[R-sig-ME] Random effect variance = zero

[Rafael Lima Oliveira]

Hello everyone. I have a dataset of  environmental variables
(salinity, temperature, pH, dissolved oxygen, turbidity and depth) as
predictors and as response variables fish densities and rarefied
species richness.

Initially, I run a Gamma-GLMM with log link function using as response
variable fish density and it came up with the error "*Error in
pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GHrule(0L), compDev =
compDev, : pwrssUpdate did not converge in (maxit) iterations*"

As suggested by Ben Bolker comments, I created two model as follow:

m1 <- glm(Density ~ Locality +Salinity + Temperature +pH + DO +
Turbidity + Depth, family= Gamma(link= log), data = dados)

m2<- glmer(Density ~ Salinity + Temperature +pH + DO + Turbidity +
Depth + (1 |Month) + (1|Locality/Site), family= Gamma(link= log), data
= dados, start=list(fixef=coef(gama1)),
control=glmerControl(nAGQ0initStep=FALSE), verbose = 100)

In this case, the first model was fitted to get starting values.

Now, I change my response variable and I'm using  Rarefied Species
Richness. I used, initially, Poisson distribution to my count data
(Richness). However, to avoid comparison bias caused by differences in
total abundance among samples I'm using rarefied fish species richness
(based on 10 individuals).

When I run the model, this warning message appears repeatedly:

- Boundary (singular) fit: see help('isSingular')

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge with max|grad| = 0.0529464 (tol = 0.002, component 1)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :

I'm using gamma distribution instead of Poisson to fit rarefied
species richness. The summary output showed random-effect variance and
Std.Dev values as zero.

The random-effect variances being estimated as zero indicates that my model
should be simplified? Should I remove the random effects terms without
substantial loss of fidelity to the data? The Random structure that I
created in my model account for my nested design, where: (1 |Month) account
for temporal variability of my dataset collected montly during 1 year and
(1|Locality/Site) where a indicated that , spatially my data are nested, in
this case "Site" nested in "Locality".

If any anybody has any tips on this please give me a hand.
Hope you can understand it.
Thanks.

-- 
*Rafael Lima Oliveira*
Doutorando em Biologia Animal
Universidade Federal do Espírito Santo - UFES
Laboratório de Ecologia de peixes marinhos - CEUNES/UFES
*Contato:* (75) 98873-1548 / (27) 99526-3612
*E-mail alternativo:* rafael.l.oliveira using edu.ufes.br
*Currículo Lattes*:  http://lattes.cnpq.br/5215941704013482

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