[Rasch] Fit statistics

Mike Linacre (RMT) rmt at rasch.org
Wed Dec 2 09:29:12 EST 2009


There are two different approaches to evaluating Rasch fit statistics:

1. Do the data fit the Rasch model exactly?  The standardized fit 
statistics (reported as chi-squares or t-statistics) answer this. Also 
overall chi-square statistics. They are interpreted in the same way as 
statistical tests of the fit of a model to the data. "Significant" fit 
statistics indicate that we reject the hypothesis that the data (exactly) 
fit the Rasch model.


2. Do the data fit the Rasch model usefully? An answer to this is given at 
"Reasonable mean-square fit statistics" http://www.rasch.org/rmt/rmt83b.htm 
- but this answer is rejected by Smith et al. in their 1998 paper. They 
follow philosophy 1.


Mike L.

At 12/1/2009, you wrote:
>Dear all,
>I wonder whether you have any idea about the criteria proposed by Smith 
>(1998) regarding fit statistics. I don't have the paper but it seems that 
>the issue is discussed in:
>Smith, R.M., Schumacker, R.E. and Bush, M.J. 1998: Using item mean squares 
>to evaluate fit to the Rasch model. Journal of outcome Measurement 2, 66-78.
>Moreover, what is "overall (chi-square based) summary tests of fit"  (in 
>Rum 2020) ? What are the ideal and accepted values? How should it be 
>I'd be grateful if you help me out.
>All the best,

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  23:2 Autumn 2009

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