Using Multiple Imputation to Account for the Uncertainty Due to Missing Data in the Context of Factor Retention

Although parallel analysis has been found to be an accurate method for determining the number of factors in many conditions with complete data, its application under missing data is limited. The existing literature recommends that, after using an appropriate multiple imputation method, researchers either apply parallel analysis to every imputed data set and use the number of factors suggested by most of the data copies or average the correlation matrices across all data copies, followed by applying the parallel analysis to the average correlation matrix. Both approaches for pooling the results provide a single suggested number without reflecting the uncertainty introduced by missing values. The present study proposes the use of an alternative approach, which calculates the proportion of imputed data sets that result in k (k = 1, 2, 3 . . .) factors. This approach will inform applied researchers of the degree of uncertainty due to the missingness. Results from a simulation experiment show that the proposed method can more likely suggest the correct number of factors when missingness contributes to a large amount of uncertainty.