Comparison of Maximum Likelihood with Conditional Pairwise Likelihood Estimation of Person Parameters in the Rasch Model

2016 ◽  
Vol 45 (6) ◽  
pp. 2007-2017 ◽  
Author(s):  
Clemens Draxler ◽  
Gerhard Tutz ◽  
Katharina Zink ◽  
Can Gürer
Keyword(s):  
Maximum Likelihood ◽  
Rasch Model ◽  
Likelihood Estimation ◽  
Pairwise Likelihood ◽  
The Rasch Model

The Rasch Model and Multistage Testing

1988 ◽  
Vol 13 (1) ◽  
pp. 45-52 ◽  
Author(s):  
C. A. W. Glas
Keyword(s):  
Maximum Likelihood ◽  
Rasch Model ◽  
Latent Trait ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Marginal Maximum Likelihood ◽  
Marginal Maximum Likelihood Estimation ◽  
Multistage Testing ◽  
Estimation Equations ◽  
The Rasch Model

This paper concerns the problem of estimating the item parameters of latent trait models in a multistage testing design. It is shown that using the Rasch model and conditional maximum likelihood estimates does not lead to solvable estimation equations. It is also shown that marginal maximum likelihood estimation, which assumes a sample of subjects from a population with a specified distribution of ability, will lead to solvable estimation equations, both in the Rasch model and in the Birnbaum model.

A Review of Estimation Procedures for the Rasch Model with an Eye toward Longish Tests

1980 ◽  
Vol 5 (1) ◽  
pp. 35-64 ◽  
Author(s):  
Howard Wainer ◽  
Anne Morgan ◽  
Jan-Eric Gustafsson
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Rasch Model ◽  
Likelihood Estimation ◽  
New Developments ◽  
Conditional Maximum Likelihood ◽  
English Writing ◽  
Estimation Procedures ◽  
Conditional Maximum ◽  
The Rasch Model

Two estimation procedures for the Rasch Model are reviewed in detail, particularly with respect to new developments that make the more statistically rigorous Conditional Maximum Likelihood estimation practical for use with longish tests. Emphasis of the review is on European developments which are not well known in the English writing world.

scholarly journals A Comparison of Estimation Methods for the Rasch Model

2021 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Rasch Model ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Item Parameter ◽  
Estimation Methods ◽  
Limited Information ◽  
The Impact ◽  
The Rasch Model

The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are compared through a simulation study. The type of ability distribution, the number of items, and sample sizes were varied. It is shown that variants of joint maximum likelihood estimation and conditional likelihood estimation are competitive to marginal maximum likelihood estimation. However, efficiency losses of limited-information estimation methods are only modest. It can be concluded that in empirical studies using the Rasch model, the impact of the choice of an estimation method with respect to item parameters is almost negligible for most estimation methods. Interestingly, this sheds a somewhat more positive light on old-fashioned joint maximum likelihood and limited information estimation methods.

Maximum Likelihood Estimation in Generalized Rasch Models

1986 ◽  
Vol 11 (3) ◽  
pp. 183-196 ◽  
Author(s):  
Jan De Leeuw ◽  
Norman Verhelst
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Rasch Model ◽  
General Model ◽  
Item Analysis ◽  
Likelihood Estimation ◽  
Marginal Maximum Likelihood ◽  
Important Special Case ◽  
Marginal Maximum Likelihood Estimation ◽  
Special Case

We review various models and techniques that have been proposed for item analysis according to the ideas of Rasch. A general model is proposed that unifies them, and maximum likelihood procedures are discussed for this general model. We show that unconditional maximum likelihood estimation in the functional Rasch model, as proposed by Wright and Haberman, is an important special case. Conditional maximum likelihood estimation, as proposed by Rasch and Andersen, is another important special case. Both procedures are related to marginal maximum likelihood estimation in the structural Rasch model, which has been studied by Sanathanan, Andersen, Tjur, Thissen, and others. Our theoretical results lead to suggestions for alternative computational algorithms.

Bayesian Estimation in the Rasch Model

1982 ◽  
Vol 7 (3) ◽  
pp. 175-191 ◽  
Author(s):  
Hariharan Swaminathan ◽  
Janice A. Gifford
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Hierarchical Model ◽  
Rasch Model ◽  
Small Samples ◽  
Simulation Studies ◽  
Bayesian Procedure ◽  
Maximum Likelihood Procedure ◽  
Estimation Procedures ◽  
The Rasch Model

Bayesian estimation procedures based on a hierarchical model for estimating parameters in the Rasch model are described. Through simulation studies it is shown that the Bayesian procedure is superior to the maximum likelihood procedure in that the estimates are (a) more accurate, at least in small samples; and (b) meaningful in that parameters corresponding to perfect item and ability responses can be estimated.

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