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Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli

The conventional approach of parameter estimation technique, such as maximum likelihood estimation (MLE), can be negatively affected by the skewed distributions of the data. Consequently, estimates of the parameters in the model produced by the MLE in this condition are more likely to be biased. Thi...

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Main Authors: Azizan, Nurul Hafizah, Mahmud, Zamalia, Rambli, Adzhar
Format: Article
Language:English
Published: Unit Penerbitan UiTM Kelantan 2021
Subjects:
Study and teaching. Research
Theory and method of social science statistics
Online Access:https://ir.uitm.edu.my/id/eprint/56382/1/56382.pdf
https://ir.uitm.edu.my/id/eprint/56382/
https://jmcs.com.my/
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spelling my.uitm.ir.563822022-10-03T03:40:32Z https://ir.uitm.edu.my/id/eprint/56382/ Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli Azizan, Nurul Hafizah Mahmud, Zamalia Rambli, Adzhar Study and teaching. Research Theory and method of social science statistics The conventional approach of parameter estimation technique, such as maximum likelihood estimation (MLE), can be negatively affected by the skewed distributions of the data. Consequently, estimates of the parameters in the model produced by the MLE in this condition are more likely to be biased. This article explores the biases in the Rasch rating scale person estimates while using the MLE approach against skewed distributions. The Markov Chain Monte Carlo (MCMC) simulation analysis was carried out with 1000 iterations based on 126 simulation conditions. These simulation conditions were formed using three criteria, which are the number of sample sizes, the number of items, and the type of distributions (i.e., standard normal distribution and skew-normal distribution). The bias in estimation was calculated based on the mean squared difference between the estimated values and actual values of the person parameter. Overall, the findings obtained from the simulation analysis proved that, in skewed distributions, the MLE approach is prone to produce biased person estimates, and the results are getting worse in small sample sizes. Thus, the MLE approach is strongly not recommended when estimating person parameters in Rasch rating scale model (RRSM) under skewed distributions, especially if the sample size is too small. Unit Penerbitan UiTM Kelantan 2021-12 Article PeerReviewed text en https://ir.uitm.edu.my/id/eprint/56382/1/56382.pdf Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli. (2021) Journal of Mathematics and Computing Science (JMCS), 7 (2). pp. 41-48. ISSN 0128-0767 https://jmcs.com.my/
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Study and teaching. Research
Theory and method of social science statistics
spellingShingle Study and teaching. Research
Theory and method of social science statistics
Azizan, Nurul Hafizah
Mahmud, Zamalia
Rambli, Adzhar
Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli
description The conventional approach of parameter estimation technique, such as maximum likelihood estimation (MLE), can be negatively affected by the skewed distributions of the data. Consequently, estimates of the parameters in the model produced by the MLE in this condition are more likely to be biased. This article explores the biases in the Rasch rating scale person estimates while using the MLE approach against skewed distributions. The Markov Chain Monte Carlo (MCMC) simulation analysis was carried out with 1000 iterations based on 126 simulation conditions. These simulation conditions were formed using three criteria, which are the number of sample sizes, the number of items, and the type of distributions (i.e., standard normal distribution and skew-normal distribution). The bias in estimation was calculated based on the mean squared difference between the estimated values and actual values of the person parameter. Overall, the findings obtained from the simulation analysis proved that, in skewed distributions, the MLE approach is prone to produce biased person estimates, and the results are getting worse in small sample sizes. Thus, the MLE approach is strongly not recommended when estimating person parameters in Rasch rating scale model (RRSM) under skewed distributions, especially if the sample size is too small.
format Article
author Azizan, Nurul Hafizah
Mahmud, Zamalia
Rambli, Adzhar
author_facet Azizan, Nurul Hafizah
Mahmud, Zamalia
Rambli, Adzhar
author_sort Azizan, Nurul Hafizah
title Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli
title_short Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli
title_full Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli
title_fullStr Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli
title_full_unstemmed Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli
title_sort bias in person parameter estimates: the maximum likelihood approach to rasch rating scale model against skewed distributions / nurul hafizah azizan, zamalia mahmud and adzhar rambli
publisher Unit Penerbitan UiTM Kelantan
publishDate 2021
url https://ir.uitm.edu.my/id/eprint/56382/1/56382.pdf
https://ir.uitm.edu.my/id/eprint/56382/
https://jmcs.com.my/
_version_ 1746213070768701440
score 13.211869

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