# significant predictors become non-significant in multiple logistic regression

When entered into univariate logistic regression I get the following:

Predictor 1: B = 1.049, SE = .352, Exp(B) = 2.85, 95% CI = 1.43 - 5.69, p = .003
Constant: B = -.434, SE = .217, Exp(B) = .648, p = .046

Predictor 2: B = 1.379, SE = .386, Exp(B) = 3.97, 95% CI = 1.86 - 8.47, p < .001
Constant: B = -.447, SE = .205, Exp(B) = .639, p = .029


and when entered into multiple logistic regression:

Predictor 1: B =  .556, SE = .406, Exp(B) = 1.74, 95% CI = 0.79 - 3.86, p = .171
Predictor 2: B = 1.094, SE = .436, Exp(B) = 2.99, 95% CI = 1.27 - 7.02, p = .012
Constant: B = -.574, SE = .227, Exp(B) = .563, p = .012


Both predictors are dichotomous categorical. I have checked for multicollinearity.

Not sure if I have given enough info, but I cannot understand why predictor 1 has gone from being significant to non-significant and why the odds ratios are so different in the multiple regression model.

Can anyone help (with a basic explanation of what is going on - I really struggle to understand statistics!!)

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multivariate usually indicates multiple dependent variables - you meant multiple predictors, right? That would usually be referred to as multiple regression. –  Macro Apr 27 '12 at 16:24
Also, $\beta$'s from different logistic regression models are usually not comparable. This is because the scale has changed - this is a subtle issue but the basic idea is that the total variance (on the latent scale that logistic regression naturally arises - see en.wikipedia.org/wiki/…) is not fixed across models, so you shouldn't expect the coefficients to be the same across models, although that wouldn't necessarily explain the change in statistical significance. How did you check for dependence between the two predictors? –  Macro Apr 27 '12 at 16:34
ah, ok thank you. I checked collinearity diagnostics through linear regression on spss & checked the tolerance and VIF - is this correct? –  Annie Apr 27 '12 at 16:45
Nice comment @Macro . I vaguely recall reading about ways to fix this issue about the scale, but I don't remember where. –  Peter Flom Apr 27 '12 at 16:59
@PeterFlom, one thing you can do is scale the coefficients by the variance of the linear predictors (plus $\pi^{2}/3$, the variance of the standard logistic distribution) - this puts them on the same scale. Of course, they are no longer interpretable as odds ratios once you do this. –  Macro Apr 27 '12 at 17:50