Improving Fit Assessment and Incomplete Data Diagnostics in Structural Equation Modeling

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The proposed research has the goal of developing and evaluating new methodologies to deal with missing data. Missing data are common in psychological research, particularly in studies that take place over time, take place in the real world rather than in the lab, and that collect a lot of data from participants. When analyzing a dataset with missing data, conclusions may be biased if missing data are not treated using appropriate statistical techniques, particularly when missingness is not random. Other challenging conditions are also often present in social science datasets, such as nonnormality, i.e., deviation from bell-shaped distributions. How to estimate and evaluate the fit of theoretical models that are fit to normal and nonnormal data with missing values is the focus of the present proposal. The proposal is in the context of structural equation models (SEMs), a class of statistical models that are very popular in psychology. These models can include latent variables, i.e., that are not directly observable but instead only their consequences are observable. Such variables are frequently viewed as appropriate representations for psychological constructs, such as personality traits and psychological states. SEMs include more standard statistical models such as regression as a special case. When evaluating how well a proposed SEM describes the data, model fit statistics are used. These statistics will be biased if the dataset contains missing values, and more so if some variables in the dataset are nonnormal. How to adjust the computations of model fit statistics so that they are no longer biased under these challenging circumstances is the first research direction outlined in this proposal. The second direction is to develop measures that evaluate the overall impact of missing data on models and datasets in a single summary statistic. Such statistics have not been developed or studied. Their development will help researchers gauge the overall impact of missing data on the quality of estimation of their models, and it will also help other methodologists better capture the robustness to missing data when evaluating new statistical methods. Ultimately, being able to draw correct statistical conclusions from challenging datasets will improve the quality of the science in psychology and related fields.