Estimating Latent Variable Interactions with the Unconstrained Approach: A Comparison of Methods to Form Product Indicators for Large,Unequal Numbers of Items

This Monte Carlo simulation study investigated methods of forming product indicators for the unconstrained approach for latent variable interaction estimation when the exogenous factors are measured by large and unequal numbers of indicators. Product indicators were created based on multiplying parcels of the larger scale by indicators of the smaller scale, multiplying the three most reliable indicators of each scale matched by reliability, and matching items by reliability to create as many product indicators as the number of indicators of the smallest scale. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. All methods considered provided unbiased parameter estimates. Unbiased standard errors were obtained in all conditions with the LMS approach and when the sample size was large with the unconstrained approach. Power levels to test the latent interaction and Type I error rates were similar for all methods but slightly better for the LMS approach.     

Conducting Confirmatory Latent Class Analysis Using Mplus

Latent class analysis (LCA) is an increasingly popular tool that researchers can use to identify latent groups in the population underlying a sample of responses to categorical observed variables. LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when very little prior research has been conducted in the area under study, it can be very limiting when much is already known about the variables and population. Confirmatory latent class analysis (CLCA) provides researchers with a tool for modeling and testing specific hypotheses about response patterns in the observed variables. CLCA is based on placing specific constraints on the parameters to reflect these hypotheses. The popular and easy-to-use latent variable modeling software package Mplus can be used to conduct a variety of CLCA types using these parameter constraints. This article focuses on the basic principles underlying the use of CLCA, and the Mplus programming code necessary for carrying it out.     

Statistical Power of the Multiple Domain Latent Growth Model for Detecting Group Differences

The latent growth model (LGM) in structural equation modeling (SEM) may be extended to allow for the modeling of associations among multiple latent growth trajectories, resulting in a multiple domain latent growth model (MDLGM). While the MDLGM is conceived as a more powerful multivariate analysis technique, the examination of its methodological performance is very limited. Hence, the present study compared the power of the MDLGM with that of a set of univariate LGMs for detecting group differences in growth rates over time using a Monte Carlo study with a two-group and two-domain design. The results indicated that there were different scenarios where the power rates for the MDLGM were greater than that of the set of LGMs (and vice versa) due to a joint function of the two domains’ intercorrelation size and the group difference effect size.     

Latent Curve Models and Latent Change Score Models Estimated in R

When using multiple imputation in the analysis of incomplete data, a prominent guideline suggests that more than 10 imputed data values are seldom needed. This article calls into question the optimism of this guideline and illustrates that important quantities (e.g., p values, confidence interval half-widths, and estimated fractions of missing information) suffer from substantial imprecision with a small number of imputations. Substantively, a researcher can draw categorically different conclusions about null hypothesis rejection, estimation precision, and missing information in distinct multiple imputation runs for the same data and analysis with few imputations. This article explores the factors associated with this imprecision, demonstrates that precision improves by increasing the number of imputations, and provides practical guidelines for choosing a reasonable number of imputations to reduce imprecision for each of these quantities.     

Testing Time-Invariance of Variable Specificity in Repeated Measure Designs Using Structural Equation Modeling

A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term associated with repeated administration of each measure. The procedure can be used in the search for parsimonious versions of multiwave multiple-indicator models, to test for variable specificity in them, and to examine assumptions underlying particular parameter estimation procedures in repeated measure designs. The outlined method is illustrated with empirical data.     

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.     

具有变化潜伏期的水源性疾病模型稳定性分析

建立了一类具有变化潜伏期的水源性疾病数学模型,得到了水源性疾病流行的阈值R0（基本再生数）.利用LaSalle不变集原理,通过构造新的Liapunov函数证明了平衡点的全局稳定性：当R0≤1时,系统的无病平衡点p0是全局渐近稳定的;当R0＞1时,系统的地方病平衡点p＊是全局渐近稳定的.最后利用数值模拟说明结论的正确性.     

Modeling Configural Patterns in Latent Variable Profiles: Association With an Endogenous Variable

A model is proposed for identifying latent predictor score patterns associated with a latent outcome variable. The model employs 2 new devices: (a) a path coefficient vector of contrast coefficients to describe a configural pattern in a structural model, and (b) a new type of latent variable with values that quantify the match of the person's latent predictor variable profile pattern to a theoretical pattern associated with the factor. The model is illustrated using data on perceptions and evaluations of political candidates during a debate. Findings suggest a pattern of scores on the perceptual variables associated with perceived debate success for female observers but not for male observers.     

Evaluation of Validity and Reliability for Hierarchical Scales Using Latent Variable Modeling

A latent variable modeling method is outlined, which accomplishes estimation of criterion validity and reliability for a multicomponent measuring instrument with hierarchical structure. The approach provides point and interval estimates for the scale criterion validity and reliability coefficients, and can also be used for testing composite or simple hypotheses about these coefficients. The proposed method is illustrated with a numerical example.     

Using Latent Variable Modeling for Discrete Time Survival Analysis: Examining the Links of Depression to Mortality

Using a latent variable modeling approach to discrete time survival analysis, the dynamics of the relationships of depression and body mass index to mortality are examined with data from the multiwave, nationally representative Health and Retirement Study. A set of medical and demographic variables are employed as time-invariant covariates along with lag-1 depression scores and body mass indexes as time-varying covariates for mortality within an up to 2-year follow-up interval. The results indicate marked links of immediately prior depression levels, as well as notable relations of the body mass indexes, to within-wave mortality in middle-aged and older adults. The approach highlights the benefits of using latent variable modeling for survival analysis, and its findings represent potentially important relationships of clinical and theoretical relevance.     

Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables

Exploratory structural equation modeling (ESEM) is an approach for analysis of latent variables using exploratory factor analysis to evaluate the measurement model. This study compared ESEM with two dominant approaches for multiple regression with latent variables, structural equation modeling (SEM) and manifest regression analysis (MRA). Main findings included: (1) ESEM in general provided the least biased estimation of the regression coefficients; SEM was more biased than MRA given large cross-factor loadings. (2) MRA produced the most precise estimation, followed by ESEM and then SEM. (3) SEM was the least powerful in the significance tests; statistical power was lower for ESEM than MRA with relatively small target-factor loadings, but higher for ESEM than MRA with relatively large target-factor loadings. (4) ESEM showed difficulties in convergence and occasionally created an inflated type I error rate under some conditions. ESEM is recommended when non-ignorable cross-factor loadings exist.     

Testing Measurement Invariance Across Groups in Longitudinal Data: Multigroup Second-Order Latent Growth Model

In latent growth modeling, measurement invariance across groups has received little attention. Considering that a group difference is commonly of interest in social science, a Monte Carlo study explored the performance of multigroup second-order latent growth modeling (MSLGM) in testing measurement invariance. True positive and false positive rates in detecting noninvariance across groups in addition to bias estimates of major MSLGM parameters were investigated. Simulation results support the suitability of MSLGM for measurement invariance testing when either forward or iterative likelihood ratio procedure is applied.     

On the Potential of Discrete Time Survival Analysis Using Latent Variable Modeling: An Application to the Study of the Vascular Depression Hypothesis

Analysis and modeling of time to event data have been traditionally associated with nonparametric, semiparametric, or parametric statistical frameworks. Recent advances in latent variable modeling have additionally provided unique analytic opportunities to methodologists and substantive researchers interested in survival time modeling. As a consequence, discrete time survival analyses can now be readily carried out using latent variable modeling, an approach that offers substantively important extensions to conventional survival models. Using data from the Health and Retirement Study, the discussed approach is applied to the study of the increasingly prominent vascular depression hypothesis in gerontology, geriatrics, and aging research, allowing examination of the unique predictive power of depression with respect to time to stroke in middle-aged and older adults.     

The Poor Fit of Model Fit for Selecting Number of Factors in Exploratory Factor Analysis for Scale Evaluation

Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices: root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker–Lewis index (TLI), and two equivalence test-based model fit indices: RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis. Our results show that all fit indices, except SRMR, are overly sensitive to correlated residuals and nonspecific error, resulting in solutions that are overfactored. SRMR performed well, consistently selecting the correct number of factors; however, previous research suggests it does not perform well with categorical data. In general, we do not recommend using model fit indices to select number of factors in a scale evaluation framework.     

Inference and Interval Estimation Methods for Indirect Effects With Latent Variable Models

Although much is known about the performance of recent methods for inference and interval estimation for indirect or mediated effects with observed variables, little is known about their performance in latent variable models. This article presents an extensive Monte Carlo study of 11 different leading or popular methods adapted to structural equation models with latent variables. Manipulated variables included sample size, number of indicators per latent variable, internal consistency per set of indicators, and 16 different path combinations between latent variables. Results indicate that some popular or previously recommended methods, such as the bias-corrected bootstrap and asymptotic standard errors had poorly calibrated Type I error and coverage rates in some conditions. Likelihood-based confidence intervals, the distribution of the product method, and the percentile bootstrap emerged as leading methods for both interval estimation and inference, whereas joint significance tests and the partial posterior method performed well for inference.     

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.     

Measuring Change in Students' Attitudes Toward Science Over Time: An Application of Latent Variable Growth Modeling

The purpose of this paper is to show how latent variable growth modeling can be utilized to examine change in students' attitudes toward science over the middle and high school years using data from the Longitudinal Study of American Youth (Miller, Hoffer, Suchner, Brown, & Nelson, 1992).The results of the present study show that students' attitudes toward science generally decline over the middle and high school years. Science self-concept was found to be the strongest predictor of attitudes toward science. Teacher encouragement of science and peer attitudes are also significant predictors of students' attitudes. The effect of the parent variable was found to be quite small and statistically nonsignificant, with the exception of the seventh grade. Boys were found to have higher initial status on attitudes toward science and their attitudes dropped faster than girls. Also it was found that students in metropolitan and rural schools have less positive attitudes toward science in the seventh grade compared to students in suburban schools. Latent variable growth modeling allows one to examine change in attitudes and also examine the effects of time-varying and time-invariant predictors. Substantive and methodological implications of this technique are also discussed.     

Discrete Time Survival Analysis Via Latent Variable Modeling: A Note on Lagged Depression Links to Stroke in Middle and Late Life

This article is concerned with a latent variable modeling approach to discrete time survival analysis that includes both time-invariant and time-varying covariates. The approach is illustrated with data from the Health and Retirement Study, which are utilized to study further the relationship of depression to stroke in middle and late life. Employing lag-1 depression scores as time-varying covariates, in addition to a set of relevant medical and demographic variables as time-invariant covariates collected at baseline, the article addresses a particular aspect of the prominent vascular depression hypothesis representing an important area in aging research, gerontology, geriatrics, and medicine. The results indicate considerable links of immediately prior depression levels to subsequent occurrences of stroke in middle-aged and older adults. The findings complement those reported by Raykov, Gorelick, Zajacova, and Marcoulides (2017), and are consistent with that hypothesis implying depression as a potential warning sign of an impending stroke.     

Longitudinal Dynamic Analyses of Depression and Academic Achievement in the Hawaiian High Schools Health Survey Using Contemporary Latent Variable Change Models

The scientific literature consistently supports a negative relationship between adolescent depression and educational achievement, but we are certainly less sure on the causal determinants for this robust association. In this article we present multivariate data from a longitudinal cohort-sequential study of high school students in Hawai‘i (following McArdle, 2008; McArdle, Johnson, Hishinuma, Miyamoto, & Andrade, 2001). We first describe the full set of data on academic achievements and self-reported depression. We then carry out and present a progression of analyses in an effort to determine the accuracy, size, and direction of the dynamic relationships among depression and academic achievement, including gender and ethnic group differences. We apply 3 recently available forms of longitudinal data analysis: (a) Dealing with incomplete data—We apply these methods to cohort-sequential data with relatively large blocks of data that are incomplete for a variety of reasons (Little & Rubin, 1987; McArdle & Hamagami, 1992). (b) Ordinal measurement models (Muthén & Muthén, 2006)—We use a variety of statistical and psychometric measurement models, including ordinal measurement models, to help clarify the strongest patterns of influence. (c) Dynamic structural equation models (DSEMs; McArdle, 2008). We found the DSEM approach taken here was viable for a large amount of data, the assumption of an invariant metric over time was reasonable for ordinal estimates, and there were very few group differences in dynamic systems. We conclude that our dynamic evidence suggests that depression affects academic achievement, and not the other way around. We further discuss the methodological implications of the study.     

Using Design-Based Latent Growth Curve Modeling With Cluster-Level Predictor to Address Dependency

The authors compared the effects of using the true Multilevel Latent Growth Curve Model (MLGCM) with single-level regular and design-based Latent Growth Curve Models (LGCM) with or without the higher-level predictor on various criterion variables for multilevel longitudinal data. They found that random effect estimates were biased when the higher-level predictor was not included and that standard errors of the regression coefficients from the higher-level were underestimated when a regular LGCM was used. Nevertheless, random effect estimates, regression coefficients, and standard error estimates were consistent with those from the true MLGCM when the design-based LGCM included the higher-level predictor. They discussed implication for the study with empirical data illustration.