Abstract
In this paper we study polytomous logistic regression model and the asymptotic properties of the minimum ϕ-divergence estimators for this model. A simulation study is conducted to analyze the behavior of these estimators as function of the power-divergence measure ϕ(λ)
Similar content being viewed by others
References
Agresti A (2002) Categorical data analysis, 2nd Edition. Wiley, Newyork
Ali SM, Silvey SD (1966) A general class of coefficients of divergence of one distribution from another. J R Stat Soc B 26:131–142
Amemiya T (1981) Qualitative response models: a survey. J Econ Lit 19:1483–1536
Anderson JA (1972) Separate sample logistic discrimination. Biometrika 59:19–35
Anderson JA (1982) Logistic discrimination. In: Krishnaiah PR, Kanal LN (eds) Handbook of Statistics. North-Holland, Amsterdam, pp 169–191
Anderson JA (1984) Regression and ordered categorical variables. J R Stat Soc B 46:1–30
Bunch DS, Batsell RR (1989) A Monte Carlo comparison of estimators for the multinomial logit model. J Mark Res 29:56–68
Cox C (1984) An elementary introduction to maximum likelihood estimation for multinomial model: Birch’s theorem and delta method. Am Stat 38:283–287
Cressie N, Read TRC (1984) Multinomial goodness-of-fit tests. J R Stat Soc B 46:440–464
Cressie N, Pardo L, Pardo MC (2003) Size and power considerations for testing loglinear models using ϕ-divergence test statistics. Stat Sin 13(2):550-570
Csiszár I (1963) Eine informationstheoretische ungleichung und ihre anwendung auf den beweis der ergodizität on markhoffschen ketten. Publ Math Inst Hung Acad Sci Ser A 8:85–108
Engel J (1988) Polytomous logistic regression. Stat Neerl 42:233–252
Flemming W (1997) Functions of several variables, 2nd edn. Springer, Berlin Heidelberg Newyork
Kullback S (1985) Minimum discrimination information MDI-estimation. In: Kotz S, Johnson NL (eds) Encyclopedia of Statistical Science, Vol 5. Wiley, New York, pp 527–529
Lesaffre E (1986) Logistic discrimination analysis with application in electrocardiography. Doctoral Thesis, University of Leuven
Lesaffre E, Albert A (1989) Multiple-group logistic regression diagnostic. Appl Stat 38:425–440
Mantel N (1966) Models for complex contingency tables and polychotomous dosage response curves. Biometrics 22:83–95
McCullagh P (1980) Regression models for ordinary data. J R Stat Soc B 42:109–142
Pardo L (1997) Statistical information theory (In Spanish). Hesperides, Spain
Pardo L (2005) Statistical inference based on divergence measures. Statistics: texbooks and monographs. Chapman & Hall/CRC, New York
Pardo L, Pardo MC, Zografos K (2001) Minimum ϕ–divergence estimator for homogeneity in multinomial populations. Sankhya Ser A 63(1):72–92
Pardo JA, Pardo L, Pardo MC (2003). Minimum ϕ-divergence estimator in logistic regression model. To appear in Statistical Papers
Rao CR (1973) Linear statistical inference and its applications. Wiley, Newyork
Theil H (1969) A multinomial extension of the linear logit model. Int Econ Rev 10:251–259
Vajda I (1989) Theory of statistical inference and information. Kluwer, Dordrecht
Author information
Authors and Affiliations
Corresponding author
Additional information
Research partially done when was visiting the Bowling Green State University as the Distinguished Lukacs Professor
Rights and permissions
About this article
Cite this article
Gupta, A.K., Kasturiratna, D., Nguyen, T. et al. A New Family of BAN Estimators for Polytomous Logistic Regression Models based on ϕ- Divergence Measures. Stat. Meth. & Appl. 15, 159–176 (2006). https://doi.org/10.1007/s10260-006-0008-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10260-006-0008-6
Keywords
- Multinomial sampling
- Kullback–Leibler divergence measure
- Minimum ϕ-divergence estimator
- Polytomous regression model