An investigation of quasi-likelihood methods and respnse variable transformation for analysing aggregated insect counts data

Abstract

Insect counts data arising from ecological or pest management studies usually exhibit a high degree of clustering (aggregation) which present special problems for regression modeling. In this paper, we have investigated three different methods that can be used to analyse such data. These are power transformation of response variable based on Taylor's Power Law (1961) and Quasi-likelihood modeling with variance functions based on the power law, V(Y)=αµβ and the variance function of the Negative Binomial, V(Y)= (µ+µ2/k). We apply the methods to some counts data collected on fruit fly species Bactocera zonata.The response variable transformation based on Taylor's Power Law was effective in stabilizing the variance but did not achieve normality of the transformed variable. On the other hand, Quasi-likelihood models appeared to fit the data fairly well for both variance function forms. Overall, the results show that response variable transformation of raw data is not appropriate for the fruit fly counts data used in this study or more general data of similar kind, but quasi-likelihood modeling with variance forms V(Y)=Φµβ or V(Y)=Φ(µ+µ<sup>2/k) appears to be a sensible approach.

Keywords: Aggregated insect counts data, Transformation of raw data, Quasi-likelihood, Taylor's Power Law, Negative binomial distribution

> East African Journal of Statistics Vol. 1 (2) 2006: pp. 215-224</sup>