Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing 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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A Comparison of Two Methods of Decomposing Item Difficulties

Journal of Educational Statistics ◽

10.3102/10769986012004369 ◽

1987 ◽

Vol 12 (4) ◽

pp. 369-381 ◽

Cited By ~ 10

Author(s):

Kathy E. Green ◽

Richard M. Smith

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Sample Size ◽

Test Data ◽

Simulated Data ◽

Likelihood Estimation ◽

Test Model ◽

Estimation Of Parameters ◽

Linear Logistic Test Model ◽

Conditional Maximum

This paper compares two methods of estimating component difficulties for dichotomous test data. Simulated data are used to study the effects of sample size, collinearity, a measurement disturbance, and multidimensionality on the estimation of component difficulties. The two methods of estimation used in this study were conditional maximum likelihood estimation of parameters specified by the linear logistic test model (LLTM) and estimated Rasch item difficulties regressed on component frequencies. The results of the analysis indicate that both methods produce similar results in all comparisons. Neither of the methods worked well in the presence of an incorrectly specified structure or collinearity in the component frequencies. However, both methods appear to be fairly robust in the presence of measurement disturbances as long as there is a large number of cases (n = 1,000). For the case of fitting data with uncorrelated component frequencies, 30 cases were sufficient to recover the generating parameters accurately.

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A Comparison of Estimation Methods for the Rasch Model

10.20944/preprints202103.0011.v1 ◽

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.

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