Collapsing Sparse Responses in Likert-Type Scale Data: Advantages and Disadvantages for Model Fit in CFA

Applied researchers often encounter situations where certain item response categories receive very few endorsements, resulting in sparse data. Collapsing categories may mitigate sparsity by increasing cell counts, yet the methodological consequences of this practice remain insufficiently explored. The current study examined the effects of response collapsing in Likert-type scale data through a simulation study under the confirmatory factor analysis model. Sparse response categories were collapsed to determine the impact on fit indices (i.e., chi-square, comparative fit index [CFI], Tucker-Lewis index [TLI], root mean square error of approximation [RMSEA], and standardized root mean square residual [SRMR]). Findings indicate that category collapsing has a significant impact when sparsity is severe, leading to reduced model rejections in both correctly specified and misspecified models. In addition, different fit indices exhibited varying sensitivities to data collapsing. Specifically, RMSEA was recommended for the correctly identified model, and TLI with a cut-off value of .95 was recommended for the misspecified models. The empirical analysis was aligned with the simulation results. These results provide valuable insights for researchers confronted with sparse data in applied measurement contexts.