I have activity data for 6 individuals (
ID) obtained using two different formulas (
VeDBA.X16), and I want to test which of those formulas fit better to my response variable
Here you can see the relationship of
Below you can see also a histogram of my response variable
RMS.V13AP (upper left). In the graph appears also the histogram of my response variable with different transformations.
As you can see,
RMS.V13AP is positive and continuous, so I decided to make a GLM using a Gamma distribution with a log link. I included
ID as a fixed effect and not as a random effect because I want to test if the relationship changes among individuals. To answer the main question (differences between formulas for predicting
RMS.V13AP), I did this:
mod1 <- glm(RMS.V13AP ~ VeDBA.X16+ID,data = FormulaValidation.57s, family=Gamma(link=log)) mod2 <- glm(RMS.V13AP ~ RMS.X16+ID, data = FormulaValidation.57s, family=Gamma(link=log)) AIC(mod1,mod2) df AIC mod1 8 3831.017 mod2 8 3812.568 ED.mod1 <- 100* (1-(mod1$deviance/mod1$null.deviance)) # Explained deviance ED.mod1  62.3574 ED.mod2 <- 100* (1-(mod2$deviance/mod2$null.deviance)) ED.mod2  62.54075
It seems that the formula
RMS fits better my data, however differences between
VeDBA are very low according to the explained deviance.
My doubts arise when I make some diagnostic plots. First, I show the plots I usually find in literature:
mod1.diag <- glm.diag(mod1) mod2.diag <- glm.diag(mod2) glm.diag.plots(mod1,mod1.diag) glm.diag.plots(mod2,mod2.diag)
After some searching, I found also this approach to explore residuals (simulations):
library(DHARMa) sim_nbz <- simulate(mod2, nsim =1000) str(sim_nbz) sim_nbz = do.call(cbind, sim_nbz) head(sim_nbz) sim_res_nbz = createDHARMa(simulatedResponse = sim_nbz, observedResponse = FormulaValidation.57s$RMS.V13AP, fittedPredictedResponse = predict(mod2), integerResponse = FALSE) plotSimulatedResiduals(sim_res_nbz)
The way I see it, there is clear evidence of residual patterns but I don't know what should be next step.
Should I care about those residual patterns? Should I transform my response variable and try to use another type of regression?