When the multivariate normality assumption is violated in structural equation modeling, a leading remedy involves estimation via normal theory maximum likelihood with robust corrections to standard errors. We propose that this approach might not be best for forming confidence intervals for quantities with sampling distributions that are slow to approach normality, or for functions of model parameters. We implement and study a robust analog to likelihood-based confidence intervals based on inverting the robust chi-square difference test of Satorra (2000). We compare robust standard errors and the robust likelihood-based approach versus resampling methods in confirmatory factor analysis (Studies 1 & 2) and mediation analysis models (Study 3) for both single parameters and functions of model parameters, and under a variety of nonnormal data generation conditions. The percentile bootstrap emerged as the method with the best calibrated coverage rates and should be preferred if resampling is possible, followed by the robust likelihood-based approach.

In this article, we propose integrated generalized structured component analysis (IGSCA), which is a general statistical approach for analyzing data with both components and factors in the same model, simultaneously. This approach combines generalized structured component analysis (GSCA) and generalized structured component analysis with measurement errors incorporated (GSCAM) in a unified manner and can estimate both factor- and component-model parameters, including component and factor loadings, component and factor path coefficients, and path coefficients connecting factors and components. We conduct 2 simulation studies to investigate the performance of IGSCA under models with both factors and components. The first simulation study assesses how existing approaches for structural equation modeling and IGSCA recover parameters. This study shows that only consistent partial least squares (PLSc) and IGSCA yield unbiased estimates of all parameters, whereas the other approaches always provided biased estimates of several parameters. As such, we conduct a second, extensive simulation study to evaluate the relative performance of the 2 competitors (PLSc and IGSCA), considering a variety of experimental factors (model specification, sample size, the number of indicators per factor/component, and exogenous factor/component correlation). IGSCA exhibits better performance than PLSc under most conditions. We also present a real data application of IGSCA to the study of genes and their influence on depression. Finally, we discuss the implications and limitations of this approach, and recommendations for future research. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Theories can be represented as statistical models for empirical testing. There is a vast literature on model selection and multimodel inference that focuses on how to assess which statistical model, and therefore which theory, best fits the available data. For example, given some data, one can compare models on various information criterion or other fit statistics. However, what these indices fail to capture is the full range of counterfactuals. That is, some models may fit the given data better not because they represent a more correct theory, but simply because these models have more fit propensity-a tendency to fit a wider range of data, even nonsensical data, better. Current approaches fall short in considering the principle of parsimony (Occam's Razor), often equating it with the number of model parameters. Here we offer a toolkit for researchers to better study and understand parsimony through the fit propensity of structural equation models. We provide an R package (ockhamSEM) built on the popular lavaan package. To illustrate the importance of evaluating fit propensity, we use ockhamSEM to investigate the factor structure of the Rosenberg Self-Esteem Scale. (PsycInfo Database Record (c) 2023 APA, all rights reserved).