Nonlinear Indicator-Level Moderation in Latent Variable Models

Linear, nonlinear, and nonparametric moderated latent variable models have been developed to investigate possible interaction effects between a latent variable and an external continuous moderator on the observed indicators in the latent variable model. Most moderation models have focused on moderators that vary across persons but not across the indicators (e.g., moderators like age and socioeconomic status). However, in many applications, the values of the moderator may vary both across persons and across indicators (e.g., moderators like response times and confidence ratings). Indicator-level moderation models are available for categorical moderators and linear interaction effects. However, these approaches require respectively categorization of the continuous moderator and the assumption of linearity of the interaction effect. In this article, parametric nonlinear and nonparametric indicator-level moderation methods are developed. In a simulation study, we demonstrate the viability of these methods. In addition, the methods are applied to a real data set pertaining to arithmetic ability.     

Selection Between Linear Factor Models and Latent Profile Models Using Conditional Covariances

A method for selecting between K-dimensional linear factor models and (K + 1)-class latent profile models is proposed. In particular, it is shown that the conditional covariances of observed variables are constant under factor models but nonlinear functions of the conditioning variable under latent profile models. The performance of a convenient inferential method suggested by the main result is examined via data simulation and is shown to have acceptable error rate control when deciding between the 2 types of models. The proposed test is illustrated using examples from vocational assessment and developmental psychology.     

Two-Step Estimation of Models Between Latent Classes and External Variables

We consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables. We propose a two-step method of estimating such models. In its first step, the measurement model is estimated alone, and in the second step the parameters of this measurement model are held fixed when the structural model is estimated. Simulation studies and applied examples suggest that the two-step method is an attractive alternative to existing one-step and three-step methods. We derive estimated standard errors for the two-step estimates of the structural model which account for the uncertainty from both steps of the estimation, and show how the method can be implemented in existing software for latent variable modelling.     

A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses

The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models.     

The Recovery of Correlation Between Latent Abilities Using Compensatory and Noncompensatory Multidimensional IRT Models

This research examined correlation estimates between latent abilities when using the two-dimensional and three-dimensional compensatory and noncompensatory item response theory models. Simulation study results showed that the recovery of the latent correlation was best when the test contained 100% of simple structure items for all models and conditions. When a test measured weakly discriminated dimensions, it became harder to recover the latent correlation. Results also showed that increasing the sample size, test length, or using simpler models (i.e., two-parameter logistic rather than three-parameter logistic, compensatory rather than noncompensatory) could improve the recovery of latent correlation.     

Abstract: Inference and Interval Estimation for Indirect Effects With Latent Variable Models

Models specifying indirect effects (or mediation) and structural equation modeling are both popular in the social sciences. Yet relatively little research has compared methods that test for indirect effects among latent variables and provided precise estimates of the effectiveness of different methods.

This simulation study provides an extensive comparison of methods for constructing confidence intervals and for making inferences about indirect effects with latent variables. We compared the percentile (PC) bootstrap, bias-corrected (BC) bootstrap, bias-corrected accelerated (BC _a ) bootstrap, likelihood-based confidence intervals (Neale & Miller, 1997), partial posterior predictive (Biesanz, Falk, and Savalei, 2010), and joint significance tests based on Wald tests or likelihood ratio tests. All models included three reflective latent variables representing the independent, dependent, and mediating variables. The design included the following fully crossed conditions: (a) sample size: 100, 200, and 500; (b) number of indicators per latent variable: 3 versus 5; (c) reliability per set of indicators: .7 versus .9; (d) and 16 different path combinations for the indirect effect (α = 0, .14, .39, or .59; and β = 0, .14, .39, or .59). Simulations were performed using a WestGrid cluster of 1680 3.06GHz Intel Xeon processors running R and OpenMx.

Results based on 1,000 replications per cell and 2,000 resamples per bootstrap method indicated that the BC and BC _a bootstrap methods have inflated Type I error rates. Likelihood-based confidence intervals and the PC bootstrap emerged as methods that adequately control Type I error and have good coverage rates.     

An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables

It is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations: The negative logarithm of the correlations satisfies the triangle inequality. This inequality is not implied by the condition that the correlations are nonnegative, the criterion that coefficient H exceeds 0.30, or manifest monotonicity. The inequality implies both a lower bound and an upper bound for each correlation between two items, based on the correlations of those two items with every possible third item. It is discussed how this can be used in Mokken’s (A theory and procedure of scale-analysis, Mouton, The Hague, 1971) scale analysis.     

The Relation Between Chosen Role Models and the Self-Esteem of Men and Women

This study was designed to investigate choice of role models and levels of self-esteem within a sample of college students (N = 120). Participants rated themselves and their chosen role models on 29 character traits, which allowed determination of the self-perceived likeness of the participant to their role models (difference score). The difference score was then correlated with four subtypes of self-esteem. As predicted, participants chose more same-sex than other-sex role models; women were more likely than men to choose other-sex role models. The results indicated that choice of same-sex, as opposed to other-sex role models, is not indicative of higher levels of self-esteem in general. However, self-perceived likeness of role model to participant is significantly related to self-esteem, particularly for women.     

The Consequences of Ignoring Variability in Measurement Occasions Within Data Collection Waves in Latent Growth Models

In longitudinal data collection, it is common that each wave of collection spans several months. However, researchers using latent growth models commonly ignore variability in data collection occasions within a wave. In this study, we investigated the consequences of ignoring within-wave variability in measurement occasions using a Monte Carlo simulation and an empirical study. The results of the simulation study showed that ignoring heterogeneity resulted in biased estimates for some parameters, especially when heterogeneity was large and assessment dates had a skewed distribution. Models constructed on person-specific time points yielded precise estimates and more adequate model fit. In the empirical study, we demonstrated different time coding strategies with a subsample taken from Early Childhood Longitudinal Study Kindergarten Cohort.     

The Role of Conditional Likelihoods in Latent Variable Modeling

Psychometrika - In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we...     

On the Relation Between the Linear Factor Model and the Latent Profile Model

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the unconditional covariances. In particular, a 2-class latent profile model with Gaussian components underestimates the observed covariances but not the variances, when the data are consistent with a unidimensional Gaussian factor model. In explanation of this phenomenon we provide some results relating the unconditional covariances to the goodness of fit of the latent profile model, and to its excess multivariate kurtosis. The analysis also leads to some useful parameter restrictions related to symmetry.     

Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models

Psychometrika - When latent variables are used as outcomes in regression analysis, a common approach that is used to solve the ignored measurement error issue is to take a multilevel perspective on...     

High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance

Psychometrika - The existence of differences in prediction systems involving test scores across demographic groups continues to be a thorny and unresolved scientific, professional, and societal...     

Evaluating the Viability of Neurocognition as a Transdiagnostic Construct Using Both Latent Variable Models and Network Analysis

Research on Child and Adolescent Psychopathology - The relational structure of psychological symptoms and disorders is of crucial importance to mechanistic and causal research. Methodologically,...     

Nonlinear and Quasi-Simplex Patterns in Latent Growth Models

In the SEM literature, simplex and latent growth models have always been considered competing approaches for the analysis of longitudinal data, even if they are strongly connected and both of specific importance. General dynamic models, which simultaneously estimate autoregressive structures and latent curves, have been recently proposed in the literature. We discuss the properties of Autoregressive Latent Trajectories (ALT) with the aim of deriving their relationship with nonlinear growth models. We show how the quasi-simplex part of the ALT admits an equivalent nonlinear growth representation. A simulation study is performed to examine how the relationship holds in the presence of polynomial and bounded growths over time, whereas an empirical application on student achievement highlights the usefulness of the equivalence. The evaluation of the formative process in the European University system has been assuming an ever increasing importance since the beginning of the Bologna process. In this context, the analysis of student performances and capabilities using different approaches plays a fundamental role.     

The Effects of Educational Diversity in a National Sample of Law Students: Fitting Multilevel Latent Variable Models in Data With Categorical Indicators

Controversy surrounding the use of race-conscious admissions can be partially resolved with improved empirical knowledge of the effects of racial diversity in educational settings. We use a national sample of law students nested in 64 law schools to test the complex and largely untested theory regarding the effects of educational diversity on student outcomes. Social scientists who study these outcomes frequently encounter both latent variables and nested data within a single analysis. Yet, until recently, an appropriate modeling technique has been computationally infeasible, and consequently few applied researchers have estimated appropriate models to test their theories, sometimes limiting the scope of their research question. Our results, based on disaggregated multilevel structural equation models, show that racial diversity is related to a reduction in prejudiced attitudes and increased perceived exposure to diverse ideas and that these effects are mediated by more frequent interpersonal contact with diverse peers. These findings provide support for the idea that administrative manipulation of educational diversity may lead to improved student outcomes. Admitting a racially/ethnically diverse student body provides an educational experience that encourages increased exposure to diverse ideas and belief systems.     

The Relation Between Factual and Counterfactual Conditionals

What is the relation between factual conditionals: If A happened then B happened, and counterfactual conditionals: If A had happened then B would have happened? Some theorists propose quite different semantics for the two. In contrast, the theory of mental models and its computer implementation interrelates them. It postulates that both can have a priori truth values, and that the semantic bases of both are possibilities: states that are possible for factual conditionals, and that were once possible but that did not happen for counterfactual conditionals. Two experiments supported these relations. Experiment 1 showed that, like factual conditionals, certain counterfactuals are true a priori, and others are false a priori. Experiment 2 replicated this result and showed that participants selected appropriate paraphrases, referring, respectively, to real and to counterfactual possibilities, for the two sorts of conditional. These results are contrary to alternative accounts of conditionals.     

Typing Speed as a Confounding Variable and the Measurement of Quality in Divergent Thinking

The need to control for writing or typing speed when assessing divergent-thinking performance has been recognized since the early ‘90s. An even longer tradition in divergent-thinking research has the issue of scoring the responses for quality. This research addressed both issues within structural equation modeling. Three dimensions of originality—uncommonness, remoteness, and cleverness—were used to derive an overall quality score. Mixed evidence was found in Study 1 for the direct effect of typing speed on fluency. In addition, indirect effects of typing speed via cognitive complexity on overall quality of ideas were uncovered but marginal in both Study 1 and Study 2. This indirect effect was also found for cleverness in Study 2. Another indirect effects of typing speed via fluency was found for cleverness and uncommonness. These findings indicate that controlling for typing speed is important in online divergent-thinking assessment. The inter-relations of various quality scores pertaining to the dimensions of uncommonness, remoteness, and cleverness were promising in terms of convergent validity. Important problems with respect to these scores were identified and discussed to guide future attempts to measure quality in DT.     

童年中晚期友谊质量与抑郁的关系:一项纵向研究

以友谊质量问卷和儿童抑郁量表为研究工具,对小学3到4年级847名儿童进行了18个月的追踪研究,采用交叉滞后的研究设计,考察了童年中晚期友谊质量与抑郁的关系。结果表明：（1）同一时间点的友谊质量和抑郁之间呈显著的负相关;（2）早期的友谊质量可以显著预测随后的抑郁,早期的抑郁也可以显著预测随后的友谊质量,且相对于友谊质量对抑郁的积极作用,抑郁对儿童友谊质量的瓦解作用更为突出;（3）童年中晚期友谊质量与抑郁的双向作用关系具有跨性别稳定性。     

The Relation Between Self-Continuity and Measures of Identity

Conceptualizations of Erikson's (1968) fifth psychosocial stage, identity formation, have been criticized for failing to be inclusive of an individual's sense of self-continuity. However, recent research has shown that identity commitment is significantly correlated to measures of continuity. This study further examined the relation among measures of identity, including identity commitment and continuity. The results suggest that many of the current measures of identity do indeed share a significant amount of variance with continuity. The specific results concerning identity commitment and continuity add to the growing evidence that these constructs are reliably related.