In logistic regression, I have a variable with larger coefficient and larger p-value and another variable with smaller coefficient and smaller p-value. If use p-value then the latter one is more significant, but if calculate odds ratio, the first one is more influential. How should I interpret this? Which one is more important in the model?
High: coef:-0.0153869 p-value:0.0000257266774040
Low : coef:-0.0052793 p-value: < 0.0000000000000002
It doesn't make much sense to compare coefficients to p-values like you do. This has nothing to do with logistic regression in particular, the same applies to linear regression, so let us use that as an example.
If the model is $Y_i = \beta_0 + \beta_1 x_i + \epsilon_i$, but then you transform the predictor linearly to $Y_i = \beta_0^* + \beta_1^* (1000000 \cdot x_i) + \epsilon_i$, then on the same data, $\hat{\beta_1^*} = \hat{\beta_1}/1000000$. The p-values, will be identical. So trying to interpret coefficients, forgetting about the scale of the predictors, does not make sense.
