Katerina M. Marcoulides

New Ways to Evaluate Goodness of Fit: A Note on Using Equivalence Testing to Assess Structural Equation Models

Structural equation models are typically evaluated on the basis of goodness-of-fit indexes. Despite their popularity, agreeing what value these indexes should attain to confidently decide between the acceptance and rejection of a model has been greatly debated. A recently proposed approach by means of equivalence testing has been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been proposed as providing a necessary vehicle that can be used to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this article is to introduce readers to key ideas in equivalence testing and illustrate its use for conducting model–data fit assessments. Two confirmatory factor analysis models in which a priori specified latent variable models with known structure and tested against data are used as examples. It is advocated that whenever the goodness of fit of a model is to be assessed researchers should always examine the resulting values obtained via the equivalence testing approach.

Data Integration Approaches to Longitudinal Growth Modeling

Synthesizing results from multiple studies is a daunting task during which researchers must tackle a variety of challenges. The task is even more demanding when studying developmental processes longitudinally and when different instruments are used to measure constructs. Data integration methodology is an emerging field that enables researchers to pool data drawn from multiple existing studies. To date, these methods are not commonly utilized in the social and behavioral sciences, even though they can be very useful for studying various complex developmental processes. This article illustrates the use of two data integration methods, the data fusion and the parallel analysis approaches. The illustration makes use of six longitudinal studies of mathematics ability in children with a goal of examining individual changes in mathematics ability and determining differences in the trajectories based on sex and socioeconomic status. The studies vary in their assessment of mathematics ability and in the timing and number of measurement occasions. The advantages of using a data fusion approach, which can allow for the fitting of more complex growth models that might not otherwise have been possible to fit in a single data set, are emphasized. The article concludes with a discussion of the limitations and benefits of these approaches for research synthesis.

Individual Change and the Timing and Onset of Important Life Events: Methods, Models, and Assumptions.

Researchers are often interested in studying how the timing of a specific event affects concurrent and future development. When faced with such research questions there are multiple statistical models to consider and those models are the focus of this paper as well as their theoretical underpinnings and assumptions regarding the nature of the effect of the event on the developmental process. We discuss three models, all variants of growth models specified within the multilevel modeling framework, which conceptualize the developmental process and the effect of the event in different ways. These models include the growth model with a time-invariant covariate, the growth model with a time-varying covariate, and the spline growth model. After discussing the models in detail, we applied these models to longitudinal data from the Berkeley Growth Study to examine cognitive changes during infancy and the effect of independent sitting on those changes. Results suggest that research conclusions depend on the model chosen and how certain results can be misconstrued unless the model accurately reflects the research questions. Recommendations and additional non-traditional models are discussed.

Automated Latent Growth Curve Model Fitting: A Segmentation and Knot Selection Approach

Latent growth curve models are widely used in the social and behavioral sciences to study complex developmental patterns of change over time. The trajectories of these developmental patterns frequently exhibit distinct segments in the studied variables. Latent growth models with piecewise functions for repeated measurements of variables have become increasingly popular for modeling such developmental trajectories. A major problem with using piecewise models is determining the precise location of the point where the change in the process has occurred and uncovering the related number of segments. The purpose of this paper is to introduce an optimization procedure that can be used to determine both the segments and location of the knots in piecewise linear latent growth models. The procedure is illustrated using empirical data in order to detect the number of segments and change points. The results demonstrate the capabilities of the procedure for fitting latent growth curve models.

Using an Acculturation‐Stress‐Resilience Framework to Explore Latent Profiles of Latina/o Language Brokers

With survey data from 243 Latina/o early adolescent language brokers, latent profile analyses were conducted to identify different types (i.e., profiles) of brokers. Profiles were based on how often Latina/o early adolescents brokered for family members, as well as their levels of family-based acculturation stress, negative brokering beliefs, parentification, and positive brokering beliefs. Three brokering profiles emerged: (1) infrequent-ambivalents, (2) occasional-moderates, and (3) parentified-endorsers. Profile membership was significantly predicted by ethnic identification and brokering in a medical context. Respect, brokering at school, and brokering at home did not significantly predict profile membership. In addition, parentified-endorsers had more frequent perceived ethnic/racial discrimination and depressive symptoms than other profiles. In contrast, infrequent-ambivalents engaged in risky behaviors less frequently than other profiles.

Model Specification Searches in Structural Equation Modeling with R

This article introduces and demonstrates the application of an R statistical programming environment code for conducting structural equation modeling (SEM) specification searches. The implementation and flexibility of the provided code is demonstrated using the Tabu search procedure, although the underlying code can also be directly modified to implement other search procedures like Ant Colony Optimization, Genetic Algorithms, Ruin-and-Recreate, or Simulated Annealing. The application is illustrated using data with a known common factor structure. The results demonstrate the capabilities of the program for conducting specification searches in SEM. The programming codes are provided as open-source R functions.

Careful with Those Priors: A Note on Bayesian Estimation in Two-Parameter Logistic Item Response Theory Models.

ABSTRACT This study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that the Bayesian estimates obtained with both informative and non-informative priors exhibited varying levels of bias ranging in most cases from moderate to severe bias. Results are discussed in light of these findings and recommendations concerning the use of priors in empirical research are provided.

A Bayesian Synthesis Approach to Data Fusion Using Data-Dependent Priors

The process of combining data is one in which information from disjoint data sets sharing at least a few common variables is merged. This process is commonly referred to as data fusion, with the main objective of creating a new data set permitting more flexible analyses than the separate analysis of each individual data set. Many data fusion methods have been proposed in the literature, although most utilize the frequentist framework. I investigate an approach called Bayesian synthesis in which information obtained from one data set acts as priors for the next analysis. This process continues sequentially until a single fused posterior distribution is created using all available data. These informative data-dependent priors provide an extra source of information that may aid in the accuracy of estimation. To evaluate its performance, Bayesian synthesis results of data simulated under several conditions with known population values modeled after Marcoulides and Grimm (2016) were examined. For all conditions, six different data sets were generated, each with sample sizes N = 50, N = 250, and N = 1,000, respectively. The intercept and slope means were fixed at −2 and 0.2, respectively, and the residual variance was fixed at 0.10 to reflect small residuals. The intercept and slope variances and the covariance for conditions (A) to (D) were set as A = [ 0.20 0 0 0.10 ] , B = [ 0.20 0.10 0.10 0.10 ] , C = [ 0.40 0.30 0.30 0.30 ] , and D = [ 0.60 0.50 0.50 0.50 ] . Estimation accuracy was assessed using the average relative bias, with values below 5% reflecting ignorable bias, between 5% and 10% moderate bias, and above 10% substantial bias (Muthén & Muthén, 2002). For N = 50, the relative bias was substantial for the intercept variance under all examined conditions. The relative bias for the slope variance was substantial for the conditions (A) and (B), was moderate for (C), and was ignorable for (D). The relative bias for the covariance was moderate for conditions (B) and (C) and ignorable for

Analyzing Longitudinal Data Using Natural Cubic Smoothing Splines

The analysis of longitudinal data has received widespread interest in the behavioral, educational, medical, and social sciences for many years. Many modeling techniques have been suggested for conducting such analyses, especially when the data exhibit complex nonlinear trajectory patterns. A major problem with many of these modeling techniques, however, is that they often either impose overly restrictive assumptions or can be computationally demanding. The purpose of this paper is to introduce a less known but highly effective modeling procedure that can be used to model complex nonlinear longitudinal data patterns. The procedure is illustrated using empirical data along with an easy to use computerized implementation.

Structural Equation Modeling With Many Variables: A Systematic Review of Issues and Developments

Survey data in social, behavioral, and health sciences often contain many variables (p). Structural equation modeling (SEM) is commonly used to analyze such data. With a sufficient number of participants (N), SEM enables researchers to easily set up and reliably test hypothetical relationships among theoretical constructs as well as those between the constructs and their observed indicators. However, SEM analyses with small N or large p have been shown to be problematic. This article reviews issues and solutions for SEM with small N, especially when p is large. The topics addressed include methods for parameter estimation, test statistics for overall model evaluation, and reliable standard errors for evaluating the significance of parameter estimates. Previous recommendations on required sample size N are also examined together with more recent developments. In particular, the requirement for N with conventional methods can be a lot more than expected, whereas new advances and developments can reduce the requirement for N substantially. The issues and developments for SEM with many variables described in this article not only let applied researchers be aware of the cutting edge methodology for SEM with big data as characterized by a large p but also highlight the challenges that methodologists need to face in further investigation.