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Integrative data analysis (IDA) is an analytic tool that allows researchers to combine raw data across multiple, independent studies, providing an improved measurement of latent constructs as compared to single study analysis or meta-analyses. This is often achieved through the implementation of moderated non-linear factor analysis (MNLFA), an advanced modeling approach that allows for covariate moderation of item and factor parameters. The current paper provides an overview of this modeling technique, highlighting distinct advantages most apt for IDA. We further illustrate the complex model building process involved in MNLFA by providing a tutorial using empirical data from five separate prevention trials. The code and data used for analyses are also provided. [ABSTRACT FROM AUTHOR]

Including auxiliary variables such as antecedent and consequent variables in mixture models provides valuable insight in understanding the population heterogeneity embodied by a latent class variable. The model building process regarding how to include predictors/correlates and outcomes of the latent class variables into mixture models is an area of active research. As such, new methods of including these variables continue to emerge and best practices for the application of these methods in real data settings (including simple guidelines for choosing amongst them) are still not well established. This paper focuses on one type of auxiliary variable—distal outcomes—providing an overview of the methods currently available for estimating the effects of latent class membership on subsequent distal outcomes. We illustrate the recommended methods in the software packages Mplus and Latent Gold using a latent class model to capture population heterogeneity in students' mathematics attitudes, linking latent class membership to two distal outcomes. [ABSTRACT FROM AUTHOR]

The use of latent class analysis, and finite mixture modeling more generally, has become almost commonplace in social and health science domains. Typically, research aims in mixture model applications include investigating predictors and distal outcomes of latent class membership. The most recent developments for incorporating latent class antecedents and consequences are stepwise procedures that decouple the classification and prediction models. It was initially believed these procedures might avoid the potential misspecification bias in the simultaneous models that include both latent class indicators and predictors. However, if direct effects from the predictors to the indicators are omitted in the stepwise procedure, the prediction model can yield biased estimates. This article presents a logical and principled approach, readily implemented in current software, to testing for direct effects from latent class predictors to indicators using multiple indicator multiple cause modeling. This approach is illustrated with real data and opportunities for future developments are discussed. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models. [ABSTRACT FROM PUBLISHER]