Conditional switching: a new variety of regression with many potential environmental applications

We introduce a new form of regression that has many applications to environmental studies. For a sequence composed of key variates with prototypic value chi, this form differs from the estimation of a location parameter-based curve, mu(chi), a scale parameter-based curve, sigma(chi), or other currently used types of regression. Instead of estimating a curve location, scale, or alpha-quantile parameter, it assumes that there are two or more population subgroups; for example, consisting of unsensitized and sensitized individuals, respectively. Although within each subgroup the relationships mu(chi) or sigma(chi) may or may not be horizontal, these relationships are not deemed to be of primary importance. Instead, the mixing parameter P that indexes the proportions of the two subgroups is treated as being related to the key variate value chi. In the sense that its goal is the estimation of a proportion, the new procedure resembles logit regression. But, in terms of the continuous spectrum of values attained by the response variate, the means used to attain its goal are dissimilar from those of logit regression. Specifically, group membership is not known directly but is determined from a proxy continuous variate whose values overlap between groups. Examples are given with simulated and natural data where this new form of regression is applied. We believe that conditional switching regression is a particularly valuable research tool when chemical level chi of an induced asthma attack or birthweight chi measured in a study of the biomarker cotinine's effect on pregnancy outcomes determines whether an attack or a negative outcome occurs.(ABSTRACT TRUNCATED AT 250 WORDS)