Categorical Data Analysis Using a Skewed Weibull Regression Model

In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log–log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as frequentist estimation procedures for binomial and multinomial data responses are presented in detail. The analysis of two datasets to show the efficiency of the proposed model is performed.

[1]  Gerhard Tutz,et al.  Advances in GLIM and Statistical Modelling , 1992 .

[2]  Binary data regression: Weibull distribution , 2009 .

[3]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[4]  Adelchi Azzalini,et al.  The Skew-Normal and Related Families , 2018 .

[5]  A. Whittemore.  Transformations to Linearity in Binary Regression , 1983 .

[6]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[7]  J. Gaddum.  Probit Analysis , 1948, Nature.

[8]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[9]  Claudia Czado,et al.  On Link Selection in Generalized Linear Models , 1992 .

[10]  J. H. Schuenemeyer,et al.  Generalized Linear Models (2nd ed.) , 1992 .

[11]  H. Robbins.  An Empirical Bayes Approach to Statistics , 1956 .

[12]  On the Independence Jeffreys prior for skew-symmetric models with applications , 2013, 1307.6442.

[13]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[14]  A. Agresti,et al.  Statistical Methods for the Social Sciences , 1979 .

[15]  Observations on Quantit Analysis , 1983 .

[16]  Ming-Hui Chen,et al.  Propriety of posterior distribution for dichotomous quantal response models , 2000 .

[17]  D. Dey,et al.  Flexible generalized t-link models for binary response data , 2008 .

[18]  R. Prentice,et al.  A generalization of the probit and logit methods for dose response curves. , 1976, Biometrics.

[19]  Víctor M. Guerrero,et al.  Use of the Box-Cox transformation with binary response models , 1982 .

[20]  Julio Michael Stern,et al.  SPECIAL CHARACTERIZATIONS OF STANDARD DISCRETE MODELS , 2008 .

[21]  Horst Rinne,et al.  The Weibull Distribution: A Handbook , 2008 .

[22]  Therese A. Stukel,et al.  Generalized logistic models , 1988 .

[23]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[24]  Francisco J. Aranda-Ordaz,et al.  On Two Families of Transformations to Additivity for Binary Response Data , 1981 .

[25]  Dongchu Sun.  A note on noninformative priors for Weibull distributions , 1997 .

[26]  Parametric link modification of both tails in binary regression , 1994 .

[27]  David W. Hosmer,et al.  Applied Logistic Regression , 1991 .

[28]  D. Pregibon.  Goodness of Link Tests for Generalized Linear Models , 1980 .

[29]  B. Arnold,et al.  Measuring Skewness with Respect to the Mode , 1995 .

[30]  E. Nakano,et al.  Establishment of the comet assay in the freshwater snail Biomphalaria glabrata (Say, 1818). , 2008, Mutation research.

[31]  Carlos J. Perez,et al.  Bayesian analysis of some models that use the asymmetric exponential power distribution , 2015, Stat. Comput..

[32]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[33]  Heleno Bolfarine,et al.  A Framework for Skew-Probit Links in Binary Regression , 2010 .

[34]  D. Dey,et al.  A New Skewed Link Model for Dichotomous Quantal Response Data , 1999 .

[35]  H. Akaike.  A new look at the statistical model identification , 1974 .

[36]  Alan Agresti,et al.  Categorical Data Analysis , 2003 .

[37]  G. Brier.  VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

[38]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[39]  P. McCullagh,et al.  Generalized Linear Models , 1984 .