Item and person parameter estimation using hierarchical generalized linear models and polytomous item response theory models
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The use of hierarchical generalized linear modeling (HGLM) in social science research is becoming increasingly popular when dealing with nested data (Cheong & Raudenbush, 2000). This technique allows researchers to use loglinear modeling of ordinal variables while taking into account the dependencies inherent in clustered data. Kamata (1999; 2001) investigated the relationship between HGLM and item response theory (IRT) by using HGLM to analyze items nested within people. One of the benefits of using HGLM to model this relationship is that predictor variables can be added to the model while item and person ability parameters are being estimated. By including predictors in the model during the estimation procedure additional information is provided about the parameter estimates at each level of the model. Traditional IRT estimation does not take the nested structure of the data into account beyond the second level. Kamata (1999) demonstrated that parameter estimates vii obtained using HGLM and IRT model estimation were comparable for dichotomously scored items. However, the comparison of estimates for polytomous items has not yet been investigated. Three studies were conducted to assess the use of HGLM with two level IRT data. The first study used IRT and HGLM estimation approaches to analyze a real data set. Results indicated that the parameter estimates obtained for the two approaches were highly correlated. The second study compared the item location and person ability estimates obtained for polytomously scored items across three different models (Murakiís rating scale model, a constrained version of Murakiís rating scale model, and HGLM). The resulting HGLM parameter estimates were comparable to the estimates resulting from Murakiís rating scale model and the constrained version of this model. The third study introduced a person level predictor to investigate the use of HGLM as a tool to detect differential item functioning (DIF) for polytomous items. A comparison between the HGLM approach and the generalized MantelHaenszel statistic for DIF detection demonstrated that both approaches successfully identified DIF items. Implications and limitations for the three studies are discussed and suggestions for future research are presented.