Regression Analysis of Multivariate Fractional Data

Abstract

The present article discusses alternative regression models and estimation methods for dealing with multivariate fractional response variables. Both conditional mean models, estimable by nonlinear least squares and quasi-maximum likelihood, and fully parametric models (Dirichlet and Dirichlet-multinomial), estimable by maximum likelihood, are considered.In contrast to previous papers but similarly to the univariate case, a new parameterization is proposed here for the parametric models, which allows the same specification of the conditional mean of interest to be used in all models, irrespective of the specific functional form adopted for it. 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.JEL classification code: C35.

Factors Affecting the Choice, Intensity, and Allocation of Irrigation Technologies by U.S. Cotton Farmers

“…The estimated parameter will only be consistent and asymptotically normal if E(Y|X) is correctly defined. For a univariate case, a fractional regression model based on the quasi-likelihood and logistic conditional mean functions is useful [18,19]. Here, regression is done simultaneously by adopting a multivariate specification as cotton farmers select multiple irrigation technologies and those are correlated.…”

“…The following functional form of generalization of univariate specification to a multivariate specification with multinomial logit link and multivariate Bernoulli distribution [19] is useful for the fractional regression.…”

“…First, we describe the methods used in the paper. The methods used include probit, Poisson, and fractional multivariate specification with a multinomial logit link and a multivariate Bernoulli distribution [19]. Next, we describe the survey data collection procedure and explanatory variables included in the model.…”

“…Explanatory variables affecting a fractional dependent variable require analysis by using a fractional regression model. We follow the method developed by Murteira and Ramalho [19] to identify the impact of explanatory variables for the allocation of land using multiple irrigation technologies.…”

Multivariate Beta Regression with Application in Small Area Estimation

“…However, their approach does not account for any hierarchical structure of the population and no extension to the multivariate case is discussed. Melo et al (2009), Fabrizi et al (2011) and Murteira and Ramalho (2014) propose and apply multivariate models for dealing with fractional data.…”