Development of weighted model fit indexes for structural equation models using multiple imputation.

摘要

Researchers are often forced to handle missing data when fitting models to their data. One classification of models frequently used in the social sciences is structural equation models (SEMs). These models allow for researchers to account for observed variables as well as their underlying constructs. When the missing data are random or ignorable, a common practice with SEMs is to use full information maximum likelihood (FIML) to manage the missing information. An alternative to FIML would be to use multiple imputation (MI). The benefits of MI have made it a viable alternative for other modeling techniques and of interest within the SEM framework. Although research has progressed on the fundamentals of MI and SEMs, questions still remain in regard to the calculation of power and interpretation of model fit indexes within this environment.;To begin, we develop four SEMs that include a fully specified model, a structural misspecified model, a measurement misspecified model, and a misspecified model. These models are established using our motivating data set, the Family Transitions Project. The first goal is to discover the practical advantages of MI over FIML regarding estimation, analysis, and computational time. Next we explore the power for detecting the correct SEM using likelihood ratio tests to compare models and missing data methods. As a result of concerns raised by other researchers in regard to using model fit indexes when MI is implemented, we develop several weights for model fit indexes. These weights account for the amount of missing information, size of the models, and number of imputed data sets. Our weights are applicable to the chi-squared test statistic and root mean square error of approximation value provided from software output. With the utilization of the weights, the model fit indexes and power are more reasonable in their description of the SEMs.