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I'm after a bit of advice. I've fitted some multi-level models with income as the outcome variable and a range of covariates. I'm interested in the coefficients of the main independent variable/covariate (ethnic group) when I enter various other covariates into the model (so how does income change for each ethnic group when I enter other covariates into the model etc). So I've done all this and got some interesting results.

However, one of my models includes an interaction of ethnic group*age. So what I need to do is calculate the coefficient for each each group with the interaction term included (the coefficients that don't include the interaction make no sense).

Does anyone know if there a formula to do this - I'm guessing there must be?!

Hope that all makes sense :-)

Thanks Vanessa

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  • $\begingroup$ This is likely due to the fact that some of the relationship between the predictor and income is taken up by the interaction term. Thus, if you believe that age has a positive relationship with income (as you'd hope), but the coefficent is negative you might be concerned (I assume this is your problem). But you should calculate the change in the income between different ages keeping ethnic group constant. This will likely show you there is still the positive association you expect. If you share your models I'd be happy to summarize this in your context. $\endgroup$
    – a.powell
    Commented Jun 28, 2017 at 16:14

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I am not quite sure what you mean by the "the coefficients that don't include the interaction make no sense", but there are some general formulas for calculating simple slopes and their statistical significance. In this case you are interested in the simple slope that describes the linear association between age and income for each ethnic group separately.

See the following links for various resources on how to do this:

http://www.jeremydawson.co.uk/slopes.htm

Interpretation of simple slopes

http://www.quantpsy.org/interact/

Hope that helps a little.

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