Can you say a little more about why you expect q1 to be
Poisson-distributed, or more generally what mean-variance relationship
you expect? Is there a mechanistic/theoretical framework for the
distribution of this variable? Some reason not to find a transform that
makes the responses reasonably homoscedastic and linear?
In general, it *only* makes sense to compute/test dispersion for model
families where the variance has a fixed relationship with the mean
(binomial, Poisson, ...), not when there is an estimated scale parameter
(Gaussian, Gamma, ...)
Ben Bolker
On 18-01-19 08:29 AM, Juan Due?as wrote:
/Dear all, />//>//>/I wish to describe the relationship between the diversity of soil fungi />/and the application of different nutrients (fertilization). My response />/variable is the exponentiated Shannon index of diversity (q1). The />/explanatory variable has four levels. Each of the treatment factors was />/applied at the plot level and there are four replicates of each factor />/per elevation. Six randomly distributed soil cores were taken within />/each of the plots. />//>/For the GLMMs I used lme4 package version 1.1-15, and vegan 2.4-4 to />/estimate q1. />//>/One of the problems I have is that q1 takes decimal values, therefore it />/would be inappropriate (or impossible?) to fit my response variable with />/a poisson probability distribution. Therefore I tried gamma for the />/model specification with a log link function. I performed model />/selection with pairwise likelihood ratio tests. />//>/I then checked my favored model for over-dispersion (which is depicted />/in the output below). It seems, that the model is under dispersed! I was />/checking the literature for solutions to this issue, but I could only />/find some vague notions, namely that some level of underdispersion is />/tolerated. In the case of overdispersion, it is recommended to use />/quasilikelihood, but apparently this solution has been disabled a while />/ago in lme4. />//>/Generalized linear mixed model fit by maximum likelihood (Laplace />/Approximation) ['glmerMod'] />/Family: Gamma ( log ) />/Formula: q1 ~ Treatment + (1 | Elevation) + (1 | Elevation:Plot) />/Data: dat />/Control: glmerControl(optimizer = "nlminbw") />//>/AIC BIC logLik deviance df.resid />/1523.6 1547.9 -754.8 1509.6 231 />//>/Scaled residuals: />/Min 1Q Median 3Q Max />/-2.0938 -0.6378 -0.0694 0.5815 3.1634 />//>/Random effects: />/Groups Name Variance Std.Dev. />/Elevation:Plot (Intercept) 0.02632 0.1622 />/Elevation (Intercept) 0.01366 0.1169 />/Residual 0.17924 0.4234 />/Number of obs: 238, groups: Elevation:Plot, 47; Elevation, 3 />//>/Fixed effects: />/Estimate Std. Error t value Pr(>|z|) />/(Intercept) 2.63742 0.16504 15.981 <2e-16 *** />/TreatmentN -0.08395 0.13284 -0.632 0.527 />/TreatmentNP -0.15163 0.12964 -1.170 0.242 />/TreatmentP -0.12925 0.12998 -0.994 0.320 />/--- />/Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 />//>/Correlation of Fixed Effects: />/(Intr) TrtmnN TrtmNP />/TreatmentN -0.412 />/TreatmentNP -0.418 0.522 />/TreatmentP -0.417 0.524 0.535 />//>//>/chisq ratio rdf p />/38.4696552 0.1658175 232.0000000 1.0000000 />//>//>/My concrete questions are: Should I be concerned that my model is />/underdispersed? Will the coeficients of the fixed terms be reliable in />/this scenario? />//>//>/I appreciate any help on this regard. />//>//>/Best regards, />//>/Juan F. Due?as />//>/_______________________________________________ />/R-sig-mixed-models at r-project.org