##### Calculating Variance Inflation Factors (VIF) in R 


###Import Data


datum=read.csv(file.choose())
head(datum)


### Run a GLM containing all the x variables of interest


results=lm(Size~Age+Sex+MotherSize+FatherSize,data=datum) ###linear model
summary(results)
#notice that p-values and standard errors are really high
#estimated effects are within 2 se of truth
#notice that estimated residual error is spot on


### variance inflation


library(car) ###function is in the 'car' package
vif(results) ###calculates vif for all independent variables
#note that y variable is disregarded in vif analysis - doesn't matter what it is
#Note that like an ANOVA p-value, vif doesn't tell you which variables are collinear
# and not all of them may be collinear. VIF just tells you that the collinearity is there


### Relationship between VIF and r^2


results=lm(Age~Sex+MotherSize+FatherSize,data=datum)
summary(results) ### look at r^2
#VIF = 1/(1-r^2)


### Calculate Collinearity between individual, independent variables


results=lm(Age~Sex,data=datum) ### to get R^2 between sex and Age
summary(results) ### look at r^2
# Repeat for all variables


### Correlation matrix for calculating collinearity among all individual variables


datum2=data.frame(Age=datum$Age,MotherSize=datum$MotherSize,FatherSize=datum$FatherSize) #New data frame with only continuous variables
head(datum2) #make sure it worked
cor(datum2) #correlation matrix - provides r (not r^2) among all continuous variables
cor(datum2)^2 ### R^2 among all variables