In structural equation modeling, analysts usually ask whether the hypothesized model fits the obtained data. Model fit can be addressed by chi-square test of absolute fit. However, the chi-square test evaluates the perfect fit. Therefore, when sample size increases, a minor misspecification from the perfect model (such as error correlation of 0.2) can lead to rejection by the chi-square test. In fact, researchers wish to check whether the hypothesized model approximates the obtained data such that trivial details within the hypothesized model (e.g., minor cross factor loadings) could be ignored. Therefore, model fit indices have been developed, such as RMSEA, SRMR, CFI, TLI, and more than 30 other fit indices. Researchers usually use the fit index cutoff (e.g., RMSEA < .05) to decide whether the model approximately fit the data or not. However, the consensus of which cutoffs researchers should use is not established. I try to find alternative methods, beside fit indices, for evaluating approximate fit. Currently, I developed the unified approach for model fit evaluation. I also investigated the performance of other alternative approaches, such as Monte Carlo approach and Bayesian approach. Also, I am developing R packages called simsem and semTools. One of the objectives of these packages is to implement the alternative approaches for model fit evaluation. See the software page for further details.
I am interested in research planning before collecting any data. I am interested in sample size estimation and planned missing design that help researchers saving money and resources and still achieving desired characteristics (such as enough statistical power or enough accuracy in parameter estimation). I developed the PAWS program for sample size estimation in clustered randomized design, as well as several functions in the MBESS package. Also, I am developing the simsem package for R to help researchers planning their designs easier in structural equation modeling. See the software page for further details.
I have studies on Bayesian analysis, multilevel structural equation modeling, sampling theory, and modeling latent variable interaction in structural equation modeling.