On the effect of the number of quadrature points in a logistic random-effects model: an example

Although generalized linear mixed models are recognized to be of major prac tical importance, it is also known that they can be computationally demandi ng. The problem is the evaluation of the integral in calculating the margin alized likelihood. The straightforward method is based on the Gauss-Hermite technique, based on Gaussian quadrature points. Another approach is provid ed by the class of penalized quasi-likelihood methods. It is commonly belie ved that the Gauss-Hermite method works relatively well in simple situation s but fails in more complicated structures. However, we present here a stri kingly simple example of a logistic random-intercepts model in the context of a longitudinal clinical trial where the method gives valid results only for a high number of quadrature points (Q). As a consequence, this result w arns the practitioner to examine routinely the dependence of the results on Q. The adaptive Gaussian quadrature, as implemented in the new SAS procedu re NLMIXED, offered the solution to our problem. However, even the adaptive version of Gaussian quadrature needs careful handling to ensure convergenc e.