Dear all,

I have the following dataset: each row corresponds to count of forest floor small mammal captured in a plot and vegetation characteristics measured at that plot

> sotr
     plot cnt herbc herbht
1     1A1   0 37.08  53.54
2     1A3   1 36.27  26.67
3     1A5   0 32.50  30.62
4     1A7   0 56.54  45.63
5     1B2   0 41.66  38.13
6     1B4   0 32.08  37.79
7     1B6   0 33.71  30.62
...

I am interested in comparing fit of different specification of Generalized Linear Models (although there are some issues with using AIC or BIC for comparison, but this is the question that I like to post here). Here are two of the several models that I am interested in:

(1) Poission log-linear model
> pois<-glm(cnt~herbc+herbht,family=poisson,data=sotr)
> summary(pois)
Call:
glm(formula = cnt ~ herbc + herbht, family = poisson, data = sotr)

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.341254   0.089969 -14.908   <2e-16 ***
herbc       -0.007303   0.003469  -2.105   0.0353 *  
herbht       0.024064   0.002659   9.051   <2e-16 ***
---
    Null deviance: 1699.0  on 1180  degrees of freedom
Residual deviance: 1569.8  on 1178  degrees of freedom
AIC: 2311.4


(2) Gaussian with sqrt link model
> gaus.sqrt<-glm(cnt~herbc+herbht,family=gaussian(link="sqrt"),data=sotr,start=c(0.1,-0.004,0.01))
> summary(gaus.sqrt)
Call:
glm(formula = cnt ~ herbc + herbht, family = gaussian(link = "sqrt"), 
    data = sotr, start = c(0.1, -0.004, 0.01))

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.462211   0.043475  10.632  < 2e-16 ***
herbc       -0.003315   0.001661  -1.996   0.0461 *  
herbht       0.010241   0.001291   7.935 4.86e-15 ***
---
    Null deviance: 1144.6  on 1180  degrees of freedom
Residual deviance: 1062.9  on 1178  degrees of freedom
AIC: 3235.0

> logLik(gaus.sqrt)
'log Lik.' -1613.524 (df=4)

>From the glm() help file that I read, family=gaussian() accepts the links "identity", "log" and "inverse". There is no mentioning of gaussian() accepting "sqrt" link. Although "sqrt" link is available for family=poisson()

A. Therefore, is the code in (2) actually computing Maximum Likelihood Estimates (MLE) of the coefficients using Gaussian family with "sqrt" link or is it computing MLE of something else?

B. If the code in (2) is computing the MLE with gaussian(link="sqrt"), then will the maximized value of log-likelihood function using logLik() be valid (other than the issue that the dispersion parameter is counted as a parameter in aic() within glm())?

Thank you in advance and I appreciate it very much for any advices that are offered.

Best regards,
TzengYih Lam


TzengYih Lam, PhD Student
College of Forestry
Oregon State University








	[[alternative HTML version deleted]]

