Consider data involving replicate measures (i=1,2) of anchovy larvae counts (y_{i j}) over (j=) 1, .. ,
Question:
Consider data involving replicate measures \(i=1,2\) of anchovy larvae counts \(y_{i j}\) over \(j=\) 1, .. , 49 larvae pairs (Booth et al., 2003). Predictors in a negative binomial regression are logarithms of water volumes (in cubic meters) and day when the readings were made. A code allowing for a random pair effect and homogeneous predictor effects is
Assess the assumption of normality in the pair (cluster) random effects \(u_{0 j}\). Consider gains in fit, and other inferences (e.g. regarding the density of the cluster effects) under a two group discrete mixture allowing distinct \(\beta_{k m}\) coefficients \((\mathrm{k}=0,1,2)\) by group \(m\), distinct negative binomial parameters \(\alpha_{m}\), and distinct pair variances \(\tau_{0 m}^{2}\).
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