Identifying dyslexia with confirmatory latent profile analysis

Confirmatory latent profile analysis (CLPA) was used with the normative sample from the Kaufman Test of Educational Achievement, 3rd ed. (KTEA‐3) to determine whether it was possible to identify a latent class of individuals whose scores were consistent with the academic strengths and weaknesses related to dyslexia. The CLPA identified a class of individuals consistent with dyslexia across four‐grade level groups (first–second, third–fifth, sixth–eighth, and ninth–twelfth). The results of the CLPA were applied to the KTEA‐3 clinical samples of those with known clinical diagnoses. Individuals with Specific Learning Disorder in Reading and/or Written Expression had a higher probability of being in the dyslexia latent class. The use of CLPA as a tool for learning disability diagnosis appears plausible, though much more research is needed. The strengths, limitations, and future directions for the use of CLPA in diagnosis are discussed.     

Covariates and Mixture Modeling: Results of a Simulation Study Exploring the Impact of Misspecified Effects on Class Enumeration

For some time, there have been differing recommendations about how and when to include covariates in the mixture model building process. Some have advocated the inclusion of covariates after enumeration, whereas others recommend including them early on in the modeling process. These conflicting recommendations have led to inconsistent practices and unease in trusting modeling results. In an attempt to resolve this discord, we conducted a Monte Carlo simulation to examine the impact of covariate exclusion and misspecification of covariate effects on the enumeration process. We considered population and analysis models with both direct and indirect paths from the covariates to the latent class indicators. As expected, misspecified covariate effects most commonly led to the overextraction of classes. Findings suggest that the number of classes could be reliably determined using the unconditional latent class model, thus our recommendation is that class enumeration be done prior to the inclusion of covariates.     

A Comparison of Three-Step Approaches for Auxiliary Variables in Latent Class and Latent Profile Analysis

In this article, 3-step methods to include predictors and distal outcomes in commonly used mixture models are evaluated. Two Monte Carlo simulation studies were conducted to compare the pseudo class (PC), Vermunt’s (2010), and the Lanza, Tan, and Bray (LTB) 3-step approaches with respect to bias of parameter estimates in latent class analysis (LCA) and latent profile analysis (LPA) models with auxiliary variables. For coefficients of predictors of class membership, results indicated that Vermunt’s method yielded more accurate estimates for LCA and LPA compared to the PC method. With distal outcomes of latent classes and latent profiles, the LTB method produced the lowest relative bias of coefficient estimates and Type I error rates close to nominal levels.     

A Note on Cluster Effects in Latent Class Analysis

This article examines the effects of clustering in latent class analysis. A comprehensive simulation study is conducted, which begins by specifying a true multilevel latent class model with varying within- and between-cluster sample sizes, varying latent class proportions, and varying intraclass correlations. These models are then estimated under the assumption of a single-level latent class model. The outcomes of interest are measures of bias in the Bayesian Information Criterion (BIC) and the entropy R ² statistic relative to accounting for the multilevel structure of the data. The results indicate that the size of the intraclass correlation as well as between- and within-cluster sizes are the most prominent factors in determining the amount of bias in these outcome measures, with increasing intraclass correlations combined with small between-cluster sizes resulting in increased bias. Bias is particularly noticeable in the BIC. In addition, there is evidence that class separation interacts with the size of the intraclass correlations and cluster sizes in producing bias in these measures.     

Robustness of Stepwise Latent Class Modeling With Continuous Distal Outcomes

Recently, several bias-adjusted stepwise approaches to latent class modeling with continuous distal outcomes have been proposed in the literature and implemented in generally available software for latent class analysis. In this article, we investigate the robustness of these methods to violations of underlying model assumptions by means of a simulation study. Although each of the 4 investigated methods yields unbiased estimates of the class-specific means of distal outcomes when the underlying assumptions hold, 3 of the methods could fail to different degrees when assumptions are violated. Based on our study, we provide recommendations on which method to use under what circumstances. The differences between the various stepwise latent class approaches are illustrated by means of a real data application on outcomes related to recidivism for clusters of juvenile offenders.     

A General 3-Step Maximum Likelihood Approach to Estimate the Effects of Multiple Latent Categorical Variables on a Distal Outcome

The 3-step approach has been recently advocated over the simultaneous 1-step approach to model a distal outcome predicted by a latent categorical variable. We generalize the 3-step approach to situations where the distal outcome is predicted by multiple and possibly associated latent categorical variables. Although the simultaneous 1-step approach has been criticized, simulation studies have found that the performance of the two approaches is similar in most situations (Bakk & Vermunt, 2016). This is consistent with our findings for a 2-LV extension when all model assumptions are satisfied. Results also indicate that under various degrees of violation of the normality and conditional independence assumption for the distal outcome and indicators, both approaches are subject to bias but the 3-step approach is less sensitive. The differences in estimates using the two approaches are illustrated in an analysis of the effects of various childhood socioeconomic circumstances on body mass index at age 50.     

Building Latent Class Growth Trees

Researchers use latent class growth (LCG) analysis to detect meaningful subpopulations that display different growth curves. However, especially when the number of classes required to obtain a good fit is large, interpretation of the encountered class-specific curves might not be straightforward. To overcome this problem, we propose an alternative way of performing LCG analysis, which we call LCG tree (LCGT) modeling. For this purpose, a recursive partitioning procedure similar to divisive hierarchical cluster analysis is used: Classes are split until a certain criterion indicates that the fit does not improve. The advantage of the LCGT approach compared to the standard LCG approach is that it gives a clear insight into how the latent classes are formed and how solutions with different numbers of classes relate. The practical use of the approach is illustrated using applications on drug use during adolescence and mood regulation during the day.     

A metric measure for direct comparison of competing models in covariance structure analysis

Comparing the fit of alternative models has become a standard procedure for analyzing covariance structure analysis. Comparison of alternative models is typically accomplished by examining the fit of each model to sample data. It is argued that rather than using this indirect approach, one should do direct comparisons of the similarities and differences among competing models. It is shown that among the existing good‐ness‐of‐fit indexes, the root mean square residual (RMSR) is the only one that can be used for this purpose. However, the RMSR fails to satisfy some important statistical desiderata. Rao's Distance (RD), an alternate measure, is shown to overcome this limitation of RMSR. The preference for RD over RMSR for model comparisons is illustrated through a detailed analysis of a particular sample of multitrait‐multimethod data. A simulation study conducted to empirically investigate the sampling behavior of RD reveals that the true orderings of intermodel proximities are recovered (on average) with a fair degree of accuracy.     

Relating Latent Class Membership to Continuous Distal Outcomes: Improving the LTB Approach and a Modified Three-Step Implementation

Latent class analysis often aims to relate the classes to continuous external consequences (“distal outcomes”), but estimating such relationships necessitates distributional assumptions. Lanza, Tan, and Bray (2013) suggested circumventing such assumptions with their LTB approach: Linear logistic regression of latent class membership on each distal outcome is first used, after which this estimated relationship is reversed using Bayes’ rule. However, the LTB approach currently has 3 drawbacks, which we address in this article. First, LTB interchanges the assumption of normality for one of homoskedasticity, or, equivalently, of linearity of the logistic regression, leading to bias. Fortunately, we show introducing higher order terms prevents this bias. Second, we improve coverage rates by replacing approximate standard errors with resampling methods. Finally, we introduce a bias-corrected 3-step version of LTB as a practical alternative to standard LTB. The improved LTB methods are validated by a simulation study, and an example application demonstrates their usefulness.     

Psychosocial factors impacting STEM career selection

Attention on P-20 science, technology, engineering, and mathematics (STEM) education has increased tremendously in recent years. Many efforts are underway to promote STEM major and career selection across the nation; specifically, in engineering and computer science. The authors' purpose was to examine an underlying profile combinations of latent traits that influence student STEM career selection while designing serious educational games (SEGs). The authors combine a number of quantitative analysis methods in an effort to develop a rich understanding of how a profile combination of traits interact with one another to effect selection of STEM careers and majors. Study participants were 585 students enrolled in a full-time traditional high school. The addition of SEG design experiences into the student profile increases the probability of STEM career selection by 5.1 times.     

Bias-Adjusted Three-Step Latent Markov Modeling With Covariates

Latent Markov models with covariates can be estimated via 1-step maximum likelihood. However, this 1-step approach has various disadvantages, such as that the inclusion of covariates in the model might alter the formation of the latent states and that parameter estimation could become infeasible with large numbers of time points, responses, and covariates. This is why researchers typically prefer performing the analysis in a stepwise manner; that is, they first construct the measurement model, then obtain the latent state classifications, and subsequently study the relationship between covariates and latent state memberships. However, such a stepwise approach yields downward-biased estimates of the covariate effects on initial state and transition probabilities. This article, shows how to overcome this problem using a generalization of the bias-corrected 3-step estimation method proposed for latent class analysis (Asparouhov & Muthén, 2014; Bolck, Croon, & Hagenaars, 2004; Vermunt, 2010). We give a formal derivation of the generalization to latent Markov models and discuss how it can be used with many time points by incorporating it into a Baum–Welch type of expectation-maximization algorithm. We evaluate the method through a simulation study and illustrate it using an application on household financial portfolio change. Our study shows that the proposed correction method yields unbiased parameter estimates and accurate standard errors, except for situations with very poorly separated classes and a small sample.     

Exploratory Structural Equation Modeling

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as well as sample reallocation to latent classes. The results show that the clarity of remaining latent classes, as measured by the entropy statistic depends on the number of observations in the omitted latent class—but this statistic is not reliable. Specification error in the latent Markov model focuses on the transition probabilities when a longitudinal Guttman process is incorrectly specified. The findings show that specifying a longitudinal Guttman process that is not true in the population impacts other transition probabilities through the covariance matrix of the logit parameters used to calculate those probabilities.     

A new perspective on memorization practices among East Asian students based on PISA 2012

Abstract

This study examined learning strategy use in mathematics among East Asian students in East Asian educational systems. By employing latent class analysis on the Programme for International Student Assessment (PISA) 2012 data, we found four classes of learning strategy types, namely memorization with metacognitive strategies (17.49%), metacognitive strategies with memorization (50.70%), elaboration only (10.33%), and metacognitive strategies with elaboration (16.47%). The results showed that the majority of the students in all seven East Asian educational systems belonged to the ‘metacognitive strategies with memorization’ class, and most students adopted more than one type of learning strategy when learning mathematics. Additionally, students who reported the use of metacognitive strategies along with either memorization or elaboration showed higher mathematics achievement. We conclude that the cognitive processes employed by students of East Asian backgrounds are more complex and nuanced than the previous perception that they relied heavily on memorization.     

Are young dual language learners homogeneous? Identifying subgroups using latent class analysis

Although dual language learners (DLLs) are linguistically, culturally, and socially diverse, researchers usually study them in aggregate and compare them to non-DLLs. The authors' purpose was to identify subgroups of preschool DLLs using latent class analysis. There were 7,361 DLLs and 69,457 non-DLLs. Results revealed three distinct classes. Children in class 1 (emergent bilingual children) tended to speak mostly their native language but some English at home and in the classroom. Children in class 2 (bilingual children) tended to speak English only in the classroom, but spoke both languages at home. Children in class 3 (heritage language speakers) tended to speak only their native language at home and in the classroom. Different demographic profiles and levels of development and learning were observed across classes. The DLL subgroups and their profiles provide important information about how educational programs may be tailored to meet the diverse needs of young DLLs.     

Performance of the Grade of Membership Model Under a Variety of Sample Sizes,Group Size Ratios,and Differential Group Response Probabilities for Dichotomous Indicators

Social scientists are frequently interested in identifying latent subgroups within the population, based on a set of observed variables. One of the more common tools for this purpose is latent class analysis (LCA), which models a scenario involving k finite and mutually exclusive classes within the population. An alternative approach to this problem is presented by the grade of membership (GoM) model, in which individuals are assumed to have partial membership in multiple population subgroups. In this respect, it differs from the hard groupings associated with LCA. The current Monte Carlo simulation study extended on prior work on the GoM by investigating its ability to recover underlying subgroups in the population for a variety of sample sizes, latent group size ratios, and differing group response profiles. In addition, this study compared the performance of GoM with that of LCA. Results demonstrated that when the underlying process conforms to the GoM model form, the GoM approach yielded more accurate classification results than did LCA. In addition, it was found that the GoM modeling paradigm yielded accurate results for samples as small as 200, even when latent subgroups were very unequal in size. Implications for practice were discussed.     

Finite Feedback Cycling in Structural Equation Models

In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few effect cycles, many coefficient estimates are substantially biased. If the world permits additional partial-cycle use in addition to full cyclings around the causal loop, some of the effect estimates are proper, and a full set of proper effect estimates can be recovered by hand calculations involving the model total effects. If the world permits no additional partial-cycle use, it might not be possible to recover proper estimates from the usual output.

It is not the equations representing the causal model, but rather the calculations of the covariance implications of the model, that change with limited cycling possibilities. Unfortunately, the features required to permit direct estimation of limited-cycle effects are not under user control in common structural equation programs, so estimation and detailed investigation of models with finite cycling of effects around feedback loops awaits new programming. To obtain unbiased estimates with limited causal cyclings, the researcher must continue to strive to specify the proper effect locations but must also attend to the number of full and partial causal cyclings permitted by the world. Determining the appropriate number of cycles is not a matter to be delegated to a statistician; it is something the researcher must attend to as a matter of substantive theory, methodology, and model interpretation.     

Latent Class Analysis for Multiple Discrete Latent Variables: A Study on the Association Between Violent Behavior and Drug-Using Behaviors

This article proposes a new type of latent class analysis, joint latent class analysis (JLCA), which provides a set of principles for the systematic identification of the subsets of joint patterns for multiple discrete latent variables. Inferences about the parameters are obtained by a hybrid method of expectation-maximization and Newton–Raphson algorithms. We apply JLCA in an investigation of adolescent violent behavior and drug-using behaviors. The data are from 4,957 male high-school students who participated in the Youth Risk Behavior Surveillance System in 2015. The JLCA approach identifies the different joint patterns of 4 latent variables: violent behavior, alcohol consumption, tobacco cigarette smoking, and other drug use. The JLCA uncovers 4 common violent behaviors and 3 representative behavioral patterns for each of 3 other latent variables. In addition, the JLCA supports 3 common joint classes, representing the most probable simultaneous patterns for being violent and being a drug user among adolescent males.     

Modeling Unobserved Heterogeneity Using Latent Profile Analysis: A Monte Carlo Simulation

Latent profile analysis (LPA) has become a popular statistical method for modeling unobserved population heterogeneity in cross-sectionally sampled data, but very few empirical studies have examined the question of how well enumeration indexes accurately identify the correct number of latent profiles present. This Monte Carlo simulation study examined the ability of several classes of enumeration indexes to correctly identify the number of latent population profiles present under 3 different research design conditions: sample size, the number of observed variables used for LPA, and the separation distance among the latent profiles measured in Mahalanobis D units. Results showed that, for the homogeneous population (i.e., the population has k = 1 latent profile) conditions, many of the enumeration indexes used in LPA were able to correctly identify the single latent profile if variances and covariances were freely estimated. However, for a heterogeneous population (i.e., the population has k = 3 distinct latent profiles), the correct identification rate for the enumeration indexes in the k = 3 latent profile conditions was typically very low. These results are compared with the previous cross-sectional mixture modeling studies, and the limitations of this study, as well as future cross-sectional mixture modeling and enumeration index research possibilities, are discussed.     

Exploratory Structural Equation Modeling,Integrating CFA and EFA: Application to Students' Evaluations of University Teaching

This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching (SETs). For these data, there is a well established ESEM structure but typical CFA models do not fit the data and substantially inflate correlations among the nine SET factors (median rs = .34 for ESEM, .72 for CFA) in a way that undermines discriminant validity and usefulness as diagnostic feedback. A 13-model taxonomy of ESEM measurement invariance is proposed, showing complete invariance (factor loadings, factor correlations, item uniquenesses, item intercepts, latent means) over multiple groups based on the SETs collected in the first and second halves of a 13-year period. Fully latent ESEM growth models that unconfounded measurement error from communality showed almost no linear or quadratic effects over this 13-year period. Latent multiple indicators multiple causes models showed that relations with background variables (workload/difficulty, class size, prior subject interest, expected grades) were small in size and varied systematically for different ESEM SET factors, supporting their discriminant validity and a construct validity interpretation of the relations. A new approach to higher order ESEM was demonstrated, but was not fully appropriate for these data. Based on ESEM methodology, substantively important questions were addressed that could not be appropriately addressed with a traditional CFA approach.