Asymmetric circular-linear multivariate regression models with applications to environmental data

Abstract

We propose asymmetric angular-linear multivariate regression models, which were motivated by the need to predict some environmental characteristics based on some circular and linear predictors. A measure of fit is provided through the residual analysis. Some applications using data from solar energy radiation experiment and wind energy are given.

Logistic regression for circular data

“…The estimates of the parameters are also the same despite using the least square estimating method. The article [15] introduces a regression model to represent the relationship between a linear response with a circular predictor and a set of linear covariates. [16] provides a case study to illustrate the importance of circular statistics in analysing the relationship between the ozone level and the wind direction.…”

A New Discordancy Test on a Regression for Cylindrical Data

“…Johnson and Wehrly (1978) proposed a regression of a linear variate on other linear and circular variates in which the model follows closely the linear regression; the leastsquare method is used to find the parameter estimates. Then, SenGupta and Ugwuowo (2006) proposed three different models of circular-linear regression for multivariate data based on both circular and linear predictors. These models can be used to deal with both symmetric and asymmetric model forms.…”

NPCirc: AnRPackage for Nonparametric Circular Methods

“…In the available literature, most efforts have been focused on the development of parametric models. For instance, Presnell, Morrison, and Littel (1998) and the references therein dealt with a circular response and linear covariates; SenGupta and Ugwuowo (2006) proposed some asymmetric models accounting for the circular nature of the covariate and Downs and Mardia (2002) and Kato, Shimizu, and Shieh (2008), among others, addressed the regression with circular response and covariates. Regression estimation avoiding the assumption of a specific parametric shape for the regression curve was studied by Marzio, Panzera, and Taylor (2009) who extended the least squares local polynomial to the case of d-dimensional circular predictors and real-valued responses; Qin, Zhang, and Yan (2011a,b) extended nonparametric models to the case when there is one circular predictor and one or more linear predictors and the response is real-valued, and more recently Marzio, Panzera, and Taylor (2012) proposed a nonparametric estimator for the regression function when the response is circular and the covariate is circular or linear.…”