Negative log-likelihood assuming independence within clusters.
marglik(param,xdat,ydat,margmodel,link)The vector of regression and not regression parameters.
\((\mathbf{x}_1 , \mathbf{x}_2 , \ldots , \mathbf{x}_n )^\top\), where the matrix \(\mathbf{x}_i,\,i=1,\ldots,n\) for a given unit will depend on the times of observation for that unit (\(j_i\)) and will have number of rows \(j_i\), each row corresponding to one of the \(j_i\) elements of \(y_i\) and \(p\) columns where \(p\) is the number of covariates including the unit first column to account for the intercept. This xdat matrix is of dimension \((N\times p),\) where \(N =\sum_{i=1}^n j_i\) is the total number of observations from all units.
\((y_1 , y_2 , \ldots , y_n )^\top\), where the response data vectors \(y_i,\,i=1,\ldots,n\) are of possibly different lengths for different units. In particular, we now have that \(y_i\) is (\(j_i \times 1\)), where \(j_i\) is the number of observations on unit \(i\). The total number of observations from all units is \(N =\sum_{i=1}^n j_i\). The ydat are the collection of data vectors \(y_i, i = 1,\ldots,n\) one from each unit which summarize all the data together in a single, long vector of length \(N\).
Indicates the marginal model. Choices are “poisson” for Poisson, “bernoulli” for Bernoulli, and “nb1” , “nb2” for the NB1 and NB2 parametrization of negative binomial in Cameron and Trivedi (1998).
The link function. Choices are “log” for the log link function, “logit” for the logit link function, and “probit” for the probit link function.
Minus log-likelihood assuming independence.
The negative sum of univariate marginal log-likelihoods.
Cameron, A. C. and Trivedi, P. K. (1998) Regression Analysis of Count Data. Cambridge: Cambridge University Press.