A Comparison of Penalized Maximum Likelihood Estimation and Markov Chain Monte Carlo Techniques for Estimating Confirmatory Factor Analysis Models With Small Sample Sizes

To Check or Not to Check? A Comment on the Contemporary Psychometrics (ConPsy) Checklist for the Analysis of Questionnaire Items

In a recent paper, the first version of the contemporary psychometrics (ConPsy) checklist for assessing measurement tool quality has been published. This checklist aims to provide guidelines and references to researchers to assess measurement properties for newly developed measurement instruments. The ConPsy checklist recommends appropriate statistical methods for measurement instrument evaluation to guide researchers in instrument development and to support peer review. In this opinion article, I critically review some aspects of the checklist and question the usefulness of certain psychometric analyses in research practice.

Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches

Structural equation models (SEM), or confirmatory factor analysis as a special case, contain model parameters at the measurement part and the structural part. In most social-science SEM applications, all parameters are simultaneously estimated in a one-step approach (e.g., with maximum likelihood estimation). In a recent article, Rosseel and Loh (2022, Psychol. Methods) proposed a two-step structural after measurement (SAM) approach to SEM that estimates the parameters of the measurement model in the first step and the parameters of the structural model in the second step. Rosseel and Loh claimed that SAM is more robust to local model misspecifications (i.e., cross loadings and residual correlations) than one-step maximum likelihood estimation. In this article, it is demonstrated with analytical derivations and simulation studies that SAM is generally not more robust to misspecifications than one-step estimation approaches. Alternative estimation methods are proposed that provide more robustness to misspecifications. SAM suffers from finite-sample bias that depends on the size of factor reliability and factor correlations. A bootstrap-bias-corrected LSAM estimate provides less biased estimates in finite samples. Nevertheless, we argue in the discussion section that applied researchers should nevertheless adopt SAM because robustness to local misspecifications is an irrelevant property when applying SAM. Parameter estimates in a structural model are of interest because intentionally misspecified SEMs frequently offer clearly interpretable factors. In contrast, SEMs with some empirically driven model modifications will result in biased estimates of the structural parameters because the meaning of factors is unintentionally changed.

What Is the Maximum Likelihood Estimate When the Initial Solution to the Optimization Problem Is Inadmissible? The Case of Negatively Estimated Variances

The default procedures of the software programs Mplus and lavaan tend to yield an inadmissible solution (also called a Heywood case) when the sample is small or the parameter is close to the boundary of the parameter space. In factor models, a negatively estimated variance does often occur. One strategy to deal with this is fixing the variance to zero and then estimating the model again in order to obtain the estimates of the remaining model parameters. In the present article, we present one possible approach for justifying this strategy. Specifically, using a simple one-factor model as an example, we show that the maximum likelihood (ML) estimate of the variance of the latent factor is zero when the initial solution to the optimization problem (i.e., the solution provided by the default procedure) is a negative value. The basis of our argument is the very definition of ML estimation, which requires that the log-likelihood be maximized over the parameter space. We present the results of a small simulation study, which was conducted to evaluate the proposed ML procedure and compare it with Mplus’ default procedure. We found that the proposed ML procedure increased estimation accuracy compared to Mplus’ procedure, rendering the ML procedure an attractive option to deal with inadmissible solutions.

A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model

The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model provides a general approach for estimating reciprocal effects between constructs over time. However, previous research has shown that this model is difficult to estimate using the maximum likelihood (ML) method (e.g., nonconvergence). In this article, we introduce a Bayesian approach for estimating the bivariate STARTS model and implement it in the software Stan. We discuss issues of model parameterization and show how appropriate prior distributions for model parameters can be selected. Specifically, we propose the four-parameter beta distribution as a flexible prior distribution for the autoregressive and cross-lagged effects. Using a simulation study, we show that the proposed Bayesian approach provides more accurate estimates than ML estimation in challenging data constellations. An example is presented to illustrate how the Bayesian approach can be used to stabilize the parameter estimates of the bivariate STARTS model.

Tutorial on the Use of the regsem Package in R

Sparse estimation through regularization is gaining popularity in psychological research. Such techniques penalize the complexity of the model and could perform variable/path selection in an automatic way, and thus are particularly useful in models that have small parameter-to-sample-size ratios. This paper gives a detailed tutorial of the R package regsem, which implements regularization for structural equation models. Example R code is also provided to highlight the key arguments of implementing regularized structural equation models in this package. The tutorial ends by discussing remedies of some known drawbacks of a popular type of regularization, computational methods supported by the package that can improve the selection result, and some other practical issues such as dealing with missing data and categorical variables.