Likelihood Ratio Tests for Special Rasch Models

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.

[1]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[2]  R. Darrell Bock,et al.  Fitting a response model forn dichotomously scored items , 1970 .

[3]  Cees A. W. Glas,et al.  The derivation of some tests for the rasch model from the multinomial distribution , 1988 .

[4]  Erling B. Andersen,et al.  The Numerical Solution of a Set of Conditional Estimation Equations , 1972 .

[5]  B. Lindsay,et al.  Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis , 1991 .

[6]  Dean Follmann,et al.  Consistent estimation in the rasch model based on nonparametric margins , 1988 .

[7]  A. Zwinderman.  Studies of estimating and testing Rasch models , 1991 .

[8]  H. Chernoff.  On the Distribution of the Likelihood Ratio , 1954 .

[9]  Melvin R. Novick,et al.  Some latent train models and their use in inferring an examinee's ability , 1966 .

[10]  D. Hessen.  A new class of parametric IRT models for dichotomous item scores. , 2004, Journal of applied measurement.

[11]  R. D. Bock,et al.  Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm , 1981 .

[12]  R. A. Weitzman.  The Rasch Model Plus Guessing , 1996 .

[13]  J. W. Getzels,et al.  Role conflict and personality. , 1955, Journal of personality.

[14]  N. D. Verhelst,et al.  Extensions of the partial credit model , 1989 .

[15]  A. Shapiro.  Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints , 1985 .

[16]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[17]  D. Hessen.  Constant latent odds-ratios models and the mantel-haenszel null hypothesis , 2005 .

[18]  E. B. Andersen,et al.  A goodness of fit test for the rasch model , 1973 .

[19]  E. B. Andersen,et al.  Estimating the parameters of the latent population distribution , 1977 .

[20]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[21]  David Thissen,et al.  Marginal maximum likelihood estimation for the one-parameter logistic model , 1982 .

[22]  M. Deković.  Aggressive and Nonaggressive Antisocial Behavior in Adolescence , 2003, Psychological reports.

[23]  G. Rasch,et al.  An item analysis which takes individual differences into account. , 1966, The British journal of mathematical and statistical psychology.