Sensitivity analyses for the mixed coefficients multinomial logit model

For scaling items and persons in large scale assessment studies such as Programme for International Student Assessment (PISA; OECD, PISA 2009 Technical Report. OECD Publishing, Paris, 2012) or Progress in International Reading Literacy Study (PIRLS; Martin et al., PIRLS 2006 Technical Report. TIMSS & PIRLS International Study Center, Chestnut Hill, 2007) variants of the Rasch model (Fischer and Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications. Springer, New York, 1995) are used. However, goodness-of-fit statistics for the overall fit of the models under varying conditions as well as specific statistics for the various testable consequences of the models (Steyer and Eid, Messen und Testen [Measuring and Testing]. Springer, Berlin, 2001) are rarely, if at all, presented in the published reports.In this paper, we apply the mixed coefficients multinomial logit model (Adams et al., The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23, 1997) to PISA data under varying conditions for dealing with missing data. On the basis of various overall and specific fit statistics, we compare how sensitive this model is, across changing conditions. The results of our study will help in quantifying how meaningful the findings from large scale assessment studies can be. In particular, we report that the proportion of missing values and the mechanism behind missingness are relevant factors for estimation accuracy, and that imputing missing values in large scale assessment settings may not lead to more precise results.