Modelling of non-linear growth curves on series of correlated count data measured at unequally spaced times: a full likelihood based approach

Abstract

A ''robust'' version of the gamma-Poisson model (Lambert, P., 1996, Applied Statistics, in press) for series of count data observed at unequally spaced times is used to analyze the growth of three closed colonies of Paramecium aurelium in a nutritive medium (Diggle, P. J., 1990, Time Series. A Biostatistical Introduction) where successive sample counts within each replicate are likely to be statistically dependent. A generalized form of the logistic growth curve (Nelder, J. A., 1961, Biometrika 17, 89-100; 1962, Biometrics 18, 614-616) further developed by Heitjan (1991, Statistics in Medicine 19, 1075-1088; 1991, Journal of the American Statistical Association 86, 891-898) and including the Mitscherlich, Gompertz, logistic, and exponential forms as well-known members, was chosen to model the response profile. Comparisons with other (possibly nonnested) models are made using the Akaike criterion (Akaike, H., 1973, in Second lnternational Symposium on Inference Theory Petrov).