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Alternative Specifications of Multivariate Multilevel Probit Ordinal Response Models

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  • Leonardo Grilli
  • Carla Rampichini

Abstract

Multivariate multilevel models for ordinal variables are quite complex with respect to both interpretation and estimation. The specification in terms of a multivariate latent distribution and a set of thresholds helps in the interpretation of the variance-covariance parameters. However, most existing estimation algorithms for multilevel models can be used only if the model is reparameterized as a univariate model with an additional dummy bottom level. Moreover, the univariate formulation allows the model to be cast in the framework of Generalized Linear Latent and Mixed Models ( Rabe-Hesketh, Pickles, & Skrondal, 2001a ), a rather general class that includes, as special cases, structural equations and factor models. This article outlines the multivariate latent distribution specification and the corresponding interpretation issues; it then shows the univariate formulation, along with some alternative parameterizations that are useful in the estimation phase. An application to student ratings data illustrates the interpretation of the parameters and the estimation procedures, with a discussion of some computational issues.

Suggested Citation

  • Leonardo Grilli & Carla Rampichini, 2003. "Alternative Specifications of Multivariate Multilevel Probit Ordinal Response Models," Journal of Educational and Behavioral Statistics, , vol. 28(1), pages 31-44, March.
  • Handle: RePEc:sae:jedbes:v:28:y:2003:i:1:p:31-44
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    Cited by:

    1. Makoto Chikaraishi & Akimasa Fujiwara & Junyi Zhang & Kay Axhausen, 2011. "Identifying variations and co-variations in discrete choice models," Transportation, Springer, vol. 38(6), pages 993-1016, November.
    2. Leonardo Grilli & Carla Rampichini, 2007. "A multilevel multinomial logit model for the analysis of graduates’ skills," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 381-393, November.
    3. Li Yu & Peter F. Orazem, 2014. "O-Ring production on U.S. hog farms: joint choices of farm size, technology, and compensation," Agricultural Economics, International Association of Agricultural Economists, vol. 45(4), pages 431-442, July.
    4. Pier Ferrari & Laura Pagani & Carlo Fiorio, 2011. "A Two-Step Approach to Analyze Satisfaction Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 104(3), pages 545-554, December.
    5. Yu, Li & Orazem, Peter F., 2008. "Human Capital, Complex Technologies, Firm Size and Wages: A Test of the O-Ring Production Hypotheses," Working Papers 44873, Iowa State University, Department of Economics.
    6. Ralitza V. Gueorguieva, 2005. "Comments about Joint Modeling of Cluster Size and Binary and Continuous Subunit-Specific Outcomes," Biometrics, The International Biometric Society, vol. 61(3), pages 862-866, September.
    7. Yu, Li, 2008. "Three essays on technology adoption, firm size, wages and human capital," ISU General Staff Papers 2008010108000016715, Iowa State University, Department of Economics.

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