Exploratory Factor Analysis: Model Selection and Identifying Underlying Symptoms
Cole, Matthew Kevin
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Exploratory factor analysis (EFA) is a common yet powerful tool to better understand the theoretical structure of a set of variables. A core problem of conducting an EFA is determining the number of factors (m) to extract and examine. In this thesis, we examined the performance of existing methods of estimating m while proposing and assessing a cross validated method for estimating m across various settings. These methods were then considered in a study incorporating EFA to assess the relationship and categorization of self-reported chronic rhinosinusitis (CRS) symptoms, a common sinus inflammatory disease, within three cross sectional questionnaires as well as within the in the changes in symptoms between questionnaires. A cross validated approach (trace) was developed by which m increases until the discrepancy between the implied correlation of a partition of data and the observed correlation of the other data partition increases. In order to assess the performance of this new method as well as other, common approaches, a simulation study was designed in which valid factor loading matrices were simulated using a new procedure, and random samples were drawn from their respective correlation matrices. The trace method displayed quickly increasing accuracy when more samples were drawn, a phenomenon not observed in other methods. Trace was also applied to the CRS data, suggesting 13 factors to be extracted, more than other methods. This non-agreement possibly highlights the differences in factor extraction interpretations, and the different meanings of “correct” m. An EFA was carried out on self-reported CRS symptoms as well as changes in symptom responses over time in order to identify any relationships between or categorization of CRS symptoms. A total of 3535 primary care patients were included this study having responded to three questionnaires of 37 repeated questions spanning a 16-month period. After extracting factors from all three questionnaires and two symptom difference scores, five stable factors were identified in each. The factors of congestion and discharge, facial pain and pressure, smell loss, asthma and constitutional as well as ear and eye symptoms were consistent with the hypothesis that CRS symptoms are measuring several distinct biological processes.