scholarly journals A note on a computationally efficient implementation of the EM algorithm in item response models

2021 ◽  
Vol 1 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Em Algorithm ◽  
Item Response ◽  
Expectation Maximization ◽  
Computation Time ◽  
Computationally Efficient ◽  
Multidimensional Item Response ◽  
Response Models ◽  
Item Response Models ◽  
The Em Algorithm ◽  
Software Implementations

This note sketches two computational shortcuts for estimating unidimensional item response models and multidimensional item response models with between-item dimensionality utilizing an expectation-maximization (EM) algorithm that relies on numerical integration with fixed quadrature points. It is shown that the number of operations required in the E-step can be reduced in situations of many cases and many items by appropriate shortcuts. Consequently, software implementations of a modified E-step in the EM algorithm could benefit from gains in computation time.

scholarly journals A Note on a Computationally Efficient Implementation of the EM Algorithm in Item Response Models

2020 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Em Algorithm ◽  
Item Response ◽  
Expectation Maximization Algorithm ◽  
Computation Time ◽  
Computationally Efficient ◽  
Response Models ◽  
Item Response Models ◽  
The Em Algorithm ◽  
Software Implementations ◽  
Performance Gains

This note sketches two computational shortcuts for estimating multidimensional item response models with an expectation-maximization algorithm relying on numerical integration. It is shown that he number of operations required in the E-step can be substantially reduced. As a consequence, software implementations of a modified E-step in the EM algorithm could benefit from performance gains in computation time.

scholarly journals Extreme Response Style: A Simulation Study Comparison of Three Multidimensional Item Response Models

2018 ◽  
Vol 43 (4) ◽  
pp. 322-335 ◽  
Author(s):  
Brian C. Leventhal
Keyword(s):  
Item Response ◽  
Partial Credit Model ◽  
Response Model ◽  
Multidimensional Item Response ◽  
Generalized Partial Credit Model ◽  
Response Models ◽  
Item Response Models ◽  
Nominal Response Model ◽  
Extreme Response ◽  
Generalized Partial Credit

Several multidimensional item response models have been proposed for survey responses affected by response styles. Through simulation, this study compares three models designed to account for extreme response tendencies: the IRTree Model, the multidimensional nominal response model, and the modified generalized partial credit model. The modified generalized partial credit model results in the lowest item mean squared error (MSE) across simulation conditions of sample size (500, 1,000), survey length (10, 20), and number of response options (4, 6). The multidimensional nominal response model is equally suitable for surveys measuring one substantive trait using responses to 10 four-option, forced-choice Likert-type items. Based on data validation, comparison of item MSE, and posterior predictive model checking, the IRTree Model is hypothesized to account for additional sources of construct-irrelevant variance.

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