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If a multivariate design controls for other predictors when calculating the effect of a predictor, shouldn't it give paler P values (less significant ones, or less vivid odds ratios)? I am seeing quite the opposite.

Is it normal or possible or usual?

Detailed explanation on the case: When I analyze the the correlations between my outcome variable and my five predictors using bivariate correlation coefficients, sporadic few significant P values emerge (all only significant at 0.05 level). However, modeling the same variables within a multivariate logistic regression analysis gives me lots of significant P values, many of which are highly significant (at 0.01 level).

I should add that I have modeled independent variables' interactions as well (only their 2-sided interactions). But even if I do not add the interaction terms to the model, still I am getting better results with the multivariate analysis.

I should add that none of the variance inflation factors (VIFs) are greater than 2, and I am rather confident multicollinearity is not disrupting my model. So it is interesting to see a multivariate analysis is giving better results.

So I wonder is it OK? Or perhaps it is the way it should be (meaning that on the contrary to my belief, a multivariate analysis usually gives better results).

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It is certainly possible and not necessarily bad. It's not even unusual.

You haven't told us what your variables are (it's usually useful for us to know that) but here's an abstract case.

Model 1 $Y = a + b_1X_1$ Model 2 $Y = a + b_1X_1 + b_2X_2$

These models ask different questions. M1 asks about the relationship between Y and X, uncontrolled. M2 adds control for X2. Could $b_1$ in M2 be more significant than in M1? Sure. For example, suppose the sample is American adults, Y is probability of voted for Obama, $X_1$ is income and $X_2$ is education. Because the probability of voting for Obama goes up with education but down with income, the effect of income will be more pronounced with education controlled for.

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  • $\begingroup$ WOW such a nice answer. THANKS. (Since you were interested in my design, it had a binary variable (absence/presence of a disease) and 5 predictors (demographics and treatment) including binary (such as gender) and continuous (actually ordinal -age for example) ones.) Thanks again :) $\endgroup$
    – Vic
    Commented May 9, 2013 at 11:04
  • $\begingroup$ But another problem emerged right now! :) which one should I trust? The OR of treatment in the bivariate analysis (chi-squared contingency table) is something reasonable, but the OR of the same predictor (treatment) is extreme (it is about 0.1) and differs with the OR if bivariate (about 0.3 or so). $\endgroup$
    – Vic
    Commented May 9, 2013 at 11:08
  • $\begingroup$ So in this case, which one would you trust? :) I tend to trust the multivariate one, but it is a little bit too high! $\endgroup$
    – Vic
    Commented May 9, 2013 at 11:09
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    $\begingroup$ Trust both. They answer different questions. Which one do you want to answer? Maybe both! Do you want the OR controlled or uncontrolled? Also, check the CI. $\endgroup$
    – Peter Flom
    Commented May 9, 2013 at 11:10
  • $\begingroup$ Many many thanks Peter :) Ok I would trust both :) yes yes the CIs are reported. I am reporting both actually (multi and bivariate). $\endgroup$
    – Vic
    Commented May 9, 2013 at 11:11

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