Item response theory for longitudinal data: population parameter estimation

In this work we propose IRT models to estimate ability distribution parameters of a population of individuals submitted to different tests along the time, having or not common items. The item parameters are considered known and several covariance structures are proposed to accommodate the possible dependence among the abilities of the same individual, measured at different instants. Maximum likelihood equations and some simulation results are presented.

[1]  F. Lord Applications of Item Response Theory To Practical Testing Problems , 1980 .

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

[3]  Russell D. Wolfinger,et al.  A comparison of two approaches for selecting covariance structures in the analysis of repeated measurements , 1998 .

[4]  G. Zyskind Introduction to Matrices with Applications in Statistics , 1970 .

[5]  Ronald K. Hambleton,et al.  Handbook of Modern Item Response Theory. , 1997 .

[6]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[7]  J-P Fox Stochastic EM for estimating the parameters of a multilevel IRT model. , 2003, The British journal of mathematical and statistical psychology.

[8]  J. Gill Hierarchical Linear Models , 2005 .

[9]  R. Darrell Bock,et al.  Multiple Group IRT , 1997 .

[10]  J. Fox,et al.  Bayesian estimation of a multilevel IRT model using gibbs sampling , 2001 .

[11]  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 .

[12]  Heping Zhang,et al.  Analysis of Longitudinal Data , 1999 .

[13]  Lalitha Sanathanan,et al.  The Logistic Model and Estimation of Latent Structure , 1978 .

[14]  Norman Verhelst,et al.  Maximum Likelihood Estimation in Generalized Rasch Models , 1986 .

[15]  R. Hambleton,et al.  Fundamentals of Item Response Theory , 1991 .

[16]  Michel Loève,et al.  Probability Theory I , 1977 .

[17]  H. Teicher,et al.  Probability theory: Independence, interchangeability, martingales , 1978 .