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

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Exploring DIF using explanatory IRT models

JörgTobias Kuhn University of Münster Psychoco 2011 University of Tübingen

Outline

Logistic mixed models for DIF „Student PISA“ Discussion

Logistic mixed models for DIF

IRT models can be regarded as logistic mixed models (e.g., Adams, Wilson, & Wu, 1997; de Bock & Wilson, 2004; Kamata, 2001) Formulation of the Rasch model (Rasch, 1960) as a logistic mixed model

Logistic mixed models for DIF

For Persons j, …, J and items i, …, I, the Rasch model can be specified as

• With

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Logistic mixed models for DIF

DIF is regarded as a groupspecific difference in item parameter(s) (while controlling for

• verall group differences in ability)

Female Male

w =m j P(Y=1|j , i) Pf  Pm

A B

Logistic mixed models for DIF Logistic mixed models for DIF

Specification of a (uniform) DIF model in the logistic mixed model (assuming items as fixed; cf. van den Noortgate & de Boeck, 2005)

• With

as a group membership indicator, as a group main effect, as an itemspecific indicator for (uniform) DIF

Logistic mixed models for DIF

Specification of a (uniform) DIF model in the logistic mixed model (assuming items as random; cf. van den Noortgate & de Boeck, 2005)

• With

as a group membership indicator, as a group main effect,

as the random main effect for item i , as the random effect of belonging to group h for item i ,

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„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?

Age Gender Logit Person P(X=1|parameters) logit link

Person-side of model

Field of study Media usage

Person*item-side of model (DIF- Parameter)

Item*gender Level 3 (Field of study) Level 2 (Persons) Level 1 (Items)

Item-side of model

Item*field of study Level1*Level3 Level1*Level2 Item

„Student PISA“ „Student PISA“

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„Student PISA“ Discussion

Logistic mixed models can be used to test for DIF Flexible model specification is possible Estimation of complex logistic mixed using ML: quasilikelihood prcodures are usually preferred Extension of the framework (Bayesian modeling) feasible

Thanks for your attention