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Maximum Likelihood Inference for Log-linear Models Subject to Constraints of Double Monotone Dependence

Author

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  • Manuela Cazzaro

    (Università di Milano Bicocca)

  • Roberto Colombi

    (Università di Bergamo)

Abstract

To model an hypothesis of double monotone dependence between two ordinal categorical variables A and B usually a set of symmetric odds ratios defined on the joint probability function is subject to linear inequality constraints. Conversely in this paper two sets of asymmetric odds ratios defined, respectively, on the conditional distributions of A given B and on the conditional distributions of B given A are subject to linear inequality constraints. If the joint probabilities are parameterized by a saturated log-linear model, these constraints are nonlinear inequality constraints on the log-linear parameters. The problem here considered is a non-standard one both for the presence of nonlinear inequality constraints and for the fact that the number of these constraints is greater than the number of the parameters of the saturated log-linear model.

Suggested Citation

  • Manuela Cazzaro & Roberto Colombi, 2006. "Maximum Likelihood Inference for Log-linear Models Subject to Constraints of Double Monotone Dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(2), pages 177-190, August.
    • Handle: RePEc:spr:stmapp:v:15:y:2006:i:2:d:10.1007_s10260-006-0011-y
    DOI: 10.1007/s10260-006-0011-y
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    References listed on IDEAS

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    1. Bartolucci F. & Forcina A. & Dardanoni V., 2001. "Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1497-1505, December.
    2. Agresti, Alan & Coull, Brent A., 1998. "Order-restricted inference for monotone trend alternatives in contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 139-155, August.
    3. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    4. Bartolucci, F. & Scaccia, L., 2004. "Testing for positive association in contingency tables with fixed margins," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 195-210, August.
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    Cited by:

    1. R. Colombi & A. Forcina, 2016. "Testing order restrictions in contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 73-90, January.

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