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6 Command file: Specifying the terms in the mixed model 100likelihood or PQL (Breslow and Clayton, 1993). The technique is also knownby other names, including Schall’s technique (Schall, 1991), pseudo-likelihood(Wolfinger and O’Connell, 1993) and joint maximisation (Harville and Mee, 1984,Gilmour et al., 1985). It is implemented in many statistical packages, for instance,in the GLMM procedure (Welham, 2005) and the IRREML procedure of Genstat(Keen, 1994), in MLwiN (Goldstein et al., 1998), in the GLMMIXED macro inSAS and in the GLMMPQL function in R, to name a few.The PQL technique is based on a first order Taylor series approximation to thelikelihood. It has been shown to perform poorly for certain types of GLMMs.In particular, for binary GLMMs where the number of random effects is largecompared to the number of observations, it can underestimate the variance componentsseverely (50%) (e.g. Breslow and Lin, 1995, Goldstein and Rasbash,1996, Rodriguez and Goldman, 2001, Waddington et al., 1994). For other typesof GLMMs, such as Poisson data with many observations per random effect, ithas been reported to perform quite well (e.g. Breslow, 2003). As well as the abovereferences, users can consult McCulloch and Searle (2001) for more informationabout GLMMs.Most studies investigating PQL have focussed on estimation bias. Much lessattention has been given to the wider inferential issues such as hypothesis testing.In addition, the performance of this technique has only been assessed on a smallset of relatively simple GLMMs. Anecdotal evidence from users suggests thatthis technique can give very misleading results in certain situations.CautionCautionTherefore we cannot recommend the use of this technique for general use. It isincluded in the current version of ASReml for advanced users. It is highly recommendedthat its use be accompanied by some form of cross-validatory assessmentfor the specific dataset concerned. For instance, one way of doing this would beby simulating data using the same design and using parameter values similar tothe parameter estimates achieved, such as used in Millar and Willis (1999).The standard GLM Analysis of Deviance (!AOD) should not be used when thereare random terms in the model as the variance components are reestimated foreach submodel.