I have data on the severity of weed pressure for an agricultural study with a factorial, RCBD. The weed pressure variable is the area in square footage within a plot where weeds were measured to be above a certain height. It is an atypical metric for weediness, and I have not been able to find anything in the literature like it, so I'm unsure of how to analyze this data.
The raw, untransformed variable "Area_Weed", in units of square feet, exhibits right-skewness. A few of the observations are zero. The histogram is shown below:
One approach that I've tried is to convert the response variable "Area_Weed", in square feet, to a proportion of weed area divided by total plot area, the apply an arcsine transformation. The residuals plot exhibits non-constant variance. The code and residuals are shown below:
proc glimmix data=df plots=studentpanel method=rspl;
class Trt_Amend_App Trt_CC Block;
model Area_Weed_PROP_ANG = Trt_Amend_App | Trt_CC / ddfm=kr2;
random Block;
run;
Considering an alternative distribution for the untransformed response variable "Area_Weed", which is positive and right-skewed, the gamma distribution seems promising, aside from the fact that it can't accommodate zeros in the data. If I apply a transformation of adding a small constant (+1) then I can get the model to run using PROC GENMOD, with the caveat that I can't include the variable "Block" as a random effect.
proc genmod data=df plots=all;
class Trt_Amend_App Trt_CC Block;
model Area_Weed_PLUS = Trt_Amend_App | Trt_CC / dist=gamma link=log;
ods output ParameterEstimates=pe;
output out=outmean pred=mu;
run;
My questions amount to the following:
Based on what I've presented here, is the gamma distribution appropriate for my response variable, which is positive, right-skewed, and includes a few zeros?
If I use PROC GENMOD and a gamma distribution to model, how might I go about evaluating the residual plots? What might be a good option for the parameter plots aside from "all"?
If I attempt to incorporate Block as a random effect using PROC GLIMMIX, the model does not converge. How can I address this issue?
Thank you for reading. Please let me know if I can provide any other information.
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