In analyzing longitudinal data with growth curve models, a critical assumption is that changes in the observed measures reflect construct changes and not changes in the manifestation of the construct over time. However, growth curve models are often fit to a repeated measure constructed as a sum or mean of scale items, making an implicit assumption of constancy of measurement. This practice risks confounding actual construct change with changes in measurement (i.e., differential item functioning [DIF]), threatening the validity of conclusions. An improved method that avoids such confounding is the second-order growth curve (SGC) model. It specifies a measurement model at each occasion of measurement that can be evaluated for invariance over time. The applicability of the SGC model is hindered by key limitations: (a) the SGC model treats time as continuous when modeling construct growth but as discrete when modeling measurement, reducing interpretability and parsimony; (b) the evaluation of DIF becomes increasingly error-prone given multiple timepoints and groups; (c) DIF associated with continuous covariates is difficult to incorporate. Drawing on moderated nonlinear factor analysis, we propose an alternative approach that provides a parsimonious framework for including many time points and DIF from different types of covariates. We implement this model through Bayesian estimation, allowing for incorporation of regularizing priors to facilitate efficient evaluation of DIF. We demonstrate a two-step workflow of measurement evaluation and growth modeling, with an empirical example examining changes in adolescent delinquency over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
A data matrix, where rows represent persons and columns represent measured subtests, can be viewed as a stack of person profiles, as rows are actually person profiles of observed responses on column subtests. Profile analysis seeks to identify a small number of latent profiles from a large number of person response profiles to identify central response patterns, which are useful for assessing the strengths and weaknesses of individuals across multiple dimensions in domains of interest. Moreover, the latent profiles are mathematically proven to be summative profiles that linearly combine all person response profiles. Since person response profiles are confounded with profile level and response pattern, the level effect must be controlled when they are factorized to identify a latent (or summative) profile that carries the response pattern effect. However, when the level effect is dominant but uncontrolled, only a summative profile carrying the level effect would be considered statistically meaningful according to a traditional metric (e.g., eigenvalue ≥ 1) or parallel analysis results. Nevertheless, the response pattern effect among individuals can provide assessment-relevant insights that are overlooked by conventional analysis; to achieve this, the level effect must be controlled. Consequently, the purpose of this study is to demonstrate how to correctly identify summative profiles containing central response patterns regardless of the centering techniques used on data sets. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
Across different fields of research, the similarities and differences between various longitudinal models are not always eminently clear due to differences in data structure, application area, and terminology. Here we propose a comprehensive model framework that will allow simple comparisons between longitudinal models, to ease their empirical application and interpretation. At the within-individual level, our model framework accounts for various attributes of longitudinal data, such as growth and decline, cyclical trends, and the dynamic interplay between variables over time. At the between-individual level, our framework contains continuous and categorical latent variables to account for between-individual differences. This framework encompasses several well-known longitudinal models, including multilevel regression models, growth curve models, growth mixture models, vector-autoregressive models, and multilevel vector-autoregressive models. The general model framework is specified and its key characteristics are illustrated using famous longitudinal models as concrete examples. Various longitudinal models are reviewed and it is shown that all these models can be united into our comprehensive model framework. Extensions to the model framework are discussed. Recommendations for selecting and specifying longitudinal models are made for empirical researchers who aim to account for between-individual differences. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
Cognitive models provide a substantively meaningful quantitative description of latent cognitive processes. The quantitative formulation of these models supports cumulative theory building and enables strong empirical tests. However, the nonlinearity of these models and pervasive correlations among model parameters pose special challenges when applying cognitive models to data. Firstly, estimating cognitive models typically requires large hierarchical data sets that need to be accommodated by an appropriate statistical structure within the model. Secondly, statistical inference needs to appropriately account for model uncertainty to avoid overconfidence and biased parameter estimates. In the present work, we show how these challenges can be addressed through a combination of Bayesian hierarchical modeling and Bayesian model averaging. To illustrate these techniques, we apply the popular diffusion decision model to data from a collaborative selective influence study. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
This article discusses the robustness of the multivariate analysis of covariance (MANCOVA) test for an emergent variable system and proposes a modification of this test to obtain adequate information from heterogeneous normal observations. The proposed approach for testing potential effects in heterogeneous MANCOVA models can be adopted effectively, regardless of the degree of heterogeneity and sample size imbalance. As our method was not designed to handle missing values, we also show how to derive the formulas for pooling the results of multiple-imputation-based analyses into a single final estimate. Results of simulated studies and analysis of real-data show that the proposed combining rules provide adequate coverage and power. Based on the current evidence, the two solutions suggested could be effectively used by researchers for testing hypotheses, provided that the data conform to normality. (PsycInfo Database Record (c) 2024 APA, all rights reserved).