黄瓜片贴脸上有什么效果

Question

I am trying to apply a Gamma GLM to a dataset. The main issue is the lack of fit for quantile deviations although no other problems are detected. I have read similar posts without a conclusive answer.

My main question is if despite obtaining a poor fit regarding the quantiles but a good one in the other parameters the model is still trustworthy.

Please find a reproducible example below.

library(DHARMa)
library(car)

datos <- data.frame(
  Time = c(20.79, 387.69, 11.55, 25.63, 12.11, 34.74, 30.76, 11.69,
           11.55, 1522.86, 1742.24, 39.84, 24.26),
  Ratio = c(1.56, 2.02, 1.49, 1.55, 1.26, 1.77, 2.76, 0.86, 1.40,
            1.84, 1.21, 2.02, 2.33),
  Type = as.factor(c("NWB", "NWB", "NWB", "NWB", "NWB",
                     "WB", "WB", "WB", "WB", "WB", "WB", "WB", "WB"))
)

datos

m1<- glm(Time~ Type+Ratio,Gamma(link="log"), data=datos, control = list(maxit = 100))
Anova(m1)

residh <- simulateResiduals(m1)

plotResiduals(residh, form = datos$Ratio)
plotResiduals(residh, form = datos$Type)

testDispersion(residh)
testUniformity(residh)

Answer 1

I assume this is the complete data. Personally, I wouldn't trust any model with that many parameters that was fit to such a small dataset.

I suggest you do the very basic step of plotting the data and the predictions:

library(ggplot2)
ggplot(datos, aes(y = Time, x = Ratio, color = Type)) +
  geom_point() +
  stat_function(aes(color = "WB"), fun = \(x) predict(m1, newdata = data.frame(Ratio = x, Type = factor("WB")), type = "response")) +
  stat_function(aes(color = "NWB"), fun = \(x) predict(m1, newdata = data.frame(Ratio = x, Type = factor("NWB")), type = "response"))

I would not trust a model that is influenced that much by only three observations.

---

You should also look a bit more into the estimated dispersion / shape:

library(MASS)
gamma.shape(m1)
#Alpha: 0.4182119
#SE:    0.1332239
gamma.dispersion(m1)
#[1] 2.391132

This estimate is better than that done by summary etc. You can pass it to anova.glm but not to car::Anova:

anova(m1, dispersion = gamma.dispersion(m1))

---

If you had some strong priors for the parameters, you could maybe salvage this with a Bayesian model, e.g., with package brms. Otherwise, I would tell you to get more data.