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Methods for addressing missing data have become much more accessible to applied researchers. However, little guidance exists to help researchers systematically identify plausible missing data mechanisms in order to ensure that these methods are appropriately applied. Two considerations motivate the present study. First, psychological research is typically characterized by a large number of potential response variables that may be observed across multiple waves of data collection. This situation makes it more challenging to identify plausible missing data mechanisms than is the case in other fields such as biostatistics where a small number of dependent variables is typically of primary interest and the main predictor of interest is statistically independent of other covariates. Second, there is growing recognition of the importance of systematic approaches to sensitivity analyses for treatment of missing data in psychological science. We develop and apply a systematic approach for reducing a large number of observed patterns and demonstrate how these can be used to explore potential missing data mechanisms within multivariate contexts. A large scale simulation study is used to guide suggestions for which approaches are likely to be most accurate as a function of sample size, number of factors, number of indicators per factor, and proportion of missing data. Three applications of this approach to data examples suggest that the method appears useful in practice.