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Regression Analysis of Multivariate Fractional Data

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  • José M. R. Murteira
  • Joaquim J. S. Ramalho

Abstract

The present article discusses alternative regression models and estimation methods for dealing with multivariate fractional response variables. Both conditional mean models, estimable by quasi-maximum likelihood, and fully parametric models (Dirichlet and Dirichlet-multinomial), estimable by maximum likelihood, are considered. A new parameterization is proposed for the parametric models, which accommodates the most common specifications for the conditional mean (e.g., multinomial logit, nested logit, random parameters logit, dogit). The text also discusses at some length the specification analysis of fractional regression models, proposing several tests that can be performed through artificial regressions. Finally, an extensive Monte Carlo study evaluates the finite sample properties of most of the estimators and tests considered.

Suggested Citation

  • José M. R. Murteira & Joaquim J. S. Ramalho, 2016. "Regression Analysis of Multivariate Fractional Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 515-552, April.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:4:p:515-552
    DOI: 10.1080/07474938.2013.806849
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    1. John Mullahy, 2010. "Multivariate Fractional Regression Estimation of Econometric Share Models," NBER Working Papers 16354, National Bureau of Economic Research, Inc.
    2. Benjamin E. Hermalin & Nancy E. Wallace, 1994. "The Determinants of Efficiency and Solvency in Savings and Loans," RAND Journal of Economics, The RAND Corporation, vol. 25(3), pages 361-381, Autumn.
    3. Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-295, April.
    4. Lee, Lung-Fei & Pitt, Mark M, 1986. "Microeconometric Demand Systems with Binding Nonnegativity Constraints: The Dual Approach," Econometrica, Econometric Society, vol. 54(5), pages 1237-1242, September.
    5. David Giles & Andrea Keil, 1997. "Applying the RESET test in allocation models: a cautionary note," Applied Economics Letters, Taylor & Francis Journals, vol. 4(6), pages 359-363.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    8. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February.
    9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    10. Andrew Chesher & J. M. C. Santos Silva, 2002. "Taste Variation in Discrete Choice Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 147-168.
    11. Santos Silva, J.M.C. & Murteira, J.M.R., 2009. "Estimation of default probabilities using incomplete contracts data," Journal of Empirical Finance, Elsevier, vol. 16(3), pages 457-465, June.
    12. Gaundry, Marc J. I. & Dagenais, Marcel G., 1979. "The dogit model," Transportation Research Part B: Methodological, Elsevier, vol. 13(2), pages 105-111, June.
    13. Poterba, James M. & Samwick, Andrew A., 2003. "Taxation and household portfolio composition: US evidence from the 1980s and 1990s," Journal of Public Economics, Elsevier, vol. 87(1), pages 5-38, January.
    14. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    15. Wooldridge, Jeffrey M., 1991. "Specification testing and quasi-maximum- likelihood estimation," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 29-55.
    16. Daryl Pregibon, 1980. "Goodness of Link Tests for Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 15-24, March.
    17. Woodland, A. D., 1979. "Stochastic specification and the estimation of share equations," Journal of Econometrics, Elsevier, vol. 10(3), pages 361-383, August.
    18. Wales, T. J. & Woodland, A. D., 1983. "Estimation of consumer demand systems with binding non-negativity constraints," Journal of Econometrics, Elsevier, vol. 21(3), pages 263-285, April.
    19. Mahdi Alkhamisi & Ghadban Khalaf & Ghazi Shukur, 2008. "The effect of fat-tailed error terms on the properties of systemwise RESET test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(1), pages 101-113.
    20. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    21. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    22. Dubin, Jeffrey A., 2007. "Valuing intangible assets with a nested logit market share model," Journal of Econometrics, Elsevier, vol. 139(2), pages 285-302, August.
    23. John Mullahy & Stephanie Robert, 2010. "No time to lose: time constraints and physical activity in the production of health," Review of Economics of the Household, Springer, vol. 8(4), pages 409-432, December.
    24. Fry, Jane M. & Fry, Tim R. L. & McLaren, Keith R., 1996. "The stochastic specification of demand share equations: Restricting budget shares to the unit simplex," Journal of Econometrics, Elsevier, vol. 73(2), pages 377-385, August.
    25. Wang, Hong & Zhang, Licheng & Hsiao, William, 2006. "Ill health and its potential influence on household consumptions in rural China," Health Policy, Elsevier, vol. 78(2-3), pages 167-177, October.
    26. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    27. Pu, Cheng-yun & Lan, Virginia & Chou, Yiing-Jenq & Lan, Chung-fu, 2008. "The crowding-out effects of tobacco and alcohol where expenditure shares are low: Analyzing expenditure data for Taiwan," Social Science & Medicine, Elsevier, vol. 66(9), pages 1979-1989, May.
    28. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    29. Paulo Guimarães & Richard C. Lindrooth, 2007. "Controlling for overdispersion in grouped conditional logit models: A computationally simple application of Dirichlet-multinomial regression," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 439-452, July.
    30. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    31. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    32. Considine, Timothy J & Mount, Timothy D, 1984. "The Use of Linear Logit Models for Dynamic Input Demand Systems," The Review of Economics and Statistics, MIT Press, vol. 66(3), pages 434-443, August.
    33. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 29-59, Supplemen.
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    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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