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First-order marginalised transition random effects models with probit link function

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  • Özgür Asar
  • Ozlem Ilk

Abstract

Marginalised models, also known as marginally specified models, have recently become a popular tool for analysis of discrete longitudinal data. Despite being a novel statistical methodology, these models introduce complex constraint equations and model fitting algorithms. On the other hand, there is a lack of publicly available software to fit these models. In this paper, we propose a three-level marginalised model for analysis of multivariate longitudinal binary outcome. The implicit function theorem is introduced to approximately solve the marginal constraint equations explicitly. probit link enables direct solutions to the convolution equations. Parameters are estimated by maximum likelihood via a Fisher--Scoring algorithm. A simulation study is conducted to examine the finite-sample properties of the estimator. We illustrate the model with an application to the data set from the Iowa Youth and Families Project. The R package pnmtrem is prepared to fit the model.

Suggested Citation

  • Özgür Asar & Ozlem Ilk, 2016. "First-order marginalised transition random effects models with probit link function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(5), pages 925-942, April.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:5:p:925-942
    DOI: 10.1080/02664763.2015.1080670
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    References listed on IDEAS

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    1. Gul Inan & Ozlem Ilk, 2019. "A marginalized multilevel model for bivariate longitudinal binary data," Statistical Papers, Springer, vol. 60(3), pages 601-628, June.

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