## Applied Statistics and the SAS Pgmg Lang. by R. Cody, J. Smith

By R. Cody, J. Smith

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K ) The Rasch Model for Dichotomous Items 19 Letting βi = − log(δi ) and ϕir = log γr−1 (δ1 , . . , δi−1 , δi+1 , . . , δk ) γr (δ1 , . . , δi−1 , δi+1 , . . 5] deﬁning the ICC, but there are subtle differences that may lead to problems if they are not recognized. The most important of these is that the ICC is a function of θv whereas the CICC is a function of φir , which itself is a function of a subset of item parameters. We will return to this problem in Chapter 5. 500; where ICC values have been calculated for the three values of θ with true scores (expected scores) equal to 1, 2 and 3, respectively.

C) “Quite likely” d) “Very likely” When you start eating how a) “Very easy” easy do you ﬁnd it to stop? b) “Quite easy” c) “Not very easy” d) “Not at all easy” Do you have problems keeping a) “Never” to your diet because you b) “Sometimes” eat to cheer yourself up? c) “Usually” d) “Always” Do you have problems keeping a) “Never” to your diet because you b) “Sometimes” ﬁnd it hard saying no to c) “Usually” food you like? 1. 2. Ordered categories For each item, all response categories are ordered.

11] Again, restrictions are needed to ensure that the model is identiﬁed and this can be done by placing a linear restriction either on the item parameters or on the person parameters. Estimation of item parameters using the joint likelihood function n LJ (ψ1 , . . , ψk , θ1 , . . , θn ) = L(ψ1 , . . 12] v=1 leads to inconsistent item parameter estimates because the number of parameters increases with the number of persons [NEY 48]. Therefore, either a conditional or a marginal approach must be used when estimating item parameters.