* denotes a student
Lai, K. (2021). Using information criteria under missing data: Full information maximum likelihood versus two-stage estimation. Structural Equation Modeling, 28, 278-291. https://doi.org/10.1080/10705511.2020.1780925
Full information maximum likelihood (FIML) and the two-stage procedure (TS) are two common model estimation methods for SEM with missing data. Information criteria such as AIC and BIC can also be calculated under FIML or TS. This paper shows that the TS-based information criteria are more reasonable than those based on FIML. Model selection with FIML-based information criteria may lead to different results from those under complete data, even in large samples.
Lai, K. (2021). Correct estimation methods for RMSEA under missing data. Structural Equation Modeling, 28, 207-218. https://doi.org/10.1080/10705511.2020.1755864
This paper gives the correct point estimator and confidence interval for RMSEA when data are missing (completely) at random. All the estimation methods for RMSEA in the current literature break down under missing data.
Lai, K. (2021). Fit difference between nonnested models given categorical data: Measures and estimation. Structural Equation Modeling, 28, 99-120. https://doi.org/10.1080/10705511.2020.1763802
This paper gives point estimators and confidence intervals for ΔRMSEA, ΔCFI, and ΔSRMR between nonnested models given categorical data. The methods in this paper apply to nonnested models and categorical data, and do not assume any candidate model is correct. Common model selection tools such as AIC and BIC do not apply to categorical data SEM, because they require the distribution of the manifest variables but this distribution is not available when the manifest variables are categorical. This paper can also help solve the problems with the cutoffs for fit indices, because cutoffs are not needed if one wants to show a model has better RMSEA (or CFI, SRMR) than other competing models, rather than showing a model has "good" RMSEA (or CFI, SRMR).
Lai, K. (2020). Correct point estimator and confidence interval for RMSEA given categorical data. Structural Equation Modeling, 27, 678-695. https://doi.org/10.1080/10705511.2019.1687302
This paper gives correct methods to obtain point estimate and confidence interval for RMSEA when data are categorical. All the point estimators and confidence intervals for RMSEA in the current literature break down under categorical data.
Lai, K. (2020). Better confidence intervals for RMSEA in growth models given nonnormal data. Structural Equation Modeling, 27, 255-274. doi: 10.1080/10705511.2019.1643246
This paper gives new confidence intervals for the RMSEA fit index in SEM. The robust confidence intervals in the current literature (eg, Brosseau-Liard, Savalei, & Li, 2012; Savalei, 2018) can fail in moment structure analysis.
Lai, K. (2020) Confidence interval for RMSEA or CFI difference between nonnested models. Structural Equation Modeling, 27, 16-32. doi: 10.1080/10705511.2019.1631704
This paper gives methods to form confidence intervals for RMSEA difference and CFI difference between competing models. The competing models can be nested or nonnested. Cutoffs for RMSEA and CFI have received much criticism, but without cutoffs it is impossible to interpret fit index values. While it is hard to show a model has "good" fit, it is easy to show a model has better fit than competing models, as lower RMSEA and higher CFI always correspond to better fit. Using RMSEA or CFI to compare models does not require cutoffs or a definition of "good" fit, and thus avoids the problems with cutoffs.
Lai, K. (2019). A simple analytic confidence interval for CFI given nonnormal data. Structural Equation Modeling, 26, 757-777.
This paper gives an analytic method to form confidence intervals for the CFI fit index in SEM, and the method is robust to nonnormal data. The CFI was proposed in 1990 and has been widely used since then, but for 29 years there has been no easy way to form confidence intervals for CFI, even in the context of normal data.
Lai, K. (2019). Creating misspecified models in moment structure analysis. Psychometrika, 84, 781-801.
This paper gives a flexible, realistic, and precise method to create model misspecifications for simulation studies that use (multiple-group) mean and covariance structure analysis. The traditional method of removing paths from the true model is often difficult or even impossible to implement in moment structure analysis.
Lai, K. (2019). More robust standard error and confidence interval for SEM parameters given incorrect model and nonnormal data. Structural Equation Modeling, 26, 260-279.
This paper gives new standard error estimator and confidence interval for SEM parameters, without assuming correct model or normal distribution. The new methods outperform the sandwich estimators and the bootstrap in the current literature.
Lai, K. (2018). Estimating standardized SEM parameters given nonnormal data and incorrect model: Methods and comparison. Structural Equation Modeling, 25, 600-620.
A simulation study that compares sandwich estimators and the bootstrap for estimating standardized SEM parameters, in terms of point estimation, standard error, and confidence interval, when the assumptions of correct model and normal distribution are violated.
Lai, K., Green, S. B., & Levy, R. (2017). Graphical displays for understanding SEM model similarity. Structural Equation Modeling, 24, 803-818.
This paper gives a framework for studying the similarity in fit between two models over a wide range of data. It helps to address questions such as "For what type of data does Model A fit better than Model B?" and "How and how much does each model parameter affect the difference in fit between two models?"
Lai, K., & Zhang*, X. (2017). Standardized parameters in misspecified structural equation models: Empirical performance in point estimates, standard errors, and confidence intervals. Structural Equation Modeling, 24, 571-584.