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]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.