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I am testing the relationship between two variables (Similarity index; Years patenting) on a binomial dependent variable via a Logistic regression in SPSS.

I tried two models as you can see bellow in the links. In the first model I tested, only one variable (Years patenting) was shown significant. In the second model, where I added the interaction between the two variables, that interaction became significant as well as the other variable (Similarity index). The variable that was shown significant in the first model (Years patenting) was not significant anymore.

How would you interpret these results?

Model 1: enter image description here

Model 2: enter image description here

Also - how would I know the direction of the relationship between the predictor and the outcome? Do I look at the sign for the regression coefficient B, or do I look if Exp(B) is larger or smaller than 1?

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I would interpret your results as follows: The first model shows that the likelihood of getting the outcome (dependent variable = 1) decreases as the years of parenting increase. The odds ratio is simply the exponentiated regression coefficient ($OR=\exp(-0.532)=0.587$) and if years of parenting are continuous, represents the odds ratio per 1 unit (I assume per 1 year) of parenting. It doesn't matter whether you look at the regression coefficient or at the odds ratio to see how the relationship is: if the regression coefficient is negative, the odds ratio is < 1 and this denotes a negative relationship and vice versa. The coefficient of similarity index is positive and this means that the likelihood of getting the outcome is increasing with increasing similarity index (odds ratio = 1.08). This site offers a good starting point on how to interpret logistic regression results. This site here even discusses it with an annotated SPSS output.

In the second model containing the interaction, the interaction is significant whereas the main effect is not any more. This has been discussed in this post, for example. Interactions mean that the slope (on the log-odds scale) for years parenting differ for different levels of similarity index. Just because the inclusion of the interaction term made your main effect insignificant, you should not exclude the main effect. See here on how to report interactions in logistic regressions (this paper seems very useful too). You should also ask the question whether an interaction makes sense from a scientific point of view.

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An interaction term is usually quite correlated with its main effects variables - in your case sim index and years patenting. Therefore significance of the single coefficients may be gone but what you actually want to know is the joint significance of the main and the interaction coefficients. You can do this with an F-test. Also be aware that interactions in logistic regressions don't have the same interpretation as in linear models. See here for example under the heading "Logistic interactions are a complex concept".

For the interpretation of your regressors on the outcome you also need to calculate the marginal effects in order to make an effective statement. Since the logistic regression line is non-linear it has different slopes at different points (unlike OLS where the partial effect of your variables is linear) you have to choose where you want to evaluate the slope. Often the mean is chosen for this but it depends on your research question.

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