Distributionally-Weighted Least Squares in Growth Curve ModelingDu, Han; Bentler, Peter M.; Rosseel, Yves
doi: 10.1080/10705511.2021.1931870pmid: N/A
Growth curve modeling is commonly used in psychological, educational, and social science research. The mainstream estimators for growth curve modeling are based on normal theory, but real data are unlikely to be exactly normally distributed. To improve estimation and inference with non-normal data, various estimators have been proposed. Among these estimators, the asymptotically distribution free (ADF) estimator does not need to rely on any distribution assumption but it is not efficient with small and modest sample sizes. We propose a distributionally weighted least squares $$DLS$$ D L S estimator in the growth curve modeling framework. $$DLS$$ D L S combines normal theory based and $$ADF$$ A D F based generalized least squares estimation to balance the information from the data and the normality assumption. Computer simulation results suggest that model-implied covariance-based $$DLS$$ D L S ( $$DL{S_M}$$ D L S M ) generally provides more accurate and efficient estimates than the examined alternative methods regardless of the distribution. In addition, the relative biases of standard error estimates and the Type I error rates of the Satorra–Bentler test statistic ( $${T_{SB}}$$ T S B ) in $$DL{S_M}$$ D L S M were competitive with the classical methods including maximum likelihood and generalized least squares estimation. We illustrate how to implement $$DL{S_M}$$ D L S M and select the optimal tuning parameter by a bootstrap procedure in a real data example.
Comparison of Three Approaches to Class Enumeration in Growth Mixture Modeling when Time Structures are Variant Across Latent ClassesLee, Sooyong; Whittaker, Tiffany A.
doi: 10.1080/10705511.2021.1956320pmid: N/A
In conventional approaches to Growth Mixture Modeling (GMM), a trajectory is first estimated using latent growth curve modeling that serves as a baseline trajectory for the GMM. In this approach, time structures are held invariant across latent classes when identifying the number of latent classes. However, this popular way of conducting GMM could undermine a proper estimation, especially under the condition where a distinct trajectory exists for different classes in the population. This study compared the class enumeration performance in a conventional GMM against two alternatives in which latent classes do not take the same functional forms of change across time: (1) Unstructured Mixture Models (UMM) and (2) Latent Basis Models (LBM). Results revealed that the UMM performs well when one latent class takes a different shape of growth. Based on various design conditions, the relative performance of the three approaches in terms of class enumeration is examined and discussed.
Using Ant Colony Optimization for Sensitivity Analysis in Structural Equation ModelingLeite, Walter L.; Shen, Zuchao; Marcoulides, Katerina; Fisk, Charles L.; Harring, Jeffrey
doi: 10.1080/10705511.2021.1881786pmid: N/A
Studies using structural equation modeling (SEM) to evaluate theories against observed data rely on multiple sources of evidence to support a proposed model, such as fit indices, variance explained, and comparison of alternative models. Additional evidence can be obtained by evaluating the model results’ sensitivity to an omitted confounder. The phantom variable approach to SEM sensitivity analysis requires manual specification of sensitivity parameters. This study improves on the phantom variable approach by employing the ant colony optimization algorithm to automatically search for sensitivity parameters, if any, that would lead to a change in the study’s conclusions. The proposed method is implemented in the package SEMsens for the R statistical software, and demonstrated with a sensitivity analysis of a model of the complex relation between working memory and writing.
Can We Distinguish between Different Longitudinal Models for Estimating Nonlinear Trajectories?Ye, Ai; Bollen, Kenneth A.
doi: 10.1080/10705511.2021.1959333pmid: N/A
Substantive theory rarely provides specific enough information to guide our selection of the optimal model for longitudinal data. Instead, researchers are more likely to rely on models common to their field, even if they are not appropriate. The purpose of our study is to assess whether researchers can use overall goodness-of-fit measures from structural equation models to correctly find the data generating model (DGM) from among a broad set of different longitudinal models. We use four different DGM adapted from published empirical studies. We compare goodness-of-fit statistics (e.g., p-value, CFI, RMSEA, etc.) of the DGM with those of six alternative models. Overall, the Bayesian Information Criterion (BIC) performed best in selecting the DGM, though no fit statistic was flawless. In the absence of substantive theory, we recommend that researchers begin with the most general longitudinal model and test whether it can be simplified by eliminating parameters.
Effects of Mixing Weights and Predictor Distributions on Regression Mixture ModelsSherlock, Phillip; DiStefano, Christine; Habing, Brian
doi: 10.1080/10705511.2021.1932508pmid: 35221645
Regression mixture models (RMMs) can be used to specifically test for and model differential effects in heterogeneous populations. Based on the results of the Aim 1 simulation study, enumeration conducted with constrained predictor means appears to be advantageous. Furthermore, researchers should estimate the K and K+1 unconditional models (chosen during initial enumeration), adding the C on X paths, to investigate the potential for model instability as well as the possibility that the models are misspecified because the underlying populations contain predictor variance differences in the subgroups. The Aim 2 simulation study explored the extent to which RMMs are robust to predictor variance differences. Although the coverage rates for the simulation conditions where the predictor variances differed across classes were not the nominal rate, parameter estimates were not biased even in the presence of moderate violations of this assumption.
The Impact of Partial Measurement Invariance on Between-group Comparisons of Second-Order Factor MeansLiu, Yixing; Thompson, Marilyn S.
doi: 10.1080/10705511.2021.1936535pmid: N/A
A simulation study was conducted to explore the influence of partial measurement invariance on the second-order factor mean difference estimation. The types, positions, numbers, and directions of between-group differences for noninvariant parameters were manipulated, along with sample size and effect size of the latent mean difference. When the model was misspecified by constraining noninvariant loadings or intercepts to be equal, the latent mean difference was overestimated if the direction of the difference in noninvariant parameters was consistent with the direction of the latent mean difference, and vice versa. The numbers, types, and positions of noninvariant parameters also had an influence on the estimation bias. Power to detect the latent mean difference was influenced by the corresponding estimation bias and estimated variance, in addition to sample size and effect size.
Multilevel Dynamic Twin ModelingSchuurman, N. K.; Zheng, Y.; Dolan, C. V.
doi: 10.1080/10705511.2021.1937177pmid: N/A
Recent developments in the collection and modeling of intensive longitudinal data have enabled us to fit dynamic twin models, in which within-person processes are separated into genetic and environmental components. A well-known dynamic twin model is the genetic simplex model, which is fitted to a few repeated measures for many twins. A more recently developed model is the iFACE model, which is fitted to many repeated measures for a single pair of twins. In this paper, we introduce a missing link between these two models – a multilevel extension that allows for making both population-level and twin-level inferences. We provide a proof-of-principle simulation study for this model, and apply it to an experience sampling data set on 148 monozygotic and 88 dizygotic twins. We use the multilevel model to examine the overlap and differences between the dynamic genetic twin models and the classic twin models, as well as their interpretation.
Advantages of Spike and Slab Priors for Detecting Differential Item Functioning Relative to Other Bayesian Regularizing Priors and Frequentist LassoChen, Siyuan Marco; Bauer, Daniel J.; Belzak, William M.; Brandt, Holger
doi: 10.1080/10705511.2021.1948335pmid: N/A
An important step in scale development and assessment is to evaluate differential item functioning (DIF) across segments of the population. Recent approaches use lasso regularization to simultaneously detect DIF in all items and avoid incorrect anchor item assumptions that incur inflated error rates for classical DIF evaluation methods. Although promising, lasso methods cause underestimated standard errors and incorrect p-values. An alternative is Bayesian regularization that provides empirical standard errors. However, we point out that using empirical criteria such as credible intervals for selecting DIF parameters has limited validity. We argue that using a spike-and-slab prior with an inclusion probability criterion provides more theoretically coherent DIF selection and inference over Bayesian regularizing priors with empirical selection rules or frequentist lasso. We demonstrate this by simulation studies with Multi-group Item Response Theory and Moderated Nonlinear Factor Analysis models. Practical utility of the spike-and-slab prior selection criterion is discussed.