In this article, a general class of special Rasch models for dichotomous item scores is considered. Although Andersen’s likelihood ratio test can be used to test whether a Rasch model fits to the data, the test does not differentiate between special Rasch models. Therefore, in this article, new likelihood ratio tests are proposed for testing special Rasch models. The tests proposed do not require individual response pattern frequencies and are useful in practice when the observed total score frequencies are sufficiently large.
AndersenE. B. (1972). The numerical solution of a set of conditional likelihood equations. Journal of the Royal Statistical Society Series B, 34, 42––54.
2.
AndersenE. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38, 123––140.
3.
AndersenE. B.MadsenM. (1977). Estimating the parameters of the latent population distribution. Psychometrika, 42, 357––374.
4.
BirnbaumA. (1968). Some latent trait models and their uses in inferring an examinee’s ability. In LordF. M.NovickM. R. (Eds.), Statistical theories of mental test scores (pp. 397––479). Reading, MA: Addison-Wesley.
5.
BishopY. M. M.FienbergS. E.HollandP. W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.
6.
BockR. D.AitkinM. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443––459.
7.
BockR. D.LiebermanM. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179––197.
8.
ChernoffH. (1954). On the distribution of the likelihood ratio. Annals of Mathematical Statistics, 25, 573––578.
9.
DekovicM. (2003). Aggressive and nonaggressive antisocial behavior in adolescence. Psychological Reports, 93, 610––616.
10.
FollmannD. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika, 53, 553––562.
11.
GlasC. A. W. (1988). The derivation of some tests for the Rasch model from the multinomial model. Psychometrika, 53, 525––546.
12.
GlasC. A. W. (1989). Contributions to estimating and testing Rasch models (Doctoral thesis). University of Twente, Enschede, Netherlands.
13.
GlasC. A. W.VerhelstN. D. (1989). Extensions of the partial credit model. Psychometrika, 54, 635––659.
14.
HessenD. J. (2004). A new class of parametric IRT models for dichotomous item scores. Journal of Applied Measurement, 5, 385––397.
15.
HessenD. J. (2005). Constant latent odds-ratios models and the Mantel-Haenszel null hypothesis. Psychometrika, 70, 497––516.
16.
LindsayB.CloggC. C.GregoJ. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of American Statistical Association, 86, 96––107.
17.
RaschG. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: Nielsen and Lydiche.
18.
RaschG. (1966). An item analysis which takes individual differences into account. The British Journal of Mathematical and Statistical Psychology, 19, 49––57.
19.
ShapiroA. (1985). Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints. Biometrika, 72, 133––144.
20.
StoufferS. A.TobyJ. (1951). Role conflict and personality. American Journal of Sociology, 56, 395––406.
21.
ThissenD. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175––186.
22.
WeitzmanR. A. (1996). The Rasch model plus guessing. Educational and Psychological Measurement, 56, 779––790.
23.
ZwindermanA. H.
(1991). Studies of estimating and testing Rasch models (Doctoral thesis). University of Nijmegen, Nijmegen, The Netherlands.
