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I am testing a logistic regression model that has two continuous IVs in SPSS. The DV is of course binary. IV-1 has an odds ratio above 1 and IV-2 has an odds ratio below 1. I understand what these mean, but how can I statistically compare the strengths of the influence of the two IVs? I understand that if both of the odds ratios are on the same side of 1, I can use the CIs to make the comparison. But I'm not sure what to do with my current situation.

Thank you very much!

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In this case, just take the reciprocal and reverse the meaning. For example, an odds ratio of 0.5 means for every unit increase in the predictor, the odds of a success change by a multiple of 0.5. That's difficult to interpret, so take the reciprocal, and we can then say that for every unit decrease in the predictor, the odds of a success increase by a multiple of 1/0.5 = 2.

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Here is a quick example which you can use to understand the odd's ratio of any variable.

lets say $\beta_1$ = 0.7 and $\beta_2$ = -0.3 and let $\beta_o$ = C

So your logistic regression model will be

$$\hat y = \hat \pi = \frac {1}{1 + e^{-(C + 0.7x_1 -0.3x_2)}}$$

you see that inside part of the exponential constant is the same as a linear regression function. But now when we extract odd ratio's

The odd ratio of $\beta1$

$$\beta_1 = e^{\beta_1} = e^{0.7} = 2.01$$

The odd ratio of $\beta2$

$$\beta_2 = e^{\beta_2} = e^{-0.3} = 0.74$$

Now for $\beta1$, when every thing else is constant, 1 unit increase of $X_1$ causes a $(2.01-1)\% = 101\%$ increase in probability $\hat y$.

Now for $\beta2$, when every thing else is constant, 1 unit increase of $X_2$ causes a $(1- 0.74)\% = 26\%$ decrease in probability $\hat y$.

It can also be interpreted as 1 unit decreasae in $X_2$ causes a $\frac {1}{e^{-0.3}} = 1.35$, or the a increase of 35% in probability $\hat y$.

Finaly if odd's ratio is 1, it means there is no change in probability.

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