[R-sig-ME] glmer: variable sequence matters?

[Ken Beath]

This isn't very surprising, nonlinear optimisation tends to give slightly
different results depending on slight changes to things like starting
values or parameterisation. Sometimes this can be fixed by changes to the
convergence criteria (these don't seem to be accessible in nlmer) but
there can also be problems because the likelihood is not smooth around the
optimum due to numerical errors. There can be massive problems due to
multi-modal likelihoods but in your case results are well within the
standard errors, so there is obviously nothing wrong.

Ken


On Sun, April 19, 2009 3:56 pm, Rense Nieuwenhuis wrote:
> Dear all,
>
> while working on a package for influential data in mixed models, I
> encountered a peculiar situation. As I'll show in the examples below,
> I found that (at least in some situations) the sequence in which
> variables are entered in the model formula, influences the parameters
> of the model. In most cases, these differences are really small, but I
> did encounter an example which leads to rather huge differences.
>
> Unfortunately, I cannot publicly share the data, nor the outcomes, of
> that example, so I'll have to do with an example resulting in smaller
> differences. Nevertheless, I wouldn't expect any differences (neither
> small, nor big) when using exactly the same model formula on the same
> set of data, but only with a different sequence in which the variables
> are entered.
>
> In order to provide a reproducible example, I use the ScotsSec data
> from the mlmRev package, which I modify slightly. The first
> modifications relate to a manipulated intercept and added 'dummy'-
> variable, which is part of the procedure for determining influential
> data (but, the exact reasons for this are not very relevant for this
> problem). Note, however, that the intercept and the additional dummy
> variable (estex.2) are each others' opposite.
>
> library(mlmRev)
> data(ScotsSec)
>
> ScotsSec$intercept.alt <- ifelse(ScotsSec$second=="2", 0, 1)
> ScotsSec$estex.2 <- ifelse(ScotsSec$second=="2", 1, 0)
>
>
> I use these data, and its modifications, to estimate two models. Both
> data and variables in the model formulae are identical, except that in
> model.a the dummy-variable estex.2 is added as the last of the fixed
> effects, whereas in model.b it is added directly after the modified
> intercept-variable (intercept.alt). Also, in both models the
> 'standard' intercept is omitted. When the fixed effects of these two
> models are compared, these are exactly identical as expected.
>
>
> model.a <- lmer(attain ~ intercept.alt + verbal + social + estex.2 +
> 	(0 + intercept.alt | primary) + (0 + intercept.alt|second) -1 ,
> 	data=ScotsSec)
>
>
> model.b <- lmer(attain ~ intercept.alt + estex.2 + verbal + social +
> 	(0 + intercept.alt | primary) + (0 + intercept.alt|second) -1 ,
> 	data=ScotsSec)
>
>
> fixef(model.a)
> fixef(model.b) # Identical
>
> However, testing exactly these model formulae on a logistic set of
> data, results in (slightly) different estimates for the fixed effects.
> To illustrate this, I created a binary outcome variable ('pass'), and
> specify the same models as above, with the addition of the
> family="binomial" parameter.
>
> ScotsSec$pass <- ifelse(ScotsSec$attain > 5, 1,0)
> model.c <- lmer(pass ~ intercept.alt + verbal + social + estex.2 +
> 	(0 + intercept.alt | primary) + (0 + intercept.alt|second) -1 ,
> 	data=ScotsSec,
>      family="binomial")
>
> model.d <- lmer(pass ~ intercept.alt + estex.2 + verbal + social +
> 	(0 + intercept.alt | primary) + (0 + intercept.alt|second) -1 ,
> 	data=ScotsSec,
>      family="binomial")
>
> fixef(model.c)
> fixef(model.d) # Not Identical
>
> To my surprise, now the fixed effects differ. How is this possible,
> and, why does this only seem to occur using glmer? I would not have
> expected the model outcomes to be subject to the sequence in which the
> variables are specified.
>
> I would be grateful if anyone could shed some light on this (to me)
> rather peculiar situation,
>
> with kind regards,
>
> Rense Nieuwenhuis
>
>
>
>
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