On the existence and uniqueness of maximum-likelihood estimates in the Rasch model

Psychometrika ◽  
1981 ◽  
Vol 46 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Gerhard H. Fischer
Keyword(s):  
Maximum Likelihood ◽  
Rasch Model ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimates ◽  
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.

Estimation for the Rasch Model When Both Ability and Difficulty Parameters Are Random

1987 ◽  
Vol 12 (1) ◽  
pp. 76-86 ◽  
Author(s):  
Steven E. Rigdon ◽  
Robert K. Tsutakawa
Keyword(s):  
Item Response ◽  
Rasch Model ◽  
Simulated Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Item Response Model ◽  
Item Parameters ◽  
The Em Algorithm ◽  
Simulated Data Sets ◽  
The Rasch Model

Estimation of the parameters of the Rasch model, a one-parameter item response model, is considered when both the item parameters and the ability parameters are considered random quantities. It is assumed that the item parameters are drawn from a N(γ, τ2) distribution, and the abilities are drawn from a N(0, σ2) distribution. A variation of the EM algorithm is used to find approximate maximum likelihood estimates of γ, τ, and σ. A second approach assumes that the difficulty parameters are drawn from a uniform distribution over part of the real line. Real and simulated data sets are discussed for illustration.

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.

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.

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