Mediation analysis constitutes an important part of treatment study to identify the mechanisms by which an intervention achieves its effect. Structural equation model (SEM) is a popular framework for modeling such causal relationship. However, current methods impose various restrictions on the study designs and data distributions, limiting the utility of the information they provide in real study applications. In particular, in longitudinal studies missing data is commonly addressed under the assumption of missing at random (MAR), where current methods are unable to handle such missing data if parametric assumptions are violated.

In this paper, we propose a new, robust approach to address the limitations of current SEM within the context of longitudinal mediation analysis by utilizing a class of functional response models (FRM). Being distribution-free, the FRM-based approach does not impose any parametric assumption on data distributions. In addition, by extending the inverse probability weighted (IPW) estimates to the current context, the FRM-based SEM provides valid inference for longitudinal mediation analysis under the two most popular missing data mechanisms; missing completely at random (MCAR) and missing at random (MAR). We illustrate the approach with both real and simulated data.

Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit statistic. While a noncentrality parameter estimate is well suited for quantifying the amount of systematic error, the complex weighting function involved in its calculation makes indices derived from it challenging to interpret. Moreover, noncentrality-parameter-based fit indices yield systematically different values, depending on the indicators’ level of measurement. For instance, RMSEA and CFI yield more favorable fit indices for models with categorical as compared to metric variables under otherwise identical conditions. In the present article, approaches for obtaining an approximation discrepancy estimate that is independent from any specific weighting function are considered. From these unweighted approximation error estimates, fit indices analogous to RMSEA and CFI are calculated and their finite sample properties are investigated using simulation studies. The results illustrate that the new fit indices consistently estimate their true value which, in contrast to other fit indices, is the same value for metric and categorical variables. Advantages with respect to interpretability are discussed and cutoff criteria for the new indices are considered.

The estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures. However, sensitivity or influence analysis of the model is not well studied. We demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables; and we develop appropriate procedures based on the local influence approach of Cook (1986). The proposed procedures are computationally efficient, the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model. We consider the influence of an individual cell frequency with respect to three cases: when all parameters in an unstructured model are of interest, when the unstructured polychoric correlations are of interest, and when the structural parameters are of interest. We also consider the sensitivity of the parameters estimates. Two examples based on real data are presented for illustration.

The main purpose of this article is to develop a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data. Joint Bayesian estimates of thresholds, structural parameters and latent factor scores are obtained simultaneously. The idea of data augmentation is used to solve the computational difficulties involved. In the posterior analysis, in addition to the real missing data, latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data. An algorithm that embeds the Metropolis-Hastings algorithm within the Gibbs sampler is implemented to produce the Bayesian estimates. A goodness-of-fit statistic for testing the posited model is presented. It is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small. Computational efficiency of the proposed procedure is illustrated by simulation studies and a real example.

The longitudinal process that leads to university student dropout in STEM subjects can be described by referring to (a) inter-individual differences (e.g., cognitive abilities) as well as (b) intra-individual changes (e.g., affective states), (c) (unobserved) heterogeneity of trajectories, and d) time-dependent variables. Large dynamic latent variable model frameworks for intensive longitudinal data (ILD) have been proposed which are (partially) capable of simultaneously separating the complex data structures (e.g., DLCA; Asparouhov et al. in Struct Equ Model 24:257–269, 2017; DSEM; Asparouhov et al. in Struct Equ Model 25:359–388, 2018; NDLC-SEM, Kelava and Brandt in Struct Equ Model 26:509–528, 2019). From a methodological perspective, forecasting in dynamic frameworks allowing for real-time inferences on latent or observed variables based on ongoing data collection has not been an extensive research topic. From a practical perspective, there has been no empirical study on student dropout in math that integrates ILD, dynamic frameworks, and forecasting of critical states of the individuals allowing for real-time interventions. In this paper, we show how Bayesian forecasting of multivariate intra-individual variables and time-dependent class membership of individuals (affective states) can be performed in these dynamic frameworks using a Forward Filtering Backward Sampling method. To illustrate our approach, we use an empirical example where we apply the proposed forecasting method to ILD from a large university student dropout study in math with multivariate observations collected over 50 measurement occasions from multiple students ($N=122$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N = 122$$\end{document}). More specifically, we forecast emotions and behavior related to dropout. This allows us to predict emerging critical dynamic states (e.g., critical stress levels or pre-decisional states) 8 weeks before the actual dropout occurs.

Estimating dependence relationships between variables is a crucial issue in many applied domains and in particular psychology. When several variables are entertained, these can be organized into a network which encodes their set of conditional dependence relations. Typically however, the underlying network structure is completely unknown or can be partially drawn only; accordingly it should be learned from the available data, a process known as structure learning. In addition, data arising from social and psychological studies are often of different types, as they can include categorical, discrete and continuous measurements. In this paper, we develop a novel Bayesian methodology for structure learning of directed networks which applies to mixed data, i.e., possibly containing continuous, discrete, ordinal and binary variables simultaneously. Whenever available, our method can easily incorporate known dependence structures among variables represented by paths or edge directions that can be postulated in advance based on the specific problem under consideration. We evaluate the proposed method through extensive simulation studies, with appreciable performances in comparison with current state-of-the-art alternative methods. Finally, we apply our methodology to well-being data from a social survey promoted by the United Nations, and mental health data collected from a cohort of medical students. R code implementing the proposed methodology is available athttps://github.com/FedeCastelletti/bayes_networks_mixed_data.

The current study explored the impact of genetic relatedness differences (ΔH) and sample size on the performance of nonclassical ACE models, with a focus on same-sex and opposite-sex twin groups. The ACE model is a statistical model that posits that additive genetic factors (A), common environmental factors (C), and specific (or nonshared) environmental factors plus measurement error (E) account for individual differences in a phenotype. By extending Visscher’s (2004) least squares paradigm and conducting simulations, we illustrated how genetic relatedness of same-sex twins (HSS) influences the statistical power of additive genetic estimates (A), AIC-based model performance, and the frequency of negative estimates. We found that larger HSS and increased sample sizes were positively associated with increased power to detect additive genetic components and improved model performance, and reduction of negative estimates. We also found that the common solution of fixing the common environment correlation for sex-limited effects to .95 caused slightly worse model performance under most circumstances. Further, negative estimates were shown to be possible and were not always indicative of a failed model, but rather, they sometimes pointed to low power or model misspecification. Researchers using kin pairs with ΔH less than .5 should carefully consider performance implications and conduct comprehensive power analyses. Our findings provide valuable insights and practical guidelines for those working with nontwin kin pairs or situations where zygosity is unavailable, as well as areas for future research.

This study aimed to quantify a latent variable for body size (BS) in pigs by using five linear body measurements including body length (BL), body height (BH), chest width (CW), chest girth (CG) and tube girth (TG), and also to identify the most associated single nucleotide polymorphisms (SNP) and related genes with BS by using the genomic best linear unbiased prediction (GBLUP) based genome-wide association study (GWAS) or GBLUP-GWAS methodology. To perform a GWAS on the BS latent trait, we used a mixed linear model and identified a total of 53 significant SNPs. Additionally, we found that nine genes, including Rho GTPase activating protein 12 (ARHGAP12), transmembrane protein 108 (TMEM108), T-cell lymphoma invasion and metastasis inducing factor 1 (TIAM1), ras homologue gene family member B (RHOB), POU class 4 homeobox 1 (POU4F1), follistatin-related protein 4 (FSTL4), cellular communication network factor 2 (CCN2), beaded filament structural protein 2 (BFSP2) and attractin-like protein 1 (ATRNL1) were associated with the BS trait in pigs. These genes are involved in several biological processes, including the regulation of anatomical structure, morphogenesis, the regulation of cell size and growth. The results suggest that the identified SNP and related genes may play important roles in regulating the growth and development of pigs. The results imply that these genes could be promising candidates for further exploration of the underlying mechanisms of body size variation. Furthermore, the findings have significant practical implications for enhancing the efficiency and profitability of pig farming through genetic selection.

It is crucial to understand the genetic mechanisms and biological pathways underlying the relationship between obesity and serum lipid levels. Structural equation models (SEMs) were constructed to calculate heritability for body mass index (BMI), total cholesterol (TC), triglyceride (TG), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), and the genetic connections between BMI and the four classes of lipids using 1197 pairs of twins from the Chinese National Twin Registry (CNTR). Bivariate genomewide association studies (GWAS) were performed to identify genetic variants associated with BMI and lipids using the records of 457 individuals, and the results were further validated in 289 individuals. The genetic background affecting BMI may differ by gender, and the heritability of males and females was 71% (95% CI [.66, .75]) and 39% (95% CI [.15, .71]) respectively. BMI was positively correlated with TC, TG and LDL-C in phenotypic and genetic correlation, while negatively correlated with HDL-C. There were gender differences in the correlation between BMI and lipids. Bivariate GWAS analysis and validation stage found 7 genes (LOC105378740, LINC02506, CSMD1, MELK, FAM81A, ERAL1 and MIR144) that were possibly related to BMI and lipid levels. The significant biological pathways were the regulation of cholesterol reverse transport and the regulation of high-density lipoprotein particle clearance (p < .001). BMI and blood lipid levels were affected by genetic factors, and they were genetically correlated. There might be gender differences in their genetic correlation. Bivariate GWAS analysis found MIR144 gene and its related biological pathways may influence obesity and lipid levels.

We aim to determine the correlation between parental rearing, personality traits, and obsessive–compulsive disorder (OCD) in different quantiles. In particular, we created an intermediary effect model in which parental rearing affects OCD through personality traits. All predictors were measured at the time of the survey, comprising parental rearing (paternal rearing and maternal rearing), demographics (grade and gender), and personality traits (neuroticism, extroversion, and psychoticism). These results suggest that (a) paternal emotional warmth was negatively correlated with OCD at the 0.40–0.80 quantile, while maternal emotional warmth was positively correlated with the OCD at the 0.45–0.69 quantile. (b) The correlation between negative parental rearing and OCD ranged from the 0.67 to 0.95 quantile for paternal punishment, 0.14–0.82 quantile for paternal overprotection, 0.05–0.36 and >0.50 quantile for maternal over-intervention and overprotection, and 0.08–0.88 quantile for maternal rejection. (c) Extroversion, neuroticism, and psychoticism were not only associated with OCD in a particular quantile but also mediated between parental rearing (namely parental emotional warmth, paternal punishment, paternal overprotection, maternal rejection, maternal over-intervention, and overprotection) and OCD. These findings provide targets for early interventions of OCD to improve the form of family education and personality traits and warrant validation.

Data of 2780 Markhoz kids originated from 1216 dams and 211 sires during 1993–2016 in Markhoz Goat Breeding Station, located in Sanandaj, Iran, were used. Traits investigated were body weights at birth, weaning, six-month age [six months weight (6MW)], nine-month age and yearling age [yearling weight (YW)]. Two considered multivariate models including standard multivariate model (SMM) and fully recursive multivariate model (FRM) were compared using deviance information criterion (DIC) and predictive ability measures including mean square of error (MSE) and Pearson's correlation coefficient between the observed and predicted values $(r(y,\hat{y}))$ of records. Spearman's rank correlation coefficients between posterior means of direct genetic effects of the studied traits of kids under SMM and FRM were also calculated across all, 50, 10 and 1% top-ranked animals. In general, FRM performed better than SMM in terms of lower DIC and MSE and also higher $r\lpar y\comma \;\hat{y}\rpar$. For all traits, the lowest MSE and the highest $r\lpar y\comma \;\hat{y}\rpar$ were obtained under FRM. All structural coefficients estimated under FRM were statistically significant except for that of 6MW on YW. Comparisons of Spearman's rank correlations between posterior means of direct genetic effects of kids for growth traits under SMM and FRM revealed that taking the causal relationships among the studied growth traits of Markhoz goat into account may cause considerable re-ranking for the animals in terms of estimated breeding values, especially for the top-ranked animals. It may be concluded that FRM had more plausibility over SMM for genetic evaluation of the studied growth traits in Markhoz goat.

Creating and assessing relatively broad conservation education curricula is important when trying to reach a variety of students. We used a curriculum centred around a storybook in 12 schools in four separate areas of Indonesia, reaching 529 students. We visited each school twice, and taught the ecology and importance of the target taxa, Indonesia’s seven threatened slow loris species (Nycticebus spp.). Through cultural consensus analyses and structural equation modelling, we found that students from all regions showed improvements in knowledge, and that the distance from the forest to where children lived, teachers’ use of given education materials, and students’ use of the storybook all affected student performance in drawing and essay accuracy. Here we make suggestions for creating and evaluating multi-site environmental education programmes. We recommend creating curricula that are not inclusive of any particular community; providing teachers with materials to supplement a conservation intervention; giving each child their own copy of any visual materials used in the lessons; following up with students and teachers about the use of such materials; and interviewing teachers and students regarding their experience with and attitudes towards the study subject. Furthermore we suggest practitioners share their materials and have confidence in adapting them for other species and locations.

Optimization of production factors plays a central role in efficient milk production operations. Causal relationships between production parameters (health, fertility, feeding, performance and farm size) on the one hand and efficiency parameters on the other have been identified in several studies. In recent years, structural equation modelling (SEM) has not only gained importance in agriculture but also in milk production, providing the opportunity to investigate multilateral relationships. Additionally, SEM enables an estimation of parameters which are not themselves measurable, the so-called latent variables. The current study was based on the data of 943 branch settlements (including the years 2012 and 2013) of dairy farms keeping German Holstein cows in Schleswig-Holstein (Northern Germany) which provided a combination of the structural parameters, economic parameters and biological performance of the farms. An SEM using this combined data was applied to investigate the complexity of influences on efficiency parameters in milk production. Efficiency was sub-divided into and evaluated by two effect variables (economic efficiency and biological efficiency). Economic efficiency was defined as a conventional efficiency assessment criterion from full-cost accounting, whereas biological efficiency was used to evaluate the quality of herd management. Performance was identified as the key parameter for independent evaluation of efficiency by assessing biological (γ41 = 0.644) or economic efficiency (γ42 = 0.266). The SEM explained more than three times higher proportion of the variance in biological efficiency than in economic efficiency. The investigation proved the eligibility of partial least squares SEM for the evaluation of efficiency in milk production.

The present study aimed to estimate heritability of Hwabyung (HB) symptoms in adolescent and young adult twins in South Korea. The sample included 1,601 twins consisting of 143 pairs of monozygotic male (MZM), 67 pairs of dizygotic male (DZM), 295 pairs of monozygotic female (MZF), 114 pairs of dizygotic female (DZF), and 117 pairs of opposite-sex dizygotic (OSDZ) twins and 129 twins with non-participating co-twins (mean age = 19.1 ± 3.1 years; range: 12–29 years). An HB symptom questionnaire was given to twins via a telephone interview. Consistent with the literature of HB, the mean level of HB was significantly higher in females than in males. Maximum likelihood twin correlations for HB were 0.31 (95% CI [0.16, 0.45]) for MZM, 0.19 (95% CI [-0.05, 0.41]) for DZM, 0.50 (95% CI [0.41, 0.58]) for MZF, 0.28 (95% CI [0.11, 0.44]) for DZF, and 0.23 (95% CI [0.05, 0.40]) for OSDZ twins. These patterns of twin correlations suggested the presence of additive genetic influences on HB. Model-fitting analysis showed that additive genetic and individual-specific environmental influences on HB were 44% (95% CI [37, 51]) and 56% (95% CI [49, 63]), respectively. Shared environmental influences were not significant. These parameter estimates were not significantly different between two sexes, and did not change significantly with age in the present sample, suggesting that genetic and environmental influences on HB in both sexes are stable across adolescence and young adulthood.

The objectives of this study were to infer phenotypic causal networks involving gestation length (GL) and calving difficulty (CD) for the primiparity of 1850 Japanese Black heifers, and the birth weight (BWT), withers height (WH) and chest girth (CHG) of their full blood calves, and to compare the causal effects among them. The inductive causation (IC) algorithm was employed to search for causal links among these traits; it was applied to the posterior distribution of the residual (co)variance matrix of a multiple-trait sire-maternal grand sire (MGS) model. The IC algorithm implemented with 95% and 90% highest posterior density intervals detected only one structure with links between GL and BWT (WH or CHG) and between BWT (WH or CHG) and CD, although their directions were not resolved. Therefore, a possible causal structure based on the networks obtained from the IC algorithm [GL→BWT (WH or CHG)→CD] was fitted using a structural equation model to infer causal structure coefficients between the traits. The structural coefficients of GL on BWT and of BWT on GL on the observable scale showed that an extra day of GL led to a 270-g gain in BWT, and a 1-kg increase in BWT increased the risk for dystocia by 1.1%, in the causal structure. Similarly, an increase in GL by 1 day resulted in a 2.1 (2.0)-mm growth in WH (CHG), and a 1-cm increase in WH (CHG) increased the risk of dystocia by 1.2% (0.9%). The structural equation model was also fitted to alternative causal structures, which involved the addition of a directed link from GL to CD, or GL→CD to the structures described above. The inferred structural coefficients with the alternative structures were almost the same as the corresponding ones that had GL→BWT (WH or CHG)→CD. However, the direct causal effect of the extra link from GL on CD was similar to the indirect causal effect of GL through the mediating effect of BWT (WH or CHG) on CD and significant (P<0.05). This suggest that maternal genetic effects might not be removed completely from the residual variance components in the sire-MGS model, and the application of the IC algorithm to the variances from the model could detect an incorrect structure. Nonetheless, fitting the structural equation model to the causal structure provided useful information such as the magnitude of the causal effects between the traits.