Logistic mixed models for DIF IRT models can be regarded as logistic - PDF document

28.02.2011 Logistic mixed models for DIF � IRT models can be regarded as logistic mixed models (e.g., Adams, Wilson, & Wu, 1997; de Exploring DIF using explanatory Bock & Wilson, 2004; Kamata, 2001) IRT models � Formulation of the Rasch model (Rasch, 1960) Jörg � Tobias Kuhn University of Münster as a logistic mixed model Psychoco 2011 University of Tübingen Outline Logistic mixed models for DIF � For Persons j, …, J and items i, …, I , the Rasch � Logistic mixed models for DIF model can be specified as � � „Student PISA“ ����� � �� � � � � � �� � � � ��� With � Discussion � � �� ���������� � �� � � �� � � �� � � �� � ��������� � � � ����� �� � � 1

28.02.2011 Logistic mixed models for DIF Logistic mixed models for DIF � Specification of a (uniform) DIF model in the � DIF is regarded as a group � specific difference logistic mixed model (assuming items as fixed; cf. in item parameter(s) (while controlling for van den Noortgate & de Boeck, 2005) overall group differences in ability) � � � ����� � ��� � � � � � �� � � � � � �� � � � �� � �� � �� � � � ��� ��� ��� With � � �� as a group membership indicator, � � � as a group main effect, � � �� as an item � specific indicator for (uniform) DIF Logistic mixed models for DIF Logistic mixed models for DIF � Specification of a (uniform) DIF model in the logistic mixed model (assuming items as random; cf. van den A B Noortgate & de Boeck, 2005) Female � � Male P f ����� � ��� � � � � � �� � � � � � �� � � � �� � �� � � �  P(Y=1|  j ,  i ) P m ��� ��� With � � �� as a group membership indicator, � � � as a group main effect,  j  w =  m � � � � �� as the random main effect for item i , � �� ����� � � � � � � �� as the random effect of belonging to group h for item i , � �� ����� � � 2

28.02.2011 „Student PISA“ „Student PISA“ � Voluntary knowledge test for university students, conducted online by Spiegel magazine � 700,000 participants (subsamples analysed here) � Each participant received 45 items from 5 knowledge domains: politics, history, economics, culture and nature � Question: Can manifest gender differences be attributed to item bias? Person-side of model Level 3 Field of study (Field of „Student PISA“ study) Gender Age Level 2 (Persons) Person Media usage Item-side of model Level 1 (Items) Item logit link P(X=1|parameters) Logit Person*item-side of model (DIF- Parameter) Level1*Level2 Item*gender Level1*Level3 Item*field of study 3

28.02.2011 „Student PISA“ Thanks for your attention Discussion � Logistic mixed models can be used to test for DIF � Flexible model specification is possible � Estimation of complex logistic mixed using ML: quasi � likelihood prcodures are usually preferred � Extension of the framework (Bayesian modeling) feasible 4