Extension of an iterative hybrid ordinal logistic regression/item response theory approach to detect and account for differential item functioning in longitudinal data.

Many constructs are measured using multi-item data collection instruments. Differential item functioning (DIF) occurs when construct-irrelevant covariates interfere with the relationship between construct levels and item responses. DIF assessment is an active area of research, and several techniques are available to identify and account for DIF in cross-sectional settings. Many studies include data collected from individuals over time; yet appropriate methods for identifying and accounting for items with DIF in these settings are not widely available. We present an approach to this problem and apply it to longitudinal Modified Mini-Mental State Examination (3MS) data from English speakers in the Canadian Study of Health and Aging. We analyzed 3MS items for DIF with respect to sex, birth cohort and education. First, we focused on cross-sectional data from a subset of Canadian Study of Health and Aging participants who had complete data at all three data collection periods. We performed cross-sectional DIF analyses at each time point using an iterative hybrid ordinal logistic regression/item response theory (OLR/IRT) framework. We found that item-level findings differed at the three time points. We then developed and applied an approach to detecting and accounting for DIF using longitudinal data in which covariation within individuals over time is accounted for by clustering on person. We applied this approach to data for the "entire" dataset of English speaking participants including people who later dropped out or died. Accounting for longitudinal DIF modestly attenuated differences between groups defined by educational attainment. We conclude with a discussion of further directions for this line of research.