From my results, it appears that GLM Gamma meets most assumptions, but is it a worthwhile improvement over the log-transformed LM? Most literature I've found deals with Poisson or Binomial GLMs. I found the article EVALUATION OF GENERALIZED LINEAR MODEL ASSUMPTIONS USING RANDOMIZATION very useful, but it lacks the actual plots used to make a decision. Hopefully someone with experience can point me in right direction.
I want to model the distribution of my response variable T, whose distribution is plotted below. As you can see, it is positive skewness:
I have two categorical factors to consider: METH and CASEPART.
Note that this study is mainly exploratory, essentially serving as a pilot study before theorizing a model and performing DoE around it.
I have the following models in R, with their diagnostic plots:
LM.LOG <- lm(log10(T) ~ factor(METH) + factor(CASEPART), data=tdat)
GLM.GAMMA <- glm(T ~ factor(METH) * factor(CASEPART), data=tdat, family="Gamma"(link='log'))
GLM.GAUS <- glm(T ~ factor(METH) * factor(CASEPART), data=tdat, family="gaussian"(link='log'))
I also attained the following P-values via Shapiro-Wilks test on residuals:
LM.LOG: 2.347e-11 GLM.GAMMA: 0.6288 GLM.GAUS: 0.6288
I calculated AIC and BIC values, but if I am correct, they don't tell me much due to different families in the GLMs/LM.
Also, I noted the extreme values, but I cannot classify them as outliers as there is no clear "special cause".