Modelling skewed data with many zeros: A simple approach combining ordinary and logistic regression

Abstract

We discuss a method for analyzing data that are positively skewed and contain a substantial proportion of zeros. Such data commonly arise in ecological applications, when the focus is on the abundance of a species. The form of the distribution is then due to the patchy nature of the environment and/or the inherent heterogeneity of the species. The method can be used whenever we wish to model the data as a response variable in terms of one or more explanatory variables. The analysis consists of three stages. The first involves creating two sets of data from the original: one shows whether or not the species is present; the other indicates the logarithm of the abundance when it is present. These are referred to as the 'presence data' and the 'log-abundance' data, respectively. The second stage involves modelling the presence data using logistic regression, and separately modelling the log-abundance data using ordinary regression. Finally, the third stage involves combining the two models in order to estimate the expected abundance for a specific set of values of the explanatory variables. A common approach to analyzing this sort of data is to use a ln (y+c) transformation, where c is some constant (usually one). The method we use here avoids the need for an arbitrary choice of the value of c, and allows the modelling to be carried out in a natural and straightforward manner, using well-known regression techniques. The approach we put forward is not original, having been used in both conservation biology and fisheries. Our objectives in this paper are to (a) promote the application of this approach in a wide range of settings and (b) suggest that parametric bootstrapping be used to provide confidence limits for the estimate of expected abundance.

Effects of stock type, irrigation and effluent dispersal on earthworm species composition, densities and biomasses in New Zealand pastures

“…Building stable predictive models with well distributed residuals proved impossible in the case of Aporrectodea longa (Ude, 1885) because there were a large number of zero counts (absences). We therefore followed the approach recommended by Fletcher et al, (2005) by splitting the modelling (still using REML) into (i) a binary regression step (predicting the probability of A. longa presence in a given ESL for each treatment), followed by (ii) an ordinary regression analysis in which we predicted the densities and biomasses in treatments using only those ESLs in which !1 A. longa individual was found. The first step used the logistic probability model and second step used the normal probability model.…”

Nectar bacteria, but not yeast, weaken a plant–pollinator mutualism

“…Because of a zero-inflated distribution [28], a two-part approach [29,30] was taken to analysing seed set data. First, we used a logistic regression to model the probability of setting seeds (yes or no), with the same predictors as for stigma closure, followed by a LR test.…”

Genetic control of flowering in spotted gum, Corymbia citriodora subsp. variegata and C. maculata

“…Approaches that model the presence or absence of reproductive structures are valid in such cases (Faddy 1998;Kuhnert et al 2005). One approach is the use of a binary logistic regression model, which takes into consideration the presence or absence of a unit (Welsh et al 1996;Fletcher et al 2005). For our analysis, we had to pool observations at higher levels (i.e.…”