Abstract
In this paper, we investigate restricted inference on two types of circular regression, called circular-linear and linear-circular. Our aim in this paper is to propose an alternative method which is necessary to apply where one observes a weak association between circular dependent and linear predictor variables, or between linear dependent and circular predictor variables, having clear knowledge about the sign of slope. We illustrate that restricted inference is particularly useful for those circular regressions, which is due to weak association. Comparison between our proposed restricted inference and the unrestricted inference are given by using two examples, one from ecological study and the other from environmental study
Highlights
Circular variables are those that take any periodic measurements
When studying variables that influence the climate at a certain site, it is found that, from a meteorology point of view, most studies focus on wind direction and related variable such as rainfall (Carnicero, et al 2011)
One is called a linear-circular regression, which has a linear variable as response and a circular variable as predictor
Summary
Circular variables are those that take any periodic measurements. Two typical examples are angle, which is periodic in 360 degrees, and the hourly time, which is periodic in 24 hours. Order-restricted inference in a simple linear regression (Mukerjee and Tu, 1995) is only useful when the association between a response and predictor variables is weak in general. When the predictor or response variable is a circular variable, it is shown in this paper that the order restricted inference is useful, since a simple linear regression involving a circular variable and a linear variable tends to have a weak association.
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