
Dear R users,
I am running a mixed model on some count data (n=90) using lmer with a Poisson error distribution and have two nested random effects based on repeated sampling of locations.
One of my explanatory variables is a three level factor with n=30 observations for each level (in the R output below it's the factor "nathabcat"). When you plot this factor against the counts you can see that for one level the counts are very high, for one level low and for another level extremely low - that is all the counts for that level were zero (in the R output copied below "nathabcatlow"). In the model the difference between the very high and low levels comes out as significant but the difference between the high level and the extremely low level is non-significant. This does not make sense and it appears to come from an incredibly high standard error for the model estimate of the extremely low factor level. Intuitively I think that the standard error should not be high as all the values in that level are zero. It seems as though the model is not treating the zeros as I would expect.
If I transform the count variable to x+1 so all the zeros become 1s it runs fine with no inflated standard error and the model finds a significant difference between the extremely low and high levels of the explanatory factor. Even if I add a single 1 to the zero counts in the extremely low level of the explanatory factor the model runs normally.
Can anyone suggest why having only zeros is causing this problem?
Many thanks
Claire
 
When run on the count data:
 
model<-lmer(counts~distcat+nathabcat+avopen+(1|site:distcat),family=poisson)

summary(model)
Generalized linear mixed model fit by the Laplace approximation 
Formula: counts~ distcat + nathabcat + avopen + (1 | site:distcat) 
   AIC   BIC logLik deviance
 133.4 148.4 -60.72    121.4
Random effects:
 Groups       Name        Variance Std.Dev.
 site:distcat (Intercept) 0.47972  0.69262 
Number of obs: 90, groups: site:distcat, 30
Fixed effects:
                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)     8.926e-01  5.723e-01   1.560 0.118849    
distcat1       -1.565e+00  4.375e-01  -3.578 0.000346 ***
nathabcatlow   -1.969e+01  1.681e+03  -0.012 0.990654    
nathabcatstrip -2.743e+00  4.897e-01  -5.602 2.11e-08 ***
avopen          1.556e-02  5.474e-03   2.842 0.004480 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
Correlation of Fixed Effects:
            (Intr) dstct1 nthbctl nthbcts
distcat1    -0.392                       
nathabcatlw  0.000  0.000                
nathbctstrp -0.394  0.233  0.000         
avopen      -0.840  0.058  0.000   0.132 

 
When run on the counts+1:
 
modelb<-lmer(countsplusone~distcat+nathabcat+avopen+(1|site:distcat),family=poisson)
summary(modelb)

Generalized linear mixed model fit by the Laplace approximation 
Formula: countsplusone~ distcat + nathabcat + avopen + (1 | site:distcat) 
   AIC   BIC logLik deviance
 104.5 119.5 -46.24    92.49
Random effects:
 Groups       Name        Variance Std.Dev.
 site:distcat (Intercept) 0.12255  0.35007 
Number of obs: 90, groups: site:distcat, 30
Fixed effects:
                Estimate Std. Error z value Pr(>|z|)    
(Intercept)     1.327092   0.377347   3.517 0.000437 ***
distcat1       -0.681733   0.200206  -3.405 0.000661 ***
nathabcatlow   -1.686040   0.263526  -6.398 1.57e-10 ***
nathabcatstrip -1.399987   0.240289  -5.826 5.67e-09 ***
avopen          0.009323   0.003986   2.339 0.019352 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
Correlation of Fixed Effects:
            (Intr) dstct1 nthbctl nthbcts
distcat1    -0.262                       
nathabcatlw -0.404  0.021                
nathbctstrp -0.386  0.040  0.335         
avopen      -0.906  0.037  0.241   0.196  		 	   		  
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