Q14	FAp	FR	If allowed to, my child would eat too much
Q24	FAv	FF	My child is difficult to please with meals
Q12	FAp	FR	My child is always asking for food
Q19	FAp	FR	Given the choice, my child would
			eat most of the time
Q22	FAp	EF	My child enjoys eating
Q11	FAv	EUE	My child eats less when s/he is tired
Q6	FAp	DD	My child is always asking for a drink
Q29	FAp	DD	If given the chance, my child would drink
			continuously throughout the day
Q31	FAp	DD	If given the chance, my child would
			always be having a drink
Q23	FAv	EUE	My child eats more when she is happy

The discriminatory parameters in model (2) are modelled conditionally to a subscale-specific mean parameters , for , whose posterior distribution is reported in Fig. 5. The posterior mean and 95% credible interval for the different are concentrated around zero, with lower values obtained for the subscales Emotional Under Eating (EUE) and Desire to Drink (DD), indicating that on average the questions belonging to these subscales are less discriminatory, as it is also observed in Fig. 4 (with the exception of Question 6).

Fig. 5.

GUSTO data. Posterior distribution of the mean parameters , for

Effect of covariates

We investigate the effect of the fixed-effect covariates on the longitudinal and IRT parts of the model. Recall that the covariate Sex is not included in the model for the Z-BMI trajectories, since these are standardised by taking into account sex differences. In Fig. 6, we show the posterior mean and 95% credible intervals of the coefficients , while for , for j = 1, … , J, we only show the posterior mean to improve visualisation. Supplementary Fig. 2 shows more details. We indicate in red those estimates whose 95%CI does not contain the value zero, and that are thus considered to have a relevant effect.

Fig. 6.

GUSTO data. Posterior estimates of the regression coefficients and for the fixed covariates. Each panel refer to a different sub-model, i.e. the longitudinal and the questionnaire data. In the latter, the posterior 95% credibility intervals are omitted for visualisation purposes. Red dots denote regression coefficients whose 95% credible interval does not contain zero

The covariates Ethnicity, Maternal Education and Gestational Age have a stronger effect on the evolution of the Z-BMI trajectories.

The effect of covariates on the respondent profile and appetite behaviour is slightly different when considering the two appetite domains. In particular, Sex, Parity and maternal Education are characterised by a higher number of significant covariates (positive coefficients) for the questions relative to Food Avoidance. The variable Ethnicity has different effects on the two domains corresponding to the different categories: Malay Ethnicity has equal negative effects on both domains, while Indian Ethnicity has diametrically opposite effects on the two domains. To summarise the results regarding the effects of the covariates on the probability of answering the questions in the CEBQ, we report in Table 2 the number of significant regression effects for each covariate, grouped according to the CEBQ subscales.

Table 2.

GUSTO data. Number of regression coefficients whose posterior 95% credible interval does not contain the value zero, and are therefore considered as significant effects

Subscale
Covariate	FR	EOE	EF	DD	SR	SE	EUE	FF
GA	0	0	0	1	0	0	1	1
Edu: Uni and above	1	0	0	0	0	1	4	3
Edu: below Secondary	1	0	0	2	2	0	1	1
Ethnicity Malay	4	1	1	2	1	2	3	0
Ethnicity Indian	4	1	4	0	5	1	1	0
Parity	1	0	0	0	4	4	2	1
Sex (ref. Male)	0	0	1	0	1	2	2	0

Discussion

This study identifies six distinct trajectories of Z-BMI from infancy to school age, each associated with unique appetite-related behavioural profiles characterised by food approach and food avoidance tendencies. Three trajectories represent children who maintain a healthy BMI throughout early childhood (Clusters 1–3), while the remaining trajectories capture children who transition from healthy weight to overweight or obesity by school age (Cluster 4), those who remain underweight (Cluster 5), and those who are overweight in infancy and develop obesity (Cluster 6). Together, these trajectories illustrate the substantial heterogeneity in early growth patterns and their close correspondence with appetite phenotypes.

The six trajectories align closely with eating behaviours in the expected directions. Children following healthy weight trajectories show increasing food avoidance and stable or slightly decreasing food approach behaviours over time, suggesting the gradual emergence of self-regulatory mechanisms in appetite control during early development. The results indicate that food avoidance behaviours exert a stronger influence on BMI trajectory than food approach behaviours. Among the healthy-weight clusters, children in Cluster 3 display a modest increase in BMI within the normal range, corresponding to a smaller rise in food avoidance compared to Clusters 1 and 2. No major differences emerge in food approach behaviours among these three clusters, reinforcing the interpretation that food avoidance plays a more decisive role in maintaining healthy weight.

Children in Cluster 4, who become overweight or obese by school age, show increasing food approach behaviours, such as food responsiveness, enjoyment of food, and emotional overeating, alongside persistently low levels of food avoidance. These behavioural changes likely drive higher energy intake and weight gain, consistent with previous evidence linking strong food approach tendencies to increased BMI [8, 39]. By school age, children in this group exhibit higher mean food approach scores than those with healthy weight or underweight trajectories, suggesting that elevated appetite drive combined with low avoidance contributes to excessive weight gain.

Cluster 6, representing children with obesity, displays an even more pronounced profile. At 12 months, these children have food avoidance scores approximately 50% lower than those of children with healthy weight and only reach comparable levels by school age. At the same time, they show a rapid and sustained increase in food approach behaviours not seen in any other cluster, indicating a behavioural phenotype of heightened appetite drive and diminished satiety sensitivity.

In contrast, children in Cluster 5 (underweight) show the opposite pattern: rapidly increasing food avoidance and decreasing food approach behaviours between one and five years of age. This behavioural profile likely reflects high satiety responsiveness or reluctance to eat, leading to limited energy intake and restricted weight gain. Interestingly, their early food approach scores are comparable to those of children with early obesity, highlighting how the direction and timing of behavioural changes rather than absolute levels—are crucial for understanding growth outcomes.

Across clusters, appetite-related behaviours map closely onto developmental trajectories of BMI. Food avoidance behaviours (such as fussy eating, slowness in eating, and satiety responsiveness) appear to differentiate BMI trajectories more strongly than food approach behaviours, supporting the view that lower inhibitory control over eating is a key mechanism underlying excessive weight gain [40, 41].

From a methodological perspective, this study advances research on appetite and growth by modelling eating behaviours as latent constructs of food approach and food avoidance rather than analysing subscales independently. This dimensional reduction yields a more parsimonious and interpretable framework while preserving strong associations with BMI trajectories over time. The analysis of item discrimination further identifies five weakly differentiating items—three from the Desire to Drink subscale and two from Emotional Undereating, suggesting potential redundancy of these subscales in this population. Although this approach reduces item-level granularity, it enhances conceptual clarity and interpretability in linking appetite traits to growth.

Overall, the findings demonstrate that early eating behaviours correspond closely to patterns of growth in early childhood. Food avoidance tendencies emerge as stronger and more consistent predictors of BMI trajectory than food approach tendencies. These results highlight the importance of developing interventions that foster adaptive avoidance behaviours, such as sensitivity to satiety cues and self-regulation of intake, to promote healthy growth trajectories. By integrating behavioural phenotypes with longitudinal growth modelling, this study provides new insights into the developmental mechanisms underlying childhood obesity and offers a foundation for more targeted early prevention strategies.

Authors' contributions

AC, BF, MDI, JE, AF developed the methodological aspects of the study. AC, BF, MDI performed the statistical analyses, and wrote the corresponding MCMC algorithm. MC, JYT, NM, VG, FY, YSL, JE, AF contributed with the clinical interpretation of the results. All co-authors contributed to the writing of the manuscript.

Funding

This work is partially funded by MICIU/AEI/10.13039/501100011033 and FSE+ (Grant No. RYC2024-050330-I), and by MICIU/AEI/10.13039/501100011033/FEDER, UE (Grant No. PID2024-155187OB-I00).

Data availability

The datasets analysed during the current study are not publicly available due to restrictions imposed by the GUSTO study.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.