Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models

Multiple choice items on tests and Likert items on surveys are ubiquitous in educational, social and behavioral science research; however, methods for analyzing of such data can be problematic. Multidimensional item response theory models are proposed that yield structured Poisson regression models for the joint distribution of responses to items. The methodology presented here extends the approach described in Anderson, Verkuilen, and Peyton (2010) that used fully conditionally specified multinomial logistic regression models as item response functions. In this paper, covariates are added as predictors of the latent variables along with covariates as predictors of location parameters. Furthermore, the models presented here incorporate ordinal information of the response options thus allowing an empirical examination of assumptions regarding the ordering and the estimation of optimal scoring of the response options. To illustrate the methodology and flexibility of the models, data from a study on aggression in middle school (Espelage, Holt, and Henkel 2004) is analyzed. The models are fit to data using SAS.     

日粮中不同Mn,Zn水平对雏鸡卵黄囊中Mn,Zn转移的影响

取自行孵化的新出壳ＡＡ公雏鸡５７６只分为两批分别用于Ｍｎ和Ｚｎ的试验，每批分为四组，每组随机地对应高Ｍｎ或高Ｚｎ、低Ｍｎ或低Ｚｎ，无Ｍｎ和Ｚｎ和标准Ｍｎ或Ｚｎ四种日粮水平的一种，于２，４，６，８，１２，１６，２４，３６，４８，７２，９６，１２０时龄每组分别取雏鸡６只测定卵黄囊中Ｍｎ或Ｚｎ的含量。测定结果进行方差分析和多重比较（ＳＡＳ）。试验表明，雏鸡出壳２小时内卵黄囊Ｍｎ和Ｚｎ的含量分别为０．１９