A comparison of NLMIXED and ADMB-RE | ||||||||||
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SAS PROC NLMIXED and ADMB-RE
are currenlty the only software packages that allow full flexibility in formulation of
generalized linear mixed models, and automatic fitting by maximum likelihood. It is therefore of
interest to compare the performance of these packages with respect to the following criteria:
Model 1: Poisson regression with 3 random effectsA simulated dataset with 4 measurement on 59 individuals, along with two covariates x1 and x2. The responce variable Y is drawn from a Poisson(lambda) distributionlog(lambda) = (b1 + U1) + (b2 + U2)*x1 + (b3 + U3)*x2
where b1,b2,b3 are fixed effects and U1,U2,U3 are random effects. Two different parameterizations (referred to as 1 and 2) of the likelihood were considered. In the first the random effect U=sigma*Z, is given a Z~N(0,1) distribution. The second, which appears to be the standard among NLMIXED users, is to directly declare U~N(0,sigma^2). A direct equivalent of these parameterizations was implemented in ADMB-RE. ResultsParameter estimates and run times are given in the following table. NLMIXED is seen to be sensitive to the initial value. For some intial values it does not converge, and this conclusion depends on whether parameterization 1 or 2 is used. Among the 4 runs that converge, only two give the same likelihood value (and the same parameter estimates). ADMB is seen to give the same result for all 3 starting values. The ADMB-table is for parameterization 1, but it has been confirmed that ADMB gives the same result for parameterization 2.Timing: NLMIXED used between 1.5 to 4 times that of ADMB. ConclusionNLMIXED is unstable for this model/dataset, while ADMB is not. | |||||||||