Linear mean-variance negative binomial models for analysis of orange tissue-culture data - Naratip Jansakul; John P. Hinde (Songklanakarin Journal of Science and Technology (SJST), 2004)
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.