[R-sig-ME] Interpretation of GLMM output in R
Thierry Onkelinx
thierry.onkelinx at inbo.be
Sun Aug 2 00:08:35 CEST 2015
Paul,
Note that exp(beta0 + beta1*parasitoids + btree) is equivalent to exp(beta0
+ beta1*parasitoids)*exp(btree). So the relative effect of tree doesn't
depend on the other effects.
I tend to look at the ratio of the 97.5% and 2.5% quantiles of the random
effect. exp(q*sigma)/exp(-q*sigma) or simplified exp(2*q*sigma) with q
=1.96 (97.5% quantile of a normal distribution) and sigma= the standard
deviation of the random effect. exp(2*1.96*0.3261) ~ 3.5 So the 97.5%
quantile tree has about 3.5 times the number of pollinators of the 2.5%
quantile tree.
Best regards,
Thierry
Op 1-aug.-2015 15:43 schreef "Paul Johnson" <pauljohn32 op gmail.com>:
> Hi
>
> Your message comes through with weird line breaks, you should turn off
> the HTML compose option in your mail program, just write text.
>
> On Fri, Jul 31, 2015 at 8:42 AM, Yvonne Hiller <yvonne.hiller op hotmail.de>
> wrote:
> >
> >
> >
> >
> > Dear Ben Bolker and list members,
> >
> >
> >
> > I´am a PhD-student working on tropical plant-pollinator
> > interactions (the fig-fig wasp mutualism).
> >
> > I have some difficulties with my analyses of my data
> > using lmer (family = Poisson). I have read a lot of threads and searched
> for
> > solutions in Zuur 2009, though it was not completely satisfying. I
> looked at
> > other papers using GLMM (espeacially for the fig-fig wasp mutualism),
> but there
> > were so many different ways in reporting and interpreting p-values, AICs
> etc.
> > Therefore, I would be very grateful, if you could go through my output
> and
> > answer my questions to hopefully fully understand GLMM. Thank you so
> much in
> > advance.
> >
> >
> >
> > One of my questions is:
> >
> > Have parasitoids (offspring) and the volume size an
> > effect on the number of pollinator offspring?
> >
> >
> >
> > As pollinators are parasitized by parasitoids, I would
> > expect a negative impact on pollinator offspring. As the size of the fig
> fruits
> > might be an additionally factor (due to limited oviposition sites inside
> the fruit
> > or due to the ovipositor length of a parasitoid is to short to reach
> inner most
> > ovules galled by pollinators), I included it in the model.
> >
> >
> >
> > I have poisson data (counts):
> >
> >
> >
> > Pollinator
> > = pollinator offspring
> >
> > Parasitoids = parasitoid offspring
> >
> > volume = fig fruit size measurement
> >
> > tree = Tree ID
> >
> >
> >
> > I have data from trees in the forest and in the
> > farmland, as well as data of the rainy and dry season. I have chosen to
> perform
> > lmer for each season and habitat separately. For each tree, I have
> collected 10
> > fig fruits to count offspring of wasps at the trophic level (pollinator,
> > parasitoid) and to measure the size of the fruit (volume). As I have 10
> fig
> > fruits per tree, I would use tree as a random effect, to account for
> unmeasured
> > variance between trees. I have found different approaches to that in
> > literature. For instance: We did not include‘ tree ’ and ‘
> > syconium ’ as random factors, because wasps were free to move between
> syconia
> > on the same tree, and between trees.
> >
> > Therefore,
> > I am not sure if I have to use GLMM with trees as a random effect or if
> it’s
> > also possible to use GLM without the random effect.
> >
> >
> >
> > The inclusion of
> > fig volume in this manner removed the need to use “fig” as an additional
> nested
> > factor within “tree”. Is that right?
> >
> >
> >
> > Here, I
> > present the model with the random effect.
> >
> > So, lets start with the model of the farmland during
> > the dry season:
> >
> >
> >
> > fad <-
> lmer(Pollinator~Parasitoids+volume+(1|tree),family="poisson",verbose=TRUE)
> >
> >
> >
> > summary (fad)
> >
> > Generalized linear mixed model fit by the Laplace
> > approximation
> >
> > Formula: Pollinator ~ Parasitoids + volume + (1 |
> > tree)
> >
> > Data:
> > fad.data
> >
> > AIC BIC logLik deviance
> >
> > 1166 1175
> > -578.9 1158
> >
> > Random effects:
> >
> > Groups
> > Name Variance Std.Dev.
> >
> > tree (Intercept) 0.10634 0.3261
> >
> >
> > Number of obs: 80, groups: tree, 8
> >
> >
> >
> > Fixed effects:
> >
> >
> > Estimate Std. Error z value Pr(>|z|)
> >
> > (Intercept)
> > 2.3167867 0.1632747 14.190
> > <2e-16 ***
> >
> > Parasitoids -0.0046908
> > 0.0021686 -2.163 0.0305 *
> >
> >
> > volume
> > 0.0069525 0.0006108 11.383
> > <2e-16 ***
> >
> > ---
> >
> > Signif.
> > codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05
> > ‘.’ 0.1 ‘ ’ 1
> >
> >
> >
> > Correlation of Fixed Effects:
> >
> >
> > (Intr) Prstds
> >
> > Parasitoids -0.160
> >
> > volume
> > -0.657 -0.107
> >
> >
> >
> > 1. Random effects: What does the Random
> > Effect table - the Variance, Std. Dev. and Intercept tells me?
> >
> >
> Your model assumes that the outcome is Poisson with expected value
> exp(beta0 + beta1*parasitoids + btree)
>
> btree is a unique added amount for each tree. The estimate of the
> number btree's variance across trees is 0.1.
>
> What that 0.1 means in terms of the predicted outcome? Well, that
> mostly depends on how big beta0 + beta1*parasitoids is. If that
> number is huge, say 1000, then adding a thing with variance 0.1 won't
> matter much.
>
> On the other hand, if it is 0.01, then the random effect at the tree
> level is very large, compared to the systematic components in your
> model. When the link function gets applied, the distribution of
> outcomes changes in an interesting way.
>
> If you run ranef(), it will spit out the estimates of the random
> differences among trees (btree "BLUPS"). If you run the predict
> method, you can see how those map out to predicted values (exp(beta0 +
> beta1 parasitoids + btree)
>
> >
> > So it says that the
> > between–tree variability is fairly large. But I don’t understand to what
> it
> > relates. Does it mean that pollinator offspring variance is high between
> > trees and might be overestimating the explanatory variables?
> >
> >
> >
> > 2. What can I
> > conclude from the model regarding the fixed effects and how to report
> about it
> > (with or without p-values, z-values, estimates)?
> >
> >
> >
> > So of what I know is that
> > the p-value is only a guide and that it is rather a comparison of two
> models.
> > What are the two models and can I compare them.
> >
> >
> I am puzzled why you see p values at all. In the version of lme4 I'm
> running now, I don't see p values.
>
> Lets compare versions, since I'm pretty sure p values were removed
> quite a while ago.
>
> > sessionInfo()
> R version 3.1.2 (2014-10-31)
> Platform: x86_64-pc-linux-gnu (64-bit)
>
> locale:
> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
> [9] LC_ADDRESS=C LC_TELEPHONE=C
> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
>
> attached base packages:
> [1] stats graphics grDevices utils datasets methods base
>
> other attached packages:
> [1] lme4_1.1-8 Matrix_1.2-2
>
> loaded via a namespace (and not attached):
> [1] grid_3.1.2 lattice_0.20-33 MASS_7.3-43 minqa_1.2.4
> [5] nlme_3.1-121 nloptr_1.0.4 Rcpp_0.12.0 splines_3.1.2
> [9] tools_3.1.2
>
> Anyway...
>
> If you had a huge sample, those p values would be accurate.
>
> You have a small sample, there are other, more computationally
> intensive ways, to get p values. Read the Jrnl Stat Software paper b
> y the lmer team, they describe profiling and bootstrapping. You have
> small enough sample, could do either one.
>
> >
> > 4. What does the
> > correlation of fixed effects tells me?
> >
> It is a hint about multicollinearity & numerical instability, so far as I
> know.
>
> >
> >
> > 5. Is it right
> > that the estimates tells me whether the relation of the fixed effects to
> > pollinator offspring is positive or negative?
> >
> >
> Best way to get answer is to plot the predicted values from the model.
> Use the predict function to plot for various values of the predictor.
>
> >
> > 6. Can I
> > calculate an effect size on each explanatory variable?
> >
> Only if you think the term "effect size" is meaningful. And if you
> have a formula for one. In my experience with consulting here, it
> means anything the researcher wants to call a summary number.
>
> I've come to loathe the term because somebody in the US Dept. of
> Education mandated all studies report standardized effect sizes,
> forcing everybody to make Herculean assumptions about all kinds of
> model parameters to get Cohen's D or whatnot.
>
> >
> >
> > I would highly appreciate your feedback on this.
> > Thanks so much in advance.
> >
> Good luck. Next time, use a text only email composer and try to ask 1
> specific question. You are more likely to get attention if people can
> easily read the message and see what you want. This one was difficult
> to read (for me at least) and also somewhat vague.
>
> >
> >
> > Best wishes,
> >
> > Yvonne Hiller
> >
> >
> >
> >
> >
> >
> > [[alternative HTML version deleted]]
> >
> >
> > _______________________________________________
> > R-sig-mixed-models op r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
>
>
> --
> Paul E. Johnson
> Professor, Political Science Director
> 1541 Lilac Lane, Room 504 Center for Research Methods
> University of Kansas University of Kansas
> http://pj.freefaculty.org http://crmda.ku.edu
>
> _______________________________________________
> R-sig-mixed-models op r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
[[alternative HTML version deleted]]
More information about the R-sig-mixed-models
mailing list