Regression curve changed a lot (in the same situation) after a new variable is added into the logistic regression model training I have a trained logistic regression model with 5 input variables. Then I added another new input variable and used all of them (6 input variables) to train a new logistic regression model. With the obtained coefficients, I got two values based on the logistic function when the inputs are given.
Next, I set the new variable as 0 while the other 5 input variables are all the same. Theoretically, the two values will be close since they are in the exactly same condition.
According to the equation of logistic regression:
probability=1/(1+EXP(-l)),
where l=a0+a1x1+a2x2+a3x3+a4x4+a5x5+a6x6. 

I can get the coefficients of a0 to a6 by regression. When x1 to x6 are given specific values, the probability P1 can be calculated through the above equation.
Then, I added a new variable x7 into the model. So for the new model, I have new coefficients of a0 to a7. Now I give the same value of x1 to x6 in the new equation and x7=0. This is the second probability value P2. In general, P1 should be close to P2, but in my result, they are not.
I try to use this method to check my model with the new variable. But the result shows they have an obvious difference. All the calculation part is correct. So I wonder if it is because of the logistic regression method.
 A: There is no theory that two regressions $\operatorname{E}(Y|X) = g^{-1}\left(\beta_0 + \beta_1x_1\right)$ and $\operatorname{E}(Y|X) = g^{-1}\left(\beta_0 + \beta_1x_1 + \beta_2x_2\right)$ should make the same/similar predictions when you plug in $x_2 = 0$. This would be the case only if the estimates for $\beta_0$ and $\beta_1$ are the same/close. The fact that your model is a logistic (and not, say, linear) regression and that you have more than two variables is irrelevant.
It might help to review how we interpret regression coefficients: $\beta_0$ and $\beta_1$ have a different meaning in the two models, so we can't expect them to have the same value in general. The interpretation is easier in the case of linear regression, so let's assume the link function $g$ is the identity. For illustration purposes, I'll also assume that the variable $X_1$ is gender ($x_1 = 1$ indicates males) and the variable $X_2$ is IQ standardized so that $x_2 = 0$ corresponds to the average IQ in the study population.
In the linear regression $\operatorname{E}(Y|X) = \beta_0 + \beta_1x_1$, the intercept $\beta_0$ is the expected value of Y for females and the coefficient $\beta_1$ is the expected difference in Y between males and females. In the linear regression $\operatorname{E}(Y|X) = \beta_0 + \beta_1x_1 + \beta_2x_2$, the intercept $\beta_0$ is the expected Y for females of average IQ and the coefficient $\beta_1$ is the expected difference in Y between males and females of average IQ.
So the meaning of $\beta_0$ and $\beta_1$ is different and generally we cannot expect the two models to make the same predictions, most obviously in the case when $X_2$ is predictive of the outcome $Y$. (To make the example more concrete, consider what the difference between the two regressions might be if $Y$ is test scores vs if $Y$ is height.)
