Generalized linear item response theory.

In this article generalized linear item response theory is discussed, which is based on the following assumptions: (a) A distribution of the responses occurs according to a given item format; (b) the item responses are explained by one continuous or nominal latent variable and p latent as well as observed variables that are continuous or nominal; (c) the responses to the different items of a test are independently distributed given the values ofthe explanatory variables; and (d) a monotone differentiable function g of the expected item response τ is needed such that a linear combination of the explanatory variables is a predictor of g(τ)

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

[2]  F. Samejima.  Estimation of latent ability using a response pattern of graded scores , 1968 .

[3]  Paul F. Lazarsfeld,et al.  Latent Structure Analysis. , 1969 .

[4]  K. Jöreskog.  Statistical analysis of sets of congeneric tests , 1971 .

[5]  R. Darrell Bock,et al.  Estimating item parameters and latent ability when responses are scored in two or more nominal categories , 1972 .

[6]  Robert J. Mokken,et al.  A Theory and Procedure of Scale Analysis. , 1973 .

[7]  D. Andrich.  A rating formulation for ordered response categories , 1978 .

[8]  G. J. Mellenbergh,et al.  Linear models for the analysis and construction of instruments in a facet design. , 1979 .

[9]  C. Mitchell Dayton,et al.  The Nature and Use of State Mastery Models , 1980 .

[10]  Harvey Goldstein,et al.  Dimensionality, bias, independence and measurement scale problems in latent trait test score models , 1980 .

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

[12]  Roderick P. McDonald,et al.  Linear Versus Models in Item Response Theory , 1982 .

[13]  G. Masters.  A rasch model for partial credit scoring , 1982 .

[14]  J. Greenberg,et al.  An Item Response Theory for Personality and Attitude Scales: Item Analysis Using Restricted Factor Analysis , 1983 .

[15]  G. J. G. Upton,et al.  An Introduction to Statistical Modelling , 1983 .

[16]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[17]  B. Wright,et al.  The essential process in a family of measurement models , 1984 .

[18]  David Thissen,et al.  A response model for multiple choice items , 1984 .

[19]  R. Hambleton,et al.  Item Response Theory: Principles and Applications , 1984 .

[20]  Mark D. Reckase,et al.  The Difficulty of Test Items That Measure More Than One Ability , 1985 .

[21]  David Thissen,et al.  A taxonomy of item response models , 1986 .

[22]  G. H. Fischer,et al.  Applying the principles of specific objectivity and of generalizability to the measurement of change , 1987 .

[23]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[24]  Harvey Goldstein,et al.  Five decades of item response modelling , 1989 .

[25]  Gideon J. Mellenbergh,et al.  Item bias and item response theory , 1989 .

[26]  Robert J. Mislevy,et al.  BILOG 3 : item analysis and test scoring with binary logistic models , 1990 .

[27]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[28]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[29]  Psychometric methodology : proceedings of the 7th European Meeting of the Psychometric Society in Trier , 1993 .