I'm starting to create a model for modelling the occurrence of skin cancer in patients and the patients have many available variables that may correlate to getting skin cancer (that's what I'm studying).
First I'm building a very simple model just to test some of the variables:
fit1 <- glm(cancer ~ trt, family = binomial, data = dta)
where $trt$ is a categorical variable taking values $0$ and $1$ and it signifies whether the patient has taken beta carotene supplement ($1$) or not ($0$, plasebo medicine). One expects that beta carotene should lower the risk of getting cancer, since that's what the study is essentially about.
However, the model produces the model:
$$cancer = 0.165659 + 0.5587886 \cdot trt $$
(also these coefficients are after taking
So this suggests that taking beta carotene increases the likelihood to get skin cancer by 55.87%. So this is opposite of what I expect.
Is this a problem with the model being too simple or what's wrong?
However, another post suggests that I may have been computing the
invlogit() of the coefficients wrongly. What I should perhaps do is calculate
$$-1.6167107 + 0.2362472 * 1$$
in logit-domain and then invlogit this sum
> invlogit(-1.380464)  0.2009345
so this says that if taking beta carotene then a patient has 20% risk of getting skin cancer. And
> invlogit(-1.6167107)  0.165659
i.e. 16% chance if not taking beta carotene.
Are these more reasonable?
As suggested in the comments, I've plotted: