I am trying to look at how the likelihood of event Y is influenced by two factors A (5 levels) and B (2 levels) and my model is as follows:
type3.Y <- list(A = contr.sum, B = contr.sum)
modelY<-glm(Y ~ A*B, family = binomial (link = "logit"), data = likelihood, contrasts = type3.Y)
summary(modelY)
I am currently using the Anova() function to determine the significance of each term in my model as follows:
Anova(model.Y, type = 3, test.statistic = "LR")
Analysis of Deviance Table (Type III tests)
Response: Y
LR Chisq Df Pr(>Chisq)
A 8.4573 4 0.07619 .
B 0.4137 1 0.52010
A:B 7.2847 4 0.12159
I am of the understanding that the LR Chisq values indicate, after taking into consideration all other terms, whether or not a model containing the specific term explains the data better than a model without it i.e. if the value is positive the model with the term explains the data better (if the value is negative a model without the term explains the data better).
However, I am aware that there are other test statistics that can be coded for in this function i.e. test.statistic = "F", test.statistic = "Wald"). Both of these give different slightly results so I was wondering:
a) What is the difference between these tests?
b) Am I using the correct one for my data analyses (are there specific circumstances in which you would use one over the others)? I have also noticed that if I do not specify a test statistic the function defaults to LR.
