Omissions by Design in a Survey: Is This a Good Choice when using Structural Equation Models?

Missing observations can arise due to the effort required to answer many questions in long surveys and the cost required to obtain some responses. Implementing a planned missing design in surveys helps reduce the number of questions each respondent needs to answer, thereby lowering survey fatigue and cutting down on implementation costs. The three-form and the two-method design are two different types of planned missing designs. An important consideration when designing a study with omissions by design is to know how it will affect statistical results. In this work, a simulation study is conducted to analyze how the usual fit measures, root mean square error of approximation (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker-Lewis index (TLI) perform in the adjustment of a Structural Equation Model. The results revealed that the CFI, TLI, and SRMR indices exhibit sensitivity to omissions with small samples, low factor loadings and large models. Overall, this study contributes to our understanding of the importance of considering omissions by design in market research.