I have a dependent variable $Y \in \{0, 1\}$ and 4 independent variables $X_1$ through $X_4$. First, I run a total of 5 logistic regressions:
- $Y \sim X_1$
- $Y \sim X_2$
- $Y \sim X_3$
- $Y \sim X_4$
- $Y \sim X_1, X_2, X_3, X_4$
I find that the coefficient of $X_1$ is significant in (1), but is not in (5). I also find that the coefficient of $X_2$ is not significant in (2), but is now significant in (5).
There are no interaction in the model. I don’t have many missing values in my variables. Hosmer-Lemeshow statistic gives p-value > 0.05.
Why does this happen? What should I pay attention to?
Thanks.