Why do coefficients in a binary logistic regression model differ according to the number of predictor variables? I fit a binary logistic regression model with a single categorical variable, for which I received a coefficient. When I added further categorical predictor variables, the coefficient of the original categorical variable changed. What is the reason for this? That is, why is the coefficient of a predictor variable sensitive to the presence of other predictor variables in the model? 
 A: Actually, this question deserves special consideration. This is because even if your predictors are orthogonal, addition of more predictors to a model that are predictive of the outcome will increase the logistic regression coefficients of variables that are already present in the model. By increase, I mean move them further away from zero.
The reason for this is simple. In logistic regression, the error is fixed and assumed to have a variance of $\pi^2/3$. If you create a better model for the outcome, the better model doesn't reduce the variance of the error, it increases the variance of the linear predictor on the logit scale. This causes an inflation in your coefficients.
Mathematically, in logistic regression, you're estimating:
\begin{equation}
y^*/\sigma = X\frac{\beta}{\sigma} + e
\end{equation}
$y^*$ is the continuous latent variable underlying the observed binary 0,1 and $e \sim \mathrm{Logistic}(0, 1)$. If all the determinants of $y^*$ are in the model, $\sigma$, the scaling factor of the logistic distribution is 1. If any of the predictors of $y^*$ are missing, $\sigma$ is less than one such that as you include more determinants of the underlying latent variable, your coefficients will be guaranteed to increase if they are orthogonal and non-zero. If they are not orthogonal, how they will change also depends on the traditional mechanics of omitted variable bias.
A simple simulation of the problem:
set.seed(124)
coefs <- t(replicate(1500, {
  # generate two independent random variables
  xb <- rbinom(200, 1, .5)
  xc <- rnorm(200)
  # generate outcome from both predictors
  # we care about xb, so give xc a large coefficient
  # to simulate the effect of many missing predictors
  y <- rbinom(200, 1, 1 / (1 + exp(-(.25 * xb + xc))))
  # retrieve binary coefficient in model with:
  c(
    coef(glm(y ~ xb, binomial))["xb"], # just binary predictor
    coef(glm(y ~ xb + xc, binomial))["xb"] # both predictors
  )
}))

# get average coefficient from each set of models
colMeans(coefs)

       xb        xb
0.2083103 0.2562395 

As one can see, the coefficient from the model without the continuous predictor is deflated while the one in the model with both predictors is close to the .25 value we assigned it.
This problem is described in the econometrics/sociology literature as unobserved heterogeneity. It plagues logistic and probit regression models. With these models, the extent to which the change in coefficients is caused by confounding is not clear.
Based on a quick glance, traditional omitted variable bias is explained simply on Wikipedia. See this article for a simple to read explanation of the unobserved heterogeneity process in logistic regression.
A: Unless your predictors are orthogonal, adding a new predictor to a model will always change the coefficient estimates on existing predictors. This holds for any model.
