Application of Poisson Regression to the Analysis of Bacteriological Data

Abstract This paper presents and suggests the use of Poisson regression analysis for modelling the association between bacterial counts observed in a drinking water distribution system and a set of explanatory variables. When the dependent variable is a count that follows the Poisson distribution, the procedure developed in this work is potentially much more appropriate than the conventional method of applying ordinary regress ion analysis after transforming the counts using the square root transformation, since such a transformation may not satisfy all the conditions needed for performing regression. A detailed description of the procedure used for calcul at ing the maximum likelihood estimates of the unknown parameters of the model and their standard errors is given. The method is illustrated by studying the spatial and temporal variation of heterotrophic bacterial counts in the drinking water distribution system of the city of Morsang in France. The results indicated significant variations due to both the spatial and temporal characteristics of the distribut ion of bacteria in the network and also that there was a strong interact ion between those characteristics. Further an attempt to model the temporal and spatial variation showed that a sizeable portion of the total variability could be explained by using temperature and turbidity as predictor variables.