For example, I have a 2-level factor variable (diagnose) in interaction with a 6-level factor variable (layer). Intercept by default is the first level of all. In my case intercept is control group, layer 1 (out of 6). Dependent variable is continuous (density).
Does the interaction also compare everything to the reference category (intercept)? SO for example does my significant interaction between diagnose and Layer2 mean, that the two diagnostic groups DIFFER DIFFERENTLY compared to Layer 1?
Or am I overcompliacting it?
I also have a bit of trouble interpreting the effect of covariants on the dependent variable. I mean the coefficients listed in the first column of the output. If someone could give me an example on how to interpret these, I would be veery grateful.
(I work in R, with nlme package, lme function. A model for example:
lme(density ~ diag*Layer+gender+age+pmi, random = ~1|ID, data=sumd)
Thank you in advance!
I suggest that you carefully consult: https://www.google.com/search?q=montgomery+design+and+analysis+of+experiments&rlz=1C1CHBF_enUS915US915&oq=Montgomery+Design+and+&aqs=chrome.0.0j46j0j69i57j46j0l3.31683j0j15&sourceid=chrome&ie=UTF-8 and
https://www.google.com/search?rlz=1C1CHBF_enUS915US915&ei=hVVmX_CjJZK5tAb13J6QBg&q=Interaction+plots&oq=Interaction+plots&gs_lcp=CgZwc3ktYWIQAzICCAAyAggAMgIIADICCAAyBAgAEAoyAggAMgIIADICCAAyAggAMgIIADoHCC4QQxCTAjoGCAAQFhAeOg4IABDqAhC0AhCaARDlAjoFCAAQkQI6CAgAELEDEIMBOgUIABCxAzoCCC46CwguELEDEMcBEKMCOggILhDHARCvAToECAAQQzoICC4QsQMQgwE6BwgAELEDEENQz84EWK2vBWDLzAVoAXAAeASAAaoBiAHoGJIBBTIyLjEwmAEAoAEBqgEHZ3dzLXdperABBsABAQ&sclient=psy-ab&ved=0ahUKEwiw-tfz8_XrAhWSHM0KHXWuB2IQ4dUDCA0&uact=5
These should help you a considerable amount. Best, David Booth
Make a plot of the predicted values for the 6 layers, one series for the first diagnosis and another series on top for the second diagnosis (for any given values of the covariables). Interaction means that the patterns of the two series you see are not the same. No interaction means that the patterns of the two series are similar, just (possibly) shifted vertically.
And yes, you are essentially correct: the (1st-level-)interaction is a difference in effects (difference in difference).
The coefficients of the covariables are simply the estimated effect of these covariables. For "gender" this is the mean difference in the response between the genders. One of the genders is coded as the reference level. The coefficient is then the difference of the other level to the reference level (you know that). The coefficient for "age" is the mean change in the response associated with 1 unit change in age; supposedly, the unit in age is a year, so it's the change per year). If don't know what pmi stands for but you should be able to get the meaning of its coefficient. These effect (of gender, age and pmi) are assumed to be independent of each other and of layer and diagnosis (otherwise the model would contain the respective interaction(s)).
Thank you for your fast responses!
Yes - I did some explorative interaction plots.
My main concern was whether I can interpret the significant interaction in my results as an actual difference between the two groups regarding layer 2 (even though main effect of diagnose was not significant). Based on your answer @Dr Wilhelm, I think I can.
You helped greatly with understanding the coefficients for continuous covariables, thank you!
May I also ask your opinion about determining statistical power? I received a question to present the statistical power for each variable, and I'm not very sure about that.
Ms. Tyler., Here is a good description of interaction IMO.: https://statisticsbyjim.com/regression/interaction-effects/
Power is a property of statistical tests not variables, so the question was poorly posed. Further, power is generally dependent on sample size and is often estimated before data is taken.If you take a look at this reference: https://www.google.com/search?q=power+of+a+statistical+test&rlz=1C1CHBF_enUS915US915&oq=power+of+a+stati&aqs=chrome.0.0j69i57j0l6.24037j0j4&sourceid=chrome&ie=UTF-8
you will note that power is only useful when you regect the null hypothesis. Thus I would suggest you would not want to compute power for each possible test in most circumstances. Further, there are tests that depend on more than one variable thus in some cicumstances the question would be ill posed. Best, D. Booth
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