Evaluating the Effect of Planned Missing Designs in Structural Equation Model Fit Measures

Abstract

In a planned missing design, the nonresponses occur according to the researcher’s will, with the goal of increasing data quality and avoiding overly extensive questionnaires. When adjusting a structural equation model to the data, there are different criteria to evaluate how the theoretical model fits the observed data, with the root mean square error of approximation (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI) and Tucker–Lewis index (TLI) being the most common. Here, I explore the effect of the nonresponses due to a specific planned missing design—the three-form design—on the mentioned fit indices when adjusting a structural equation model. A simulation study was conducted with correctly specified model and one model with misspecified correlation between factors. The CFI, TLI and SRMR indices are affected by the nonresponses, particularly with small samples, low factor loadings and numerous observed variables. The existence of nonresponses when considering misspecified models causes unacceptable values for all the four fit indexes under analysis, namely when a strong correlation between factors is considered. The results shown here were performed with the simsem package in R and the full information maximum-likelihood method was used for handling missing data during model fitting.