I'm confused as to the trustworthiness of the dispersion parameters reported by glm. Any help or advice would be greatly appreciated.
Context: I'm interested in using a fitted GLM to make some predictions. Along with the predicted values, I'd also like to have estimates of variance for each of those predictions. For a Gamma-family model, I believe this can be done as Var[y] = dispersion parameter * predicted value ^ 2. Thus, I'm interested in knowing the dispersion parameter for this fitted model. Specifics: The summary function says that my fitted GLM has a dispersion parameter=15.8. On the other hand, the gamma.dispersion function (MASS) says that the GLM uses a dispersion parameter of 1.86. I could understand some modest difference, as the help for gamma.shape() says that the MASS functions return a more accurate dispersion value than summary(). However, these two numbers differ by a factor of 8, which is quite a lot. Is this normal? Would you folks expect such a large difference? Which value should I trust? R terminal excerpt: > summary(tempglm_g2) Call: glm(formula = precip_sbi ~ precip_oxx + precip_oxx_sq, family = Gamma(link = identity), data = w.combo, start = c(0.1, 0.4, 0.02)) Deviance Residuals: Min 1Q Median 3Q Max -2.99999 -1.63183 -1.00720 0.04878 8.93461 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.09236 0.04834 1.911 0.0583 . precip_oxx 0.26848 0.35891 0.748 0.4558 precip_oxx_sq 0.05138 0.13418 0.383 0.7024 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for Gamma family taken to be 15.78978) Null deviance: 528.73 on 130 degrees of freedom Residual deviance: 305.81 on 128 degrees of freedom AIC: -100.33 Number of Fisher Scoring iterations: 5 > library(MASS) > gamma.shape(tempglm_g2) Alpha: 0.53807358 SE: 0.05526108 > gamma.dispersion(tempglm_g2) [1] 1.858482 Thanks, Tim Handley Research Assistant Channel Islands National Park (Will be working from both CHIS and SAMO) CHIS Phone: 805-658-5759 SAMO Phone: 805-370-2300 x2412 ______________________________________________ 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.