Constrained inference in scaled mixed effects models with applications to London Junior School Project data

Authors

  • Md Mostak Ahammed Department of Statistics, Grand Valley State University, Allendale, MI 49401, USA
  • Bhaskar Bhattacharya School of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, IL 62901, USA

DOI:

https://doi.org/10.3329/jsr.v57i12.72970

Keywords:

Chi-bar square; Constrained estimation and testing; ECME algo- rithms; Mixed effect models.

Abstract

Multiple outcomes arise frequently in many different settings. Mixed effect models are a useful tool for the analyses of such data. However, when outcomes are measured on different scales, analyses based on any one scale are misleading. Often parameters of the model are subject to known order restrictions. To incorporate heterogeneity across different outcomes, we propose a scaled linear mixed effect model. To estimate parameters, we propose a maximum likelihood estimation procedure based on a restricted version of the expectation-conditional maximization either algorithm. Constrained hypotheses testing procedures are developed using likelihood ratio tests. The empirical significance levels and powers are studied using simulations. This article shows that incorporating the restrictions improves the mean squared errors of the estimates and the power of the tests. The methodology is applied on the London Junior School Project data incorporating known restrictions of patterns of scores.

Journal of Statistical Research 2023, Vol 57, No.1-2, pp.81-94

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Published

2024-05-12

How to Cite

Ahammed, M. M. ., & Bhattacharya, B. (2024). Constrained inference in scaled mixed effects models with applications to London Junior School Project data . Journal of Statistical Research, 57(12), 81–94. https://doi.org/10.3329/jsr.v57i12.72970

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Articles