Confused with the reference level in logistic regression in R

Question

I am confused with the answer from https://stackoverflow.com/questions/23282048/logistic-regression-defining-reference-level-in-r

It said if you want to predict the probability of "Yes", you set as relevel(auth$class, ref = "YES"). However, in my experiment, if we have a binary response variable with "0" and "1". We only get the estimation for probability of "1" when we set relevel(factor(y),ref="0").

n <- 200
x <- rnorm(n)
sumx <- 5 + 3*x
exp1 <- exp(sumx)/(1+exp(sumx))
y <- rbinom(n,1,exp1) #probability here is for 1
model1 <- glm(y~x,family = "binomial")
summary(model1)$coefficients
            Estimate Std. Error  z value     Pr(>|z|)
(Intercept) 5.324099  1.0610921 5.017565 5.233039e-07
x           2.767035  0.7206103 3.839849 1.231100e-04
model2 <- glm(relevel(factor(y),ref="0")~x,family = "binomial")

summary(model2)$coefficients
            Estimate Std. Error  z value     Pr(>|z|)
(Intercept) 5.324099  1.0610921 5.017565 5.233039e-07
x           2.767035  0.7206103 3.839849 1.231100e-04

I think if we want to get probability of "Yes", we should set relevel(auth$class, ref = "No"), am I correct? And what is reference level here means? Actually, what is glm() to predict in default if we use response other than "0" and "1"?

Answer 1

The reference level is the base-line. If you wanted to predict probability of 'Yes', you'd set the base-line (i.e. reference level) "No". So you are correct, I think the answer in the other thread is incorrect.

I prefer to set up the levels of variables explicitly using the factor function. i.e.

    y = factor(y, levels=c(0,1), labels=c("No","Yes") 
    # Reference level is listed first
    # I prefer to have character labels rather than 0,1.

Sorry, but I am unsure about what you're asking about for default behavior for the glm function when you've specified family="binomial" -- the function will expect a two-level factor as the response variable.