A general non-linear multilevel structural equation mixture model

Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models

We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented. First, we show how GALAMMs can jointly model the complex lifespan trajectories of episodic memory, working memory, and speed/executive function, measured by the California Verbal Learning Test (CVLT), digit span tests, and Stroop tests, respectively. Next, we study the effect of socioeconomic status on brain structure, using data on education and income together with hippocampal volumes estimated by magnetic resonance imaging. By combining semiparametric estimation with latent variable modeling, GALAMMs allow a more realistic representation of how brain and cognition vary across the lifespan, while simultaneously estimating latent traits from measured items. Simulation experiments suggest that model estimates are accurate even with moderate sample sizes.

Automated Bot Detection Using Bayesian Latent Class Models in Online Surveys

Behavioral scientists have become increasingly reliant on online survey platforms such as Amazon's Mechanical Turk (Mturk). These platforms have many advantages, for example it provides ease of access to difficult to sample populations, a large pool of participants, and an easy to use implementation. A major drawback is the existence of bots that are used to complete online surveys for financial gain. These bots contaminate data and need to be identified in order to draw valid conclusions from data obtained with these platforms. In this article, we will provide a Bayesian latent class joint modeling approach that can be routinely applied to identify bots and simultaneously estimate a model of interest. This method can be used to separate the bots' response patterns from real human responses that were provided in line with the item content. The model has the advantage that it is very flexible and is based on plausible assumptions that are met in most empirical settings. We will provide a simulation study that investigates the performance of the model under several relevant scenarios including sample size, proportion of bots, and model complexity. We will show that ignoring bots will lead to severe parameter bias whereas the Bayesian latent class model results in unbiased estimates and thus controls this source of bias. We will illustrate the model and its capabilities with data from an empirical political ideation survey with known bots. We will discuss the implications of the findings with regard to future data collection via online platforms.

A Comparison of Penalized Maximum Likelihood Estimation and Markov Chain Monte Carlo Techniques for Estimating Confirmatory Factor Analysis Models With Small Sample Sizes

With small to modest sample sizes and complex models, maximum likelihood (ML) estimation of confirmatory factor analysis (CFA) models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood (PML) estimation, and the mean (EAP), median (Med), or mode (MAP) of the marginal posterior distribution that are calculated by using Markov Chain Monte Carlo (MCMC) methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error (RMSE). We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research.

Academic Stress and Adolescents Mental Health: A Multilevel Structural Equation Modeling (MSEM) Study in Northwest of Iran

Background: We aimed to determine the relation of different sources of academic stress and adolescents´ mental health through mediator variables on the student and school levels.

Study design: A cross-sectional study.

Methods: Overall, 1724 students aged 12-19 yr were selected from 53 high schools in Qazvin City, northwest instead of central Iran through stratified cluster sampling. The sources of academic stress include family conditions, education system, future concerns, academic competitions, interaction with teachers, school disciplines, peer pressure, parental involvement, and financial problems. Academic self-efficacy and self-concept were the mediator constructs. The students and schools´ information were considered on levels 1 and 2, respectively. A Multilevel Structural Equation Modeling (MSEM) analysis was done.

Results: High value of academic stress was associated with reduction of mental health. On the student level, the academic stress caused by the families 0.31 (95% CI: 0.28, 0.34), peers 0.29 (95% CI: 0.27, 0.32), and the education system 0.21 (95% CI: 0.18, 0.24) had the highest impact on the adolescentsˊ mental health, respectively. There was a direct and indirect relation between academic stress and mental health through the self-concept. On the school level, only family conditions stress had a relation with mental health (P=0.015, b=1.08). Academic self-efficacy showed no significant relation in the model.

Conclusion: The stress from the family is the most important source of stress associated with adolescent mental health. Self-concept unlike academic self-efficacy had an important mediating role in the relation between different sources of academic stress and adolescents' mental health.

A two-stage estimation procedure for non-linear structural equation models

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. In this article, we introduce a simple two-stage estimation technique for estimation of non-linear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the non-linear effect are predicted by their conditional means. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modeled using restricted cubic splines, and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to MLE and alternative two-stage estimation techniques.

A More Efficient Causal Mediator Model Without the No-Unmeasured-Confounder Assumption

Mediator models have been developed primarily under the assumption of no-unmeasured-confounding. In many situations, this assumption is violated and may lead to the identification of mediator variables that actually are statistical artifacts. The rank preserving model (RPM) is an alternative approach to estimate controlled direct and mediator effects. It is based on the structural mean models framework and a no-effect-modifier assumption. The RPM assumes that unobserved confounders do not interact with treatment or mediators. This assumption is often more plausible to hold than the no-unmeasured-confounder assumption. So far, models using the no-effect-modifier assumption have been rarely used, which might be due to its low power and inefficiency in many scenarios. Here, a semi-parametric nonlinear extension, the nRPM, is proposed that overcomes this inefficiency using thin plate regression splines that both increase the predictive power of the model and decrease the misspecification present in many situations. In a simulation study, it is shown that the nRPM provides estimates that are robust against the violation of the no-effect-modifier assumption and that are substantively more efficient than those of the RPM. The model is illustrated using a data set on CD4 cell counts in a context of the human immunodeficiency virus (HIV).

Modeling Psychological Attributes in Psychology - An Epistemological Discussion: Network Analysis vs. Latent Variables

Network Analysis is considered as a new method that challenges Latent Variable models in inferring psychological attributes. With Network Analysis, psychological attributes are derived from a complex system of components without the need to call on any latent variables. But the ontological status of psychological attributes is not adequately defined with Network Analysis, because a psychological attribute is both a complex system and a property emerging from this complex system. The aim of this article is to reappraise the legitimacy of latent variable models by engaging in an ontological and epistemological discussion on psychological attributes. Psychological attributes relate to the mental equilibrium of individuals embedded in their social interactions, as robust attractors within complex dynamic processes with emergent properties, distinct from physical entities located in precise areas of the brain. Latent variables thus possess legitimacy, because the emergent properties can be conceptualized and analyzed on the sole basis of their manifestations, without exploring the upstream complex system. However, in opposition with the usual Latent Variable models, this article is in favor of the integration of a dynamic system of manifestations. Latent Variables models and Network Analysis thus appear as complementary approaches. New approaches combining Latent Network Models and Network Residuals are certainly a promising new way to infer psychological attributes, placing psychological attributes in an inter-subjective dynamic approach. Pragmatism-realism appears as the epistemological framework required if we are to use latent variables as representations of psychological attributes.

The EffectLiteR Approach for Analyzing Average and Conditional Effects

We present a framework for estimating average and conditional effects of a discrete treatment variable on a continuous outcome variable, conditioning on categorical and continuous covariates. Using the new approach, termed the EffectLiteR approach, researchers can consider conditional treatment effects given values of all covariates in the analysis and various aggregates of these conditional treatment effects such as average effects, effects on the treated, or aggregated conditional effects given values of a subset of covariates. Building on structural equation modeling, key advantages of the new approach are (1) It allows for latent covariates and outcome variables; (2) it permits (higher order) interactions between the treatment variable and categorical and (latent) continuous covariates; and (3) covariates can be treated as stochastic or fixed. The approach is illustrated by an example, and open source software EffectLiteR is provided, which makes a detailed analysis of effects conveniently accessible for applied researchers.

The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data

The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application). Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models. The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000). We show that it is necessary to take nonnormality of the data into account for a correct standardization. We present an empirical example from education science applying the proposed procedure.