

   Dear list:

   I am carrying out a stepwise simplification after implementing a mixed effects model. After removing one of the variables I was analyzing before and all its interactions, I stopped getting false convergence messages and some errors which I suspect were due to overparameterization. Everything was going OK until the step when I had only 2 variables left in the model:


   summary(s.fledgemodel1.50)
Generalized linear mixed model fit by the Laplace approximation 
Formula: nfledge1 ~ sex + briventral + brithr + (1 | site) + (1 | year) 
  AIC   BIC logLik deviance
 56.2 70.86  -22.1     44.2
Random effects:
 Groups Name        Variance  Std.Dev.
 site   (Intercept) 0.0046145 0.067930
 year   (Intercept) 0.0056254 0.075003
Number of obs: 85, groups: site, 12; year, 2

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.396195   0.276410   5.051 4.39e-07 ***
sexM         0.022511   0.109711   0.205    0.837    
briventral   0.001710   0.002325   0.735    0.462    
brithr      -0.004162   0.006200  -0.671    0.502    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Correlation of Fixed Effects:
           (Intr) sexM   brvntr
sexM       -0.378              
briventral -0.599  0.137       
brithr     -0.496  0.115 -0.320


   s.fledgemodel1.52<-update(s.fledgemodel1.50,~.-brithr)
  s.fledgemodel1.53<-update(s.fledgemodel1.50,~.-briventral)
Mensajes de aviso perdidos
1: In mer_finalize(ans) :
  Cholmod warning 'not positive definite' at file:../Cholesky/t_cholmod_rowfac.c, line 432
2: In mer_finalize(ans) : singular convergence (7)

    s.fledgemodel1.54<-update(s.fledgemodel1.50,~.-sex)

   Those 3 parameters, "brithr", "briventral" and "sex" are the only ones left in the model, so I can't imagine how this could be a problem of overparameterization. When doing an ANOVA to compare models 50 and 53, instead of getting a value similar to the z value of the summary table, as usual, I got an extremely low value, as if "briventral" had a significant effect (which it doesn't). After going on with the simplification process, in the last step I only had "briventral" left, and the behaviour returned to normal:

   summary(s.fledgemodel1.55)
Generalized linear mixed model fit by the Laplace approximation 
Formula: nfledge1 ~ briventral + (1 | site) + (1 | year) 
   AIC   BIC logLik deviance
 52.66 62.43 -22.33    44.66
Random effects:
 Groups Name        Variance  Std.Dev.
 site   (Intercept) 0.0079330 0.089068
 year   (Intercept) 0.0045905 0.067753
Number of obs: 85, groups: site, 12; year, 2

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 1.323205   0.224790   5.886 3.95e-09 ***
briventral  0.001123   0.002189   0.513    0.608    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Correlation of Fixed Effects:
           (Intr)
briventral -0.938
> s.fledgemodel1.57<-update(s.fledgemodel1.55,~.-briventral)
> anova(s.fledgemodel1.55,s.fledgemodel1.57)
Data: 
Models:
s.fledgemodel1.57: nfledge1 ~ (1 | site) + (1 | year)
s.fledgemodel1.55: nfledge1 ~ briventral + (1 | site) + (1 | year)
                  Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)
s.fledgemodel1.57  3 50.925 58.253 -22.462                         
s.fledgemodel1.55  4 52.663 62.433 -22.331 0.2622      1     0.6086


   Any idea about why this happens? Eventually, the whole thing works as the error appears in a term that I don't need to simplify until the end, but I am really surprised at this unexpected error message. Any ideas will be much appreciated. 


   Thank you very much


   Iker Vaquero-Alba
   Centre for Ecology and Conservation
   Daphne du Maurier Building
   University of Exeter, Cornwall Campus
   Treliever Road
   TR10 9EZ Penryn
   U.K.

   http://biosciences.exeter.ac.uk/cec/staff/postgradresearch/ikervaquero-alba/
	[[alternative HTML version deleted]]


