Binary logistic regression: Interactions (video 3 of 3)

The last video of the series discusses how to interpret interaction effects in binary logistic regression models. Two options are presented: interpretation using predicted probabilities and interpretation using odds ratios.

Please note: we may be unable to respond to individual questions on this video.

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[edwinicq]

You have no idea how much I've searched to get to an explanation on this topic.

[cecilialuini]

Thank you for the explanation! How shall we interpret the significance instead?

[armanforthree]

absolutely the best explanation out there.

[Tenten]

Great explanation! Is there an easy way to see if two cells in the table are significantly different from another similar to pairwise comparisons in ANOVA? In other words, is there a way to test if the difference in the probability of single men and women owning a car is statistically significant?

[adamjauregui]

Awesome video and an amazing explanation. Can you explain the math behind multiplying each of the odds ratios? I love seeing formulas!

[danielolazabal]

Thanks, there are few videos online looking specifically explaining equations and probability calculations.

[karanshah]

By interactions, I presume multicollinearity.. in that case should we not remove the multicollinearity and drop the variable that is redundant for the model ?

[victorantunes]

Dear Professor, this was indeed a very nice video!

May I ask you something?

I have calculated predicted probabilities for every combination of categories of my two categorical variables (the ones that were interacted).

This is the objective of my paper: Previous research has also found that health status is negatively associated with elder mistreatment (Acierno et al. 2017; Koga et al. 2019). However, social support might moderate the relationship between health status and elder mistreatment (Acierno et al. 2017). Hence, our second objective is to investigate the possible mediating effect of social support in Brazil. We hypothesize that social support mitigates the negative relationship between health status and elder mistreatment (Acierno et al. 2017). So, I want to see if support mitigates the negative relationship between health status and elder mistreatment.

In this sense, my dependent variable is Elder Mistreatment (1 = Yes; 0 = No). My variable of health status is the self-rated health status, which has the following categories: Bad, Regular, and Good. And, my variable of social support is about how many family members the elder can count on, categorized as follows: None, One or Two, and Three or more.

I then interacted social support with health status, and got the following predicted probabilities:
* If social support is none and self-rated health is bad: Lower * Interval = 17.89; Probability = 23.68; Upper Interval = 29.47.
* If social support is none and self-rated health is good: Lower Interval = 9.46; Probability = 12.49; Upper Interval = 15.51.
* If social support is three or more and self-rated health is bad: Lower Interval = 8.47; Probability = 10.45; Upper Interval = 12.42.
* If social support is three or more and self-rated health is good: Lower Interval = 4.83; Probability = 5.86; Upper Interval = 6.89.

Based on this, could I conclude the following?

There is no crossing of predicted probabilities (and their respective confidence intervals) between the levels of bad and good health, regardless of the level of social support (none vs. three or more). That is, there is at least one statistically significant negative association between health status and elder mistreatment for each of the levels of social support. Additionally, as social support increases, the negative association found occurs at lower predicted probabilities. Therefore, we have evidence that greater social support mitigates the negative association between health status and elder mistreatment, which supports our hypothesis.

I'm confused if I can conclude such a thing. That is, if I am interpreting my results correctly.

Many many thanks for this!

[icps]

Excellent videos! thank you! one thing missing, though, is how to interpret significance with the interactions... for example, what happens if the direct effects is non significant but the interaction effect is significant?

[CamilaSanchez-exjn]

Hi Dr Heini, I would like to know how to calculate marginal effects for a binomial logistic regression with interaction term. something like when D is high and Z is high, when D is High and Z is low, when D is low and Z is high and when D is low and Z is low. I mean the possible combinations for my interaction term.Note. D would be the independent variable and Z the interaction term.

Thank you very much.
Camila.