Chapter 12 Estimation and software

The aim of this last chapter is threefold. First, we want to give the reader furt her insights into the estimation methods for the models presented in this volume. Second, we want to discuss the available software for the models presented in this volume. We will not sketch all possibilities of the software, but only those directly relevant to item response modeling as seen in this volume. Third, we want to illustrate the use of various programs for the estimation of a basic model, the Rasch model, for the verbal aggression data. 12.2 General description of estimation algorithms In this section we give abrief overview of the most common estimation methods for the item response models discussed in this volume. It is not our purpose to explain these methods in great detail but rat her to layout the fundamental ideas and discuss some advantages and drawbacks. The content of this section is closely related to theoretical material presented in Chapter 4.

[1]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[2]  Philip E. Gill,et al.  Practical optimization , 1981 .

[3]  Harvey Goldstein,et al.  Improved Approximations for Multilevel Models with Binary Responses , 1996 .

[4]  N. Breslow,et al.  Bias Correction in Generalized Linear Mixed Models with Multiple Components of Dispersion , 1996 .

[5]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[6]  Scott L. Zeger,et al.  Generalized linear models with random e ects: a Gibbs sampling approach , 1991 .

[7]  N. Laird Nonparametric Maximum Likelihood Estimation of a Mixing Distribution , 1978 .

[8]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[9]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[10]  B. D. Bunday,et al.  Basic optimisation methods , 1985, Mathematical Gazette.

[11]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[13]  Noreen Goldman,et al.  An assessment of estimation procedures for multilevel models with binary responses , 1995 .

[14]  D. Hedeker MIXNO: a computer program for mixed-effects nominal logistic regression , 1999 .

[15]  Ivo W. Molenaar,et al.  Estimation of Item Parameters , 1995 .

[16]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[17]  D. Hedeker,et al.  A random-effects ordinal regression model for multilevel analysis. , 1994, Biometrics.

[18]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[19]  Cheng Hsiao,et al.  Random Coefficients Models , 1992 .

[20]  J. Ware,et al.  Random-effects models for serial observations with binary response. , 1984, Biometrics.

[21]  S. R. Searle,et al.  Generalized, Linear, and Mixed Models , 2005 .

[22]  S. Rabe-Hesketh,et al.  Reliable Estimation of Generalized Linear Mixed Models using Adaptive Quadrature , 2002 .

[23]  R. Wolfinger,et al.  Generalized linear mixed models a pseudo-likelihood approach , 1993 .

[24]  Sophia Rabe-Hesketh,et al.  Multilevel logistic regression for polytomous data and rankings , 2003 .

[25]  N. Breslow,et al.  Bias correction in generalised linear mixed models with a single component of dispersion , 1995 .

[26]  D. Hedeker,et al.  MIXOR: a computer program for mixed-effects ordinal regression analysis. , 1996, Computer methods and programs in biomedicine.

[27]  R. Schall Estimation in generalized linear models with random effects , 1991 .

[28]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[29]  R. Littell SAS System for Mixed Models , 1996 .

[30]  H. Goldstein Nonlinear multilevel models, with an application to discrete response data , 1991 .

[31]  D. Bates,et al.  Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model , 1995 .

[32]  S. Raudenbush,et al.  Maximum Likelihood for Generalized Linear Models with Nested Random Effects via High-Order, Multivariate Laplace Approximation , 2000 .

[33]  Qing Liu,et al.  A note on Gauss—Hermite quadrature , 1994 .

[34]  H. Goldstein Restricted unbiased iterative generalized least-squares estimation , 1989 .

[35]  E. B. Andersen,et al.  Asymptotic Properties of Conditional Maximum‐Likelihood Estimators , 1970 .

[36]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

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

[38]  Risto Lethonen Multilevel Statistical Models (3rd ed.) , 2005 .