using dataset:grazing of R,1.Fit the Poisson GLM with a log link function, using the systematic component Birds ~ When * Grazed. Use influence.measures() to identify the influential points. Fit the Poisson GLM again without identified influential points.

Sure, I understand your question. To fit the Poisson GLM with a log link function using the dataset "grazing of R" and identify influential points using influence.measures(), you can follow the steps below:

1. Load the dataset "grazing of R" into R environment using the command:

data(grazing)

2. Fit the Poisson GLM model with a log link function using the command:

model <- glm(Birds ~ When * Grazed, data = grazing, family = poisson(link = "log"))

3. Identify influential points using the influence.measures() function:

infl <- influence.measures(model)

4. You can plot the Cook's distance using the command:

plot(infl$infmat, type = "o", pch = 20, main = "Cook's Distance Plot")
abline(h = 4/length(model$residuals), col = "red")

This plot will show the influential points, which are outside the red line.

5. To fit the Poisson GLM again without identified influential points, you can remove the influential points using the command:

newdata <- grazing[-which(infl$infmat[, "CookD"] > 4/length(model$residuals)), ]

6. Fit the Poisson GLM model again without the influential points using the command:

model_new <- glm(Birds ~ When * Grazed, data = newdata, family = poisson(link = "log"))

Now, you have fitted the Poisson GLM with a log link function using the systematic component Birds ~ When * Grazed, identified the influential points and removed them, and then fitted the Poisson GLM again without the influential points.