Linear mean-variance negative binomial models for analysis of orange tissue-culture data

Negative binomial maximum likelihood regression models are commonly used to analyze overdispersed Poisson data. There are various forms of the negative binomial model with different mean-variance relationships, however, the most generally used are those with linear, denoted by NB1 and quadratic relationships, represented by NB2. In literature, NB1 model is commonly approximated by quasi-likelihood approach. This paper discusses the possible use of the Newton-Raphson algorithm to obtain maximum likelihood estimates of the linear mean-variance negative binomial (NB1) regression model and of the overdispersion parameter. Description of constructing a half-normal plot with a simulated envelope for checking the adequacyof a selected NB1 model is also discussed. These procedures are applied to analyze data of a number of embryos from an orange tissue culture experiment. The experimental design is a completely randomized block design with 3 sugars: maltose, lactose and galactose at dose levels of 18, 37, 75, 110 and 150 µM. Theanalysis shows that the NB1 regression model with a cubic response function over the dose levels is consistentwith the data.