Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Educational Measurement and Research

Major Professor

Eun Sook Kim, Ph.D.

Co-Major Professor

Yi-Hsin Chen, Ph.D.

Committee Member

John Ferron, Ph.D.

Committee Member

Stephen Stark, Ph.D.


Multilevel, MIMIC, Covariates interaction, Misspecification


In multilevel MIMIC models, covariates at the between level and at the within level can be modeled simultaneously. Covariates interaction effect occurs when the effect of one covariate on the latent factor varies depending on the level of the other covariate. The two covariates can be both at the between level, both at the within level, and one at the between level and the other one at the within level. And they can create between level covariates interaction, within level covariates interaction, and cross level covariates interaction. Study One purports to examine the performance of multilevel MIMIC models in estimating the covariates interaction described above. Type I error of falsely detecting covariates interaction when there is no covariates interaction effect in the population model, and the power of correctly detecting the covariates interaction effect, bias of the estimate of interaction effect, and RMSE are examined. The design factors include the location of the covariates interaction effect, cluster number, cluster size, intra-class correlation (ICC) level, and magnitude of the interaction effect. The results showed that ML MIMIC performed well in detecting the covariates interaction effect when the covariates interaction effect was at the within level or cross level. However, when the covariates interaction effect was at the between level, the performance of ML MIMIC depended on the magnitude of the interaction effect, ICC, and sample size, especially cluster size. In Study Two, the impact of omitting covariates interaction effect on the estimate of other parameters is investigated when the covariates interaction effect is present in the population model. Parameter estimates of factor loadings, intercepts, main effects of the covariates, and residual variances produced by the correct model in Study One are compared to those produced by the misspecified model to check the impact. Moreover, the sensitivity of fit indices, such as chi-square, CFI, RMSEA, SRMR-B (between), and SRM-W (within) are also examined. Results indicated that none of the fit indices was sensitive to the omission of the covariates interaction effect. The biased parameter estimates included the two covariates main effect and the between-level factor mean.