Animal source foods (ASF) are nutrient-dense and essential for the growth and development of children. The Bangladesh Demographic and Health Survey (BDHS) 2022 reported that approximately two-thirds of children aged 6–23 months consumed eggs/flesh foods. However, overall consumption patterns, trends, and factors influencing ASF intake among children in Bangladesh were not well-documented. Therefore, the study aimed to assess the trends and associated factors of ASF consumption among children aged 6–23 months in Bangladesh. A total of 9401 children were extracted from four consecutive BDHS (2011, 2014, 2017/18, and 2022). The Cochran-Armitage test was conducted to assess the trends in ASF consumption, while a two-stage multilevel mixed-effects logistic regression was performed to identify the associated factors. The consumption of ASF significantly increased to 79.1% in 2017/18 from 67% in 2011 but decreased to 73.3% in 2022. ASF consumption was found to be higher among children whose mothers were educated (AOR = 1.60, 95% CI = 1.30–1.98), employed in either agricultural (AOR = 1.27, 95% CI = 1.04–1.54) or non-agricultural (AOR = 1.36, 95% CI = 1.07–1.72) activities, pregnant (AOR = 2.54, 95% CI = 1.66–3.87), had received ANC 1–3 times (AOR = 1.43, 95% CI = 1.20–1.72) or ≥4 times (AOR = 1.59, 95% CI = 1.29–1.95), and was exposed to media (AOR = 1.21, 95% CI = 1.04–1.39). Furthermore, consumption increased with increasing the age of children, and the wealth of their families. However, children who experienced illness were less likely to consume ASF (AOR = 0.76, 95% CI = 0.68–0.86). The recent declines in ASF consumption emphasize the need for targeted interventions to increase ASF consumption among children in Bangladesh.

Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used statistic for evaluating the adequacy of a SEM model is TML, a slight modification to the likelihood ratio statistic. Under normality assumption, TML approximately follows a chi-square distribution when the number of observations (N) is large and the number of items or variables (p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that TML rejects the correct model too often when p is not too small. Various corrections to TML have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct TML so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed corrections to TML, and they control type I errors reasonably well whenever N≥max(50,2p). The formulations of the empirically corrected statistics are further used to predict type I errors of TML as reported in the literature, and they perform well.

Model selection is a popular strategy in structural equation modeling (SEM). To select an “optimal” model, many selection criteria have been proposed. In this study, we derive the asymptotics of several popular selection procedures in SEM, including AIC, BIC, the RMSEA, and a two-stage rule for the RMSEA (RMSEA-2S). All of the results are derived under weak distributional assumptions and can be applied to a wide class of discrepancy functions. The results show that both AIC and BIC asymptotically select a model with the smallest population minimum discrepancy function (MDF) value regardless of nested or non-nested selection, but only BIC could consistently choose the most parsimonious one under nested model selection. When there are many non-nested models attaining the smallest MDF value, the consistency of BIC for the most parsimonious one fails. On the other hand, the RMSEA asymptotically selects a model that attains the smallest population RMSEA value, and the RESEA-2S chooses the most parsimonious model from all models with the population RMSEA smaller than the pre-specified cutoff. The empirical behavior of the considered criteria is also illustrated via four numerical examples.

By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the development of robust methods to reduce the influence of outliers and the distributional deviation in the analysis. In this paper we develop a maximum likelihood (ML) approach that is robust to outliers and symmetrically heavy-tailed distributions for analyzing nonlinear SEMs with ignorable missing data. The analytic strategy is to incorporate a general class of distributions into the latent variables and the error measurements in the measurement and structural equations. A Monte Carlo EM (MCEM) algorithm is constructed to obtain the ML estimates, and a path sampling procedure is implemented to compute the observed-data log-likelihood and then the Bayesian information criterion for model comparison. The proposed methodologies are illustrated with simulation studies and an example.

We aimed to identify temporal patterns of energy intake and investigate their association with adiposity. We performed a cross-sectional study of 775 adults in Iran. Information about eating occasions across the day was collected by three 24-h dietary recalls. Latent class analysis (LCA) was used to identify temporal eating patterns based on whether or not an eating occasion occurred within each hour of the day. We applied binary logistic regression to estimate the OR and 95 % CI of overweight and obesity (defined as BMI of 25–29·9 and ≥ 30 kg/m2, respectively) across temporal eating patterns while controlling for potential confounders. LCA grouped participants into three exclusive sub-groups named ‘Conventional’, ‘Earlier breakfast’ and ‘Later lunch’. The ‘Conventional’ class was characterised by high probability of eating occasions at conventional meal times. ‘Earlier breakfast’ class was characterised by high probability of a breakfast eating occasion 1 h before the conventional pattern and a dinner eating occasion 1 h after the conventional pattern, and the ‘Later lunch’ class was characterised by a high probability of a lunch eating occasion 1 h after the conventional pattern. Participants in the ‘Earlier breakfast’ pattern had a lower likelihood of obesity (adjusted OR: 0·56, 95 % CI: 0·35, 0·95) as compared with the ‘Conventional’ pattern. There was no difference in the prevalence of obesity or overweight between participants in the ‘Later lunch’ and the ‘Conventional’ patterns. We found an inverse association between earlier eating pattern and the likelihood of obesity, but reverse causation may be a plausible explanation.

There is increasing interest in modelling longitudinal dietary data and classifying individuals into subgroups (latent classes) who follow similar trajectories over time. These trajectories could identify population groups and time points amenable to dietary interventions. This paper aimed to provide a comparison and overview of two latent class methods: group-based trajectory modelling (GBTM) and growth mixture modelling (GMM). Data from 2963 mother–child dyads from the longitudinal Southampton Women’s Survey were analysed. Continuous diet quality indices (DQI) were derived using principal component analysis from interviewer-administered FFQ collected in mothers pre-pregnancy, at 11- and 34-week gestation, and in offspring at 6 and 12 months and 3, 6–7 and 8–9 years. A forward modelling approach from 1 to 6 classes was used to identify the optimal number of DQI latent classes. Models were assessed using the Akaike and Bayesian information criteria, probability of class assignment, ratio of the odds of correct classification, group membership and entropy. Both methods suggested that five classes were optimal, with a strong correlation (Spearman’s = 0·98) between class assignment for the two methods. The dietary trajectories were categorised as stable with horizontal lines and were defined as poor (GMM = 4 % and GBTM = 5 %), poor-medium (23 %, 23 %), medium (39 %, 39 %), medium-better (27 %, 28 %) and best (7 %, 6 %). Both GBTM and GMM are suitable for identifying dietary trajectories. GBTM is recommended as it is computationally less intensive, but results could be confirmed using GMM. The stability of the diet quality trajectories from pre-pregnancy underlines the importance of promotion of dietary improvements from preconception onwards.

Supplementation with n-3 fatty acids can influence inflammation and markers of arterial stiffness that are increased in patients with rheumatoid arthritis (RA). However, it is unknown whether specific patterns of dietary fatty acid intake are similarly associated. In a longitudinal study, eighty-six RA patients reported their dietary intake and had arterial stiffness measured using the augmentation index (AIx) at baseline and 8 months. Latent profile analysis (LPA) was performed to characterise patterns of fatty acid intake using sixteen major fatty acids. Models for two to six profiles were compared using the Akaike and Bayesian information criteria. Associations between AIx and the profiles were adjusted for age, sex, disease activity, fish oil supplementation, medications, physical activity and socio-economic status. LPA identified five distinct profiles. Profile 1 subjects (n 7) reported significantly higher intake of palmitoleic acid (16 : 1), arachidonic acid (20 : 4n-6), EPA (20 : 5n-3), DHA (22 : 6n-3) and docosapentaenoic acid (22 : 5n-3) (P<0·001 for each) than profiles 2 (n 14), 3 (n 19), 4 (n 23) and 5 (n 23) and significantly higher grilled and tinned fish consumption. The AIx varied significantly across the five profiles (P=0·023); subjects in profile 1 had a significantly lower AIx than those in profile 3 (β=–7·2 %; 95 % CI –11·5, –2·9; P=0·001) who had the lowest reported intake of n-3 fatty acids. Fish oil supplementation was also independently associated with lower AIx (β=–4·15 %; 95 % CI –6·73, –1·56; P=0·002). A diet characterised by a higher reported intake of n-3 fatty acids, palmitoleic acid (16 : 1) and arachidonic acid (20 : 4n-6) is associated with a lower AIx in RA patients.