[R] Interpreting coefficients in linear models with interaction terms

David Winsemius dwinsemius at comcast.net
Mon Jan 14 02:11:00 CET 2013

On Jan 12, 2013, at 7:28 PM, theundergrad wrote:

> Hi, 
> I have very limited (one class and the rest self-taught) statistics
> background (I am a comparative biology major) working on an independent
> study.

The number of major issues of confusion in what follows suggest that this is a topic for which your training has inadequately prepared you. You really need to be talking to your advisor about getting some proper directed reading. If your advisor has not the proper training in this area he should direct you to someone in your institution who has that capability.

> I think that I am beginning to understand:
> The coefficient SexM is the slope estimate for TestNumber1.

It would only make sense to talk about a "slope estimate" if there were a continuous variable in the set of independent variables ... and there is not.

> If I add the
> coefficients for the other two interaction terms to the coefficient of SexM,
> I will get the slope estimate for the other two tests. 

Not a specific enough statement from which I can extract meaning to judge truth or falsity even if you were talking about mean estimates.

> How would I quantify the significance of the interaction and SexM in the
> model? If, as I have done previously and as David suggests, I look at three
> different models each using only one test, I can quantify the effect of SexM
> simply by looking at the associated p-value.

No. You failed to comprehend what I wrote.

> If, however, I chose to look at
> the interaction model in order to reduce the number of tests conducted , I
> do not have one number to look at that quantifies the significance of sex or
> the interaction.


> I thought about doing two F-tests, one comparing this model
> to a model without interaction (to find the significance of the interaction)
> and one comparing this model to one with only TestNumber (to find the total
> significance of sex).

> When I do this, I get a p-value of 0.006 for the first
> test and 0.3 for the second. My understanding of this is that SexM is
> non-significant; however, the relationship between SexM and RateOfMotorPlay
> significantly changes with TestNumber.

Right. Sometimes there will be a "significant" interaction involving a "non-significant main effect".

> This seems strange to me, but I seem
> to be hearing that it is possible. If this is true, I think that reporting
> that sex is non-significant is adequate and I do not need to report anything
> about the interaction since my research question is related to the effect of
> sex, not the change in the effect of sex over time. Does this approach
> adequately address the issue of whether or not sex is related to
> RateOfMotorPlay?

It sounds as though you have missed the most interesting aspect. If the effect of sex varies between treatments, wouldn't that be of immense interest?

> Thank you all so much for you helpful responces

Please stop behaving as a typical Nabble user and learn to post context.

> --
> View this message in context: http://r.789695.n4.nabble.com/Interpreting-coefficients-in-linear-models-with-interaction-terms-tp4655365p4655390.html
> Sent from the R help mailing list archive at Nabble.com.

David Winsemius
Alameda, CA, USA

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