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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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    1. Tsu-Tan Fu & Lung-An Li & Yih-Ming Lin & Kamhon Kan, 2000. "A limited information estimator for the multivariate ordinal probit model," Applied Economics, Taylor & Francis Journals, vol. 32(14), pages 1841-1851.
    2. Alan Agresti & Ranjini Natarajan, 2001. "Modeling Clustered Ordered Categorical Data: A Survey," International Statistical Review, International Statistical Institute, vol. 69(3), pages 345-371, December.
    3. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    4. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    5. Tutz, Gerhard & Hennevogl, Wolfgang, 1996. "Random effects in ordinal regression models," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 537-557, September.
    6. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
    7. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    8. Renard, Didier & Molenberghs, Geert & Geys, Helena, 2004. "A pairwise likelihood approach to estimation in multilevel probit models," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 649-667, January.
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    1. 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.
    2. 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.
    3. 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.
    4. Moffa, Giusi & Kuipers, Jack, 2014. "Sequential Monte Carlo EM for multivariate probit models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 252-272.
    5. 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.
    6. 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.
    7. 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.
    8. Lisa Bellinghausen & Nicolas Gérard Vaillant, 2010. "Les déterminants du stress professionnel ressenti : une estimation par la méthode des équations d'estimation généralisées," Economie & Prévision, La Documentation Française, vol. 0(4), pages 67-82.

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