Two-stage methodology for regression, path analysis, and structural equation models with item-level missingness

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The proposed research has the goal of developing and evaluating a new methodology to deal with incomplete data, relevant for the unique situation when data are missing on the individual items, but the statistical model is at the level of composites (sums of items). This scenario often occurs in the social sciences. For example, in psychology the variables in the model are often scale scores. If the variable “self-esteem” is to be used in regression, it will be computed as the sum score of 10 items that comprise the self-esteem scale. A second application is in the context of structural equation models (SEMs)--complex multivariate regression models that may involve latent variables and allow for testing of complex psychological theories. In this case, models are often large relative to the typical sample sizes commonly used in psychology. It is recommended to reduce model size by combining items into composites. The proposed research extends the recently developed two-stage (TS) methodology for incomplete data (Savalei & Bentler, 2009; Savalei & Falk, 2014) to the scenario with composites. It is argued to be the method that does not lose any information due to missing data. The context is continuous normally distributed data, with extensions to nonnormal data. Modern approaches to missing data include maximum likelihood (ML) and multiple imputation (MI). Whenever available, ML is simpler and more elegant, and provides a unique solution. However, the ML methodology is not available for the case with composites as it cannot handle missing data on variables that do not directly enter the model. The two-stage (TS) procedure is an ML-based procedure that separates missing data treatment from model fitting. In doing so, it allows for a straight-forward treatment of composites. In Stage 1, ML is applied to obtain estimates of means and covariance matrix, as well as of the associated information matrix, of the original variables that have missing data. The estimates are then transformed to correspond to the appropriate quantities for the composites. In Stage 2, the model is fit to the means and covariance matrix of the composites from Stage 1, essentially treating these quantities as if they had come from complete data. Consistent estimates of standard errors are obtained using the sandwich estimator, where the information matrix for the composites from Stage 1 is in the “meat” of the sandwich. In this research, I will extend the TS methodology for use with composites. I will work with the developer of a free R package for SEM (lavaan) to implement this methodology in R. Because this methodology is useful even in simple regression, I will write an R package to allow a simple implementation in this context without the use of SEM packages. Extensive evaluations of the methodology will be conducted. The development, study, and popularization of this methodology will greatly benefit social scientists working with incomplete data.