Open AccessLIMITS ON LOG CROSS‐PRODUCT RATIOS FOR ITEM RESPONSE MODELS
Author(s) -
Haberman Shelby J.,
Holland Paul W.,
Sinharay Sandip
Publication year - 2006
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2333-8504.2006.tb02016.x
Subject(s) - rasch model , goodness of fit , item response theory , statistics , product (mathematics) , log linear model , mathematics , logistic regression , basis (linear algebra) , econometrics , psychometrics , linear model , geometry
Bounds are established for log cross‐product ratios (log odds ratios) involving pairs of items for item response models. First, expressions for bounds on log cross‐product ratios are provided for unidimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two‐parameter logistic (2PL) model. Results are also illustrated through an example from a study of model‐checking procedures. The bounds obtained can provide a basis for assessment of goodness of fit of these models.