I met a problem. I calculate the odd.raio by using glm.
When the predictor outcomes were "A" and "B",respectively, the odd.ratio value is 0.88. However, outcome was "C" and "B", the odd.ratio value is 1.127948.
I don't know what the difference between "AB" and "BC" in the glm. the character can affect the results of odd.ratios which is right?
example code
outcome <- as.factor(c(rep("C",30),rep("B",28)))
#outcome <- as.factor(c(rep("A",30),rep("B",28)))
a <- c(seq(1,30,1),seq(1,28,1))
glm.log <- glm(outcome ~ scale(a), control = list(maxit = 50), family = binomial(link = "logit"))
res <- summary(glm.log)$coefficients[2, 1:2]
odd.ratio <- exp(res[1])
print(odd.ratio)
The odds ratio show how the odds change if we experience a change in the predictor (formula). Here is an example with a binary group variable since here the change is easy to understand.
# generate data and run model
outcome <- as.factor(c(rep("C",30),rep("B",30)))
groups<- c(c(rep(1, 20), rep(2, 10)),
c(rep(2, 20), rep(1, 10)))
fit <- glm(outcome ~ groups, family= binomial(link = "logit"))
odds.ratio <- exp(fit$coefficients["groups"])
# calculate odds by hand
tbl <- table(outcome, groups)
a <- tbl[1,1]
b <- tbl[1,2]
c <- tbl[2,1]
d <- tbl[2,2]
odds1 <- a/c
odds2 <- b/d
odds.ratio; odds1/odds2
# both 0.25
As you can see both, odds.ratio from the model and our odds ratio odds1/odds2 are 0.25. If we run the same code with outcome <- as.factor(c(rep("A",30),rep("B",30))) instead, odds.ratio will be 4. This is because the opposite ratio is calculated, namely odds2/odds1.
Further, as @Dason points out you can calculate one odds ratio from the other one. See here
odds_ratio_a <- odds1/odds2
odds_ratio_b <- odds2/odds1
odds_ratio_a == 1/odds_ratio_b
# TRUE
odds_ratio_b == 1/odds_ratio_a
# TRUE
This is why in your case 1/ 1.127948 = 0.8865657 and 1/0.8865657 = 1.127948.
The question remains why this happens. This is easy: Because the reference level changes! In as.factor(c(rep("C",30),rep("B",28)))the reference level is "B" and in as.factor(c(rep("A",30),rep("B",28))) it is "A". To get same results for both cases you need only to use outcome <-relevel(as.factor(c(rep("A",30),rep("B",28))), ref= "B").