Item Parameter Estimation Via Marginal Maximum Likelihood and an EM Algorithm: A Didactic

1988 ◽  
Vol 13 (3) ◽  
pp. 243 ◽  
Author(s):  
Michael R. Harwell ◽  
Frank B. Baker ◽  
Michael Zwarts
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Em Algorithm ◽  
Item Parameter ◽  
Marginal Maximum Likelihood ◽  
Item Parameter Estimation ◽  
Marginal Maximum

Item Parameter Estimation Via Marginal Maximum Likelihood and an EM Algorithm: A Didactic

1988 ◽  
Vol 13 (3) ◽  
pp. 243-271 ◽  
Author(s):  
Michael R. Harwell ◽  
Frank B. Baker ◽  
Michael Zwarts
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Marginal Maximum Likelihood ◽  
Maximum Likelihood Procedure ◽  
Item Parameter Estimates ◽  
Didactic Paper ◽  
Item Parameter Estimation ◽  
Marginal Maximum

The Bock and Aitkin (1981) Marginal Maximum Likelihood/EM approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. Unfortunately, the complexity of the underlying mathematics and the terse nature of the existing literature has made understanding of the approach difficult. To make the approach accessible to a wider audience, the present didactic paper provides the essential mathematical details of a marginal maximum likelihood/EM solution and shows how it can be used to obtain consistent item parameter estimates. For pedagogical purposes, a short BASIC computer program is used to illustrate the underlying simplicity of the method.

scholarly journals Conditional Maximum Likelihood Estimation in Probability-Branched Multistage Designs

2021 ◽  
Author(s):  
Jan Steinfeld ◽  
Alexander Robitzsch
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Parameter Estimate ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Conditional Maximum Likelihood ◽  
Item Parameter Estimates ◽  
Item Parameter Estimation ◽  
Conditional Maximum

This article describes the conditional maximum likelihood-based item parameter estimation in probabilistic multistage designs. In probabilistic multistage designs, the routing is not solely based on a raw score j and a cut score c as well as a rule for routing into a module such as j < c or j ≤ c but is based on a probability p(j) for each raw score j. It can be shown that the use of a conventional conditional maximum likelihood parameter estimate in multistage designs leads to severely biased item parameter estimates. Zwitser and Maris (2013) were able to show that with deterministic routing, the integration of the design into the item parameter estimation leads to unbiased estimates. This article extends this approach to probabilistic routing and, at the same time, represents a generalization. In a simulation study, it is shown that the item parameter estimation in probabilistic designs leads to unbiased item parameter estimates.

scholarly journals Item Parameter Estimation in Multistage Designs: A Comparison of Different Estimation Approaches for the Rasch Model

Psych ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 279-307
Author(s):  
Jan Steinfeld ◽  
Alexander Robitzsch
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Trait Distribution ◽  
Item Parameter Estimates ◽  
Item Parameter Estimation ◽  
Linear Smoothing ◽  
Log Linear ◽  
Conditional Maximum

There is some debate in the psychometric literature about item parameter estimation in multistage designs. It is occasionally argued that the conditional maximum likelihood (CML) method is superior to the marginal maximum likelihood method (MML) because no assumptions have to be made about the trait distribution. However, CML estimation in its original formulation leads to biased item parameter estimates. Zwitser and Maris (2015, Psychometrika) proposed a modified conditional maximum likelihood estimation method for multistage designs that provides practically unbiased item parameter estimates. In this article, the differences between different estimation approaches for multistage designs were investigated in a simulation study. Four different estimation conditions (CML, CML estimation with the consideration of the respective MST design, MML with the assumption of a normal distribution, and MML with log-linear smoothing) were examined using a simulation study, considering different multistage designs, number of items, sample size, and trait distributions. The results showed that in the case of the substantial violation of the normal distribution, the CML method seemed to be preferable to MML estimation employing a misspecified normal trait distribution, especially if the number of items and sample size increased. However, MML estimation using log-linear smoothing lea to results that were very similar to the CML method with the consideration of the respective MST design.

scholarly journals Conditional Maximum Likelihood Estimation in Probability-Branched Multistage Designs

2021 ◽  
Author(s):  
Jan Steinfeld ◽  
Alexander Robitzsch
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Parameter Estimate ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Conditional Maximum Likelihood ◽  
Item Parameter Estimates ◽  
Item Parameter Estimation ◽  
Conditional Maximum

This article describes the conditional maximum likelihood-based item parameter estimation in probabilistic multistage designs. In probabilistic multistage designs, the routing is not solely based on a raw score j and a cut score c as well as a rule for routing into a module such as j < c or j ≤ c but is based on a probability p(j) for each raw score j. It can be shown that the use of a conventional conditional maximum likelihood parameter estimate in multistage designs leads to severely biased item parameter estimates. Zwitser and Maris (2013) were able to show that with deterministic routing, the integration of the design into the item parameter estimation leads to unbiased estimates. This article extends this approach to probabilistic routing and, at the same time, represents a generalization. In a simulation study, it is shown that the item parameter estimation in probabilistic designs leads to unbiased item parameter estimates.

scholarly journals Item Parameter Estimation With the General Hyperbolic Cosine Ideal Point IRT Model

2018 ◽  
Vol 43 (1) ◽  
pp. 18-33 ◽  
Author(s):  
Seang-Hwane Joo ◽  
Seokjoon Chun ◽  
Stephen Stark ◽  
Olexander S. Chernyshenko
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Item Response ◽  
Ideal Point ◽  
Point Estimation ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Marginal Maximum Likelihood ◽  
Hyperbolic Cosine

Over the last decade, researchers have come to recognize the benefits of ideal point item response theory (IRT) models for noncognitive measurement. Although most applied studies have utilized the Generalized Graded Unfolding Model (GGUM), many others have been developed. Most notably, David Andrich and colleagues published a series of papers comparing dominance and ideal point measurement perspectives, and they proposed ideal point models for dichotomous and polytomous single-stimulus responses, known as the Hyperbolic Cosine Model (HCM) and the General Hyperbolic Cosine Model (GHCM), respectively. These models have item response functions resembling the GGUM and its more constrained forms, but they are mathematically simpler. Despite the apparent impact of Andrich’s work on ensuing investigations, the HCM and GHCM have been largely overlooked by applied researchers. This may stem from questions about the compatibility of the parameter metric with other ideal point estimation and model-data fit software or seemingly unrealistic parameter estimates sometimes produced by the original joint maximum likelihood (JML) estimation software. Given the growing list of ideal point applications and variations in sample and scale characteristics, the authors believe these HCMs warrant renewed consideration. To address this need and overcome potential JML estimation difficulties, this study developed a marginal maximum likelihood (MML) estimation algorithm for the GHCM and explored parameter estimation requirements in a Monte Carlo study manipulating sample size, scale length, and data types. The authors found a sample size of 400 was adequate for parameter estimation and, in accordance with GGUM studies, estimation was superior in polytomous conditions.

Sign in / Sign up

Export Citation Format

Share Document