[R-sig-ME] GoodnessOfFit-and-PseudoR²computingFor-glmmTMB-models

[C. AMAL D. GLELE]

Dear paul,
again, many thanks to you for your very helpful details,precions, links and
script.
I'll apply them to my data and let you know.
Best and regards,


2018-02-07 14:46 GMT+01:00 Paul Johnson <paul.johnson at glasgow.ac.uk>:

> No problem. I didn’t read your questions properly though, apologies if
> part of my reply didn’t make sense. I'll try to answer questions 1 and 3 as
> well:
>
> Question 1.
> A good way is to plot your data over your predictions and visually assess
> fit. This isn’t always easy, especially if you have multiple continuous
> predictors, in which case you can produce multiple predicted lines
> conditioned on a few values. Another way is to plot the Pearson residuals
> against fitted values, and check for homoscedasticity along the fitted
> values axis, and absence of any nonlinear trend. A good way is to simulate
> response data from the fitted model (which must fit perfectly) a few times,
> and compare it with the real data using the methods above (plotting data vs
> predictions, residuals vs fitted values plot). If the real data fits the
> model well, it should look similar to the simulated data.
>
> Question 3.
> I’ve pasted below a script showing how to estimate R2 for a Poisson GLMM
> adapting one of the examples from glmmTMB, following this paper:
> "The coefficient of determination R2 and intra-class correlation
> coefficient from generalized linear mixed-effects models revisited and
> expanded"
> http://rsif.royalsocietypublishing.org/content/14/134/20170213
> which built on
> “A general and simple method for obtaining R2 from generalized linear
> mixed‐effects models”
> doi.org/10.1111/j.2041-210x.2012.00261.x
>
> There are a couple of packages that have functions to do this
> (piecewiseSEM, MuMIn), but they don’t work on glmmTMB (yet — piecewiseSEM
> is actively maintained so this might change).
>
> All the best,
> Paul
>
> # add observation-level factor to Salamanders data
> Salamanders$obs <- factor(1:nrow(Salamanders))
> (m1 <- glmmTMB(count~ mined + (1|site) + (1|obs),
>                family=poisson, data=Salamanders))
> summary(m1)
>
> # fixed effects variance (manually - not sure how to get
> # predict.glmmTMB to do this)
> linear.predictor <- model.matrix(m1) %*% fixef(m1)$cond
> fixed.var <- var(linear.predictor)
> # sum variance of all random effects ***excluding OLRE***
> all.ranef.var <- unlist(VarCorr(m1)$cond)
> ranef.var <- all.ranef.var[!names(all.ranef.var) %in% "obs"]
> # OLRE (additive overdispersion variance)
> olre.var <- all.ranef.var["obs"]
>
> # now the observation-level variance
> # (distinct from the observation-level random effect [OLRE])
> # here this is the variance added by the Poisson distribution
> # (aka distribution-specific variance)
>
> # first we need to estimate lambda
> # the Interface paper recommends calculating lambda as
> # exp(beta0 + total.re.var/2)   -- eqn. 5.8
> # beta0 is the intercept from an intercept-only refit of the model
> (beta0 <- fixef(update(m1, ~ . - mined))$cond)
> lambda <- exp(beta0 + (ranef.var + olre.var)/2)
>
> # observation-level variance (Table 1)
> ol.var <- trigamma(lambda)
>
> # total variance
> total.var <- fixed.var + ranef.var + olre.var + ol.var
>
> # marginal R2glmm
> fixed.var / total.var
> # conditional R2glmm
> (fixed.var + ranef.var) / total.var
>
>
>
> > On 6 Feb 2018, at 22:13, C. AMAL D. GLELE <altessedac2 at gmail.com> wrote:
> >
> > Many thanks, Paul.
> > Regards,
> >
> > 2018-02-06 15:53 GMT+01:00 Paul Johnson <paul.johnson at glasgow.ac.uk>:
> > Hi,
> >
> > My preferred approach to overdispersion is none of 1-3 but to assume it
> applies (it usually does, for biological data anyway), and make sure the
> model includes a parameter to model overdispersion. For binomial (except
> Bernoulli) and Poisson you can include an observation-level random effect
> (OLRE). You can then gauge the amount of overdispersion in the model from
> the size of the OLRE variance estimate. (Note the OLRE will mop up
> variation due to *all* sources of lack of fit, including poor model
> specification, e.g. fitting a straight line where a curve would fit better.)
> >
> > Best wishes,
> > Paul
> >
> >
> > > On 6 Feb 2018, at 14:29, C. AMAL D. GLELE <altessedac2 at gmail.com>
> wrote:
> > >
> > > Hi, dear all
> > > Please, your help for the following problem:
> > > when I fit a mixed model using glmmTMB (poisson family or others), how
> do I:
> > > 1) check, if the model fits well my data (goodness of fit)?
> > > 2) check if my model is overdisperced or not (by using sigma(model)?)
> > > 3) compute an pseudo R² to see the percentage of the variability of my
> > > response which is explained by my model?
> > > In advance, thanks for your answers.
> > > Regards,
> > >
> > >       [[alternative HTML version deleted]]
> > >
> > > _______________________________________________
> > > R-sig-mixed-models at r-project.org mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
> >
>
>

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