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Likelihood analysis of the multivariate ordinal probit regression model for repeated ordinal responses

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  • Li, Yonghai
  • Schafer, Daniel W.

Abstract

We consider the analysis of longitudinal ordinal data, meaning regression-like analysis when the response variable is categorical with ordered categories, and is measured repeatedly over time (or space) on the experimental or sampling units. Particular attention is given to the multivariate ordinal probit regression model, in which the correlation between ordered categorical responses on the same unit at different times (or locations) is modeled with a latent variable that has a multivariate normal distribution. An algorithm for maximum likelihood analysis of this model is proposed and the analysis is demonstrated on an example. Simulations clarify the extent to which maximum likelihood estimators can be more efficient than generalized estimating equations (GEE) estimators of regression coefficients and the extent to which likelihood ratio tests can be more accurate than tests based on standard errors and approximate normality of GEE estimators.

Suggested Citation

  • Li, Yonghai & Schafer, Daniel W., 2008. "Likelihood analysis of the multivariate ordinal probit regression model for repeated ordinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3474-3492, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3474-3492
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    References listed on IDEAS

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    Cited by:

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    2. Nooraee, Nazanin & Molenberghs, Geert & van den Heuvel, Edwin R., 2014. "GEE for longitudinal ordinal data: Comparing R-geepack, R-multgee, R-repolr, SAS-GENMOD, SPSS-GENLIN," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 70-83.
    3. Megan D. Higgs & Jay M. Ver Hoef, 2012. "Discretized and Aggregated: Modeling Dive Depth of Harbor Seals from Ordered Categorical Data with Temporal Autocorrelation," Biometrics, The International Biometric Society, vol. 68(3), pages 965-974, September.
    4. Higgs, Megan Dailey & Hoeting, Jennifer A., 2010. "A clipped latent variable model for spatially correlated ordered categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1999-2011, August.
    5. Moffa, Giusi & Kuipers, Jack, 2014. "Sequential Monte Carlo EM for multivariate probit models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 252-272.
    6. Celine Marielle Laffont & Marc Vandemeulebroecke & Didier Concordet, 2014. "Multivariate Analysis of Longitudinal Ordinal Data With Mixed Effects Models, With Application to Clinical Outcomes in Osteoarthritis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 955-966, September.
    7. Auld, Joshua & Mohammadian, Abolfazl(Kouros), 2012. "Activity planning processes in the Agent-based Dynamic Activity Planning and Travel Scheduling (ADAPTS) model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1386-1403.
    8. Shikur, Zewdie Habte & Legesse, Belainch & Haji, Jema & Jelata, Moti, 2020. "Governance structures and incentives in the wheat value chain in Ethiopia," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 15(2), June.

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