Not significant in bivariate chi square or bivariate logistic regression but is in multivariate logistic regresison?

[Emily Ross]

Hi, Ive come across in my analysis results that two independent variables are not significant in bivariate chi square or bivariate logistic regression but become significant in multivariate logistic regression when accompanied by other independent variables? I know multicollinearity is for the opposite but can anyone explain a possible reason for this?

Thanks.

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

While this may not be precisely correct in non-linear models, in linear models, the standard error of a parameter estimate depends on the covariance of the x's and the standard error of the regression. So, adding additional variables that explain a lot of the variance can reduce the standard error of the regression, lower the standard error on parameter estimates, and change the statistical significance of parameter estimates. A similar mechanism applies in logit.