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We develop a mixed (fixed and random effects) models approach to the age-period-cohort (APC) analysis of micro data sets in the form of a series of the repeated cross-section sample surveys that are increasingly available to sociologists. This approach recognizes the multilevel structure of the individual-level responses. As a substantive illustration, we apply our proposed methodology to data on verbal test scores from 15 cross-sections of the General Social Survey, 1974–2000. These data have been the subject of recent debates in the sociological literature. We show how our approach can be used to shed new light on these debates by identifying and estimating age, period, and cohort components of change.