Traditional regression analyses assume normality of observations and independence of mean and variance. However, there are many examples in science and Technology where the observations come from a skewed distribution and moreover there is a functional dependence between variance and mean. In this article, we propose a method for regression analysis under Inverse Gaussian model when th...

Nonparametric regression analysis provides statistical tools for estimating regression curves or surfaces from noisy data. Conventional nonparametric regression procedures, however, are only appropriate for estimating continuous regression functions. When the underlying regression function has jumps, functions estimated by the conventional procedures are not statistically consistent at the jump...

We consider the problem of regression analysis with imprecise data. By imprecise data we mean imprecise observations of precise quantities in the form of sets of values. In this paper, we explore a recently introduced likelihood-based approach to regression with such data. The approach is very general, since it covers all kinds of imprecise data (i.e. not only intervals) and it is not restricte...

Many English adjectives form the comparative in two ways, so that, for instance, prouder occurs alongside more proud. The availability of several forms raises the general questions of when and why speakers choose one variant over the other. The aim of this article is to identify factors of language structure and language use that underlie the comparative alternation and to determine their relat...

Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regressing explained variables onto the explaining...

This course is an introduction to the mainstay of quantitative empirical work in political science, the linear regression model. We begin by putting the regression model in context by discussing causation, generalization, and quasi-experimentation. We then introduce the basic two-variable regression model, discuss its assumptions, and learn how to test hypotheses with it. This is followed by th...

Finite mixture models have come to play a very prominent role in modelling data. The finite mixture model is predicated on the assumption that distinct latent groups exist in the population. The finite mixture model therefore is based on a categorical latent variable that distinguishes the different groups. Often in practice distinct sub-populations do not actually exist. For example, disease s...

This chapter describes a tree-structured extension and generalization of the logistic regression method for fitting models to a binary-valued response variable. The technique overcomes a significant disadvantage of logistic regression, which is interpretability of the model in the face of multicollinearity and Simpson’s paradox. Section 1 summarizes the statistical theory underlying the logisti...

Soyer and Hogarth’s article, “The Illusion of Predictability,” shows that diagnostic statistics that are commonly provided with regression analysis lead to confusion, reduced accuracy, and overconfidence. Even highly competent researchers are subject to these problems. This overview examines the Soyer-Hogarth findings in light of prior research on illusions associated with regression analysis. ...