[R-sig-ME] lme4, failure to converge with a range of optimisers, trust the fitted model anyway?

[Ken Beath]

No, you need to treat this still as binomial data, using cbind(y,n-y) as
the response where y is the number of positives in each group, and n is the
total in each group. I suggest reading one of the books that discusses
fitting logistic models in R, most advanced texts have a
section. Introductory Statistics with R by Peter Dalgaard has the section
available in Amazon.

You also still need a random effect for the cluster.

While I'm thinking of it, should clusters and country random effects have
been crossed. Generally the sampling is setup so that clusters are nested
within countries which requires a different syntax.

On 5 April 2015 at 10:41, Hans Ekbrand <hans.ekbrand at gmail.com> wrote:

> On Sat, Apr 04, 2015 at 07:36:04PM -0400, Ben Bolker wrote:
> > > So, perhaps I could aggregate the individual level data to the
> > > cluster level, and do without the random term for cluster? I mean,
> > > calculate the proportions of yes in each cluster and use that as
> > > the dependent variable.
> > >
> > > This would, I assume, require that each cluster was given a weight
> > > that corresponded to the number of individuals in it - or I would
> > > not be able to say anything about probabilities at the individual
> > > level, right?
> >
> >  I would say pretty much any time you can aggregate without losing
> > information, you should, for ease of computation (this accords with
> > the Murtaugh 2007 "Simplicity and complexity" paper that I cite here
> > on a regular basis).  If all of your covariates are at the cluster
> > level
>
> [ Thanks for your advice, it's much appreciated. ]
>
> The covariates are not all at the cluster level. Actually only one
> covariate is at the cluster level, the others are at the country
> level.
>
> > then this reduces to a binomial GLM (you can account for
> > overdispersion either by using a quasi-binomial model in glm() or by
> > staying with glmer() and keeping the random effect of cluster (now an
> > observation-level random effect).
>
> Since I still have the country level to account for, I need to use glmer().
>
> I have created an aggregated data set with a variable for the
> proportion deprived=TRUE in each cluster, and a variable for the
> number of cases in that cluster (to use as weight).
>
> Perhaps this is not a question specific for mixed models, but what
> family and link function would be appropriate now? This was the best I
> could come up with:
>
> library(car)
> lm1 <- lmer(logit(Prop.deprived.in.cluster) ~ (1|Country) + QoG + GDPLog +
> Rural * KilledPerMillion5Log, data = my.small.df, weights =
> my.small.df$weight)
>
> Linear mixed model fit by REML ['lmerMod']
> Formula: logit(Prop.deprived.in.cluster) ~ (1 | Country) + QoG + GDPLog +
>     Rural * KilledPerMillion5Log
>    Data: my.small.df
> Weights: my.small.df$weight
>
> REML criterion at convergence: 157709.8
>
> Scaled residuals:
>     Min      1Q  Median      3Q     Max
> -4.9983 -0.5626 -0.0622  0.4371  6.1171
>
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  Country  (Intercept)   1.768   1.33
>  Residual             139.292  11.80
> Number of obs: 38028, groups:  Country, 65
>
> Fixed effects:
>                               Estimate Std. Error t value
> (Intercept)                    1.25542    1.90567    0.66
> QoG                            0.39120    0.40850    0.96
> GDPLog                        -0.51799    0.23031   -2.25
> Ruralyes                       1.91545    0.02232   85.80
> KilledPerMillion5Log           0.06190    0.28557    0.22
> Ruralyes:KilledPerMillion5Log  0.35303    0.03728    9.47
>
> Correlation of Fixed Effects:
>             (Intr) QoG    GDPLog Rurlys KlPM5L
> QoG          0.571
> GDPLog      -0.989 -0.486
> Ruralyes    -0.013  0.001  0.006
> KlldPrMll5L -0.013  0.239 -0.009  0.045
> Rrlys:KPM5L  0.004 -0.001  0.000 -0.519 -0.084
>
> my.small.df is available here if someone wants to have a go at it
>
> http://hansekbrand.se/code/my.small.df.RData (1.1 MB)
>
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>



-- 

*Ken Beath*
Lecturer
Statistics Department
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Phone: +61 (0)2 9850 8516

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