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The Literacy Assessment and Monitoring Programme (LAMP) is an international assessment developed to measure literacy skills in developing countries. LAMP is a two-stage assessment. Due to the special data structure of multistage testing, no dimensionality assessment method can be applied directly to LAMP data. In this study, a dimensionality assessment procedure, DETECT, is modified in order to perform dimensionality analyses for LAMP data. This modified DETECT procedure can also used to analyze response data from multistage testing and beyond. It is proven that under certain conditions, the modified DETECT can successfully find the dimensionality-based partition of items for response data from multistage tests.