Dear colleagues!
I conducted an experiment with a nominal within-subject factor (type; 2 levels; unbalanced) and a continuous (age) and a nominal (sex; 2 levels; unbalanced) between-subject factor. Now I want to fit the following linear model for my outcome variable (continuous):
Y = b00 + b10*age + sex*(b01 + b11*age) + type*(b02 + b12*age)
Where sex and age are dummy variables, b0i are the intercepts and b1i the slopes.
However, I am not sure if this is the right way to do it, since I am not regarding the fact that type is not an independent measure (as it is a within-subject factor). If age would have been an ordinal variable I would have taken an repeated-measures ANOVA, but in the regression case I am not sure
My question is: Is this a valid approach?
Greetings, David
Thanks for giving a detailed explanation of your problem. You are correct that OLS regression is not appropriate here since you have repeated measures. Use a mixed effects model instead of OLS regression. In R this is implemented in the lme4::lmer function (among others); it's also doable in the other major statistics packages, R is just what I'm most familiar with.
Thanks for giving a detailed explanation of your problem. You are correct that OLS regression is not appropriate here since you have repeated measures. Use a mixed effects model instead of OLS regression. In R this is implemented in the lme4::lmer function (among others); it's also doable in the other major statistics packages, R is just what I'm most familiar with.
You need a mixed methods approach, but Repeated Measures ANOVA might not do it for you (depends on the assumptions of ANOVA, which I cannot tell if you meet).
From what you have posted, TYPE is a measure that changes over time for each person, so you are modeling the change from Pre- to Post- assessment. In a mixed methods approach, your level 1 model is simple:
Yi = P0i + P1i*(TIME) + E
where time varies from 0 (pre-assessment) to 1 (post-assessment), P0i is the pre-assessment value for person i and B1i is the change from pre to post for person i.
For level 2, you lift out the change parameter P1 to be the outcome of the analysis, so the model is:
P1 = B10 + B11*(AGE) + B12*(SEX) + R1
where B10 is the average change over time for the sample, B11 is the impact of 1 year increase in age on the change over time, and B12 is the difference in change over time from the sex coded 0 to the sex coded 1.
NOTE: You can also model the impact of your two predictors on your pre-assessment, like so:
P0 = B00 + B01*(AGE) + B02*(SEX)
I run these models using HLM, but there are also R programs and SAS programs that will run them.
A linear mixed model is a common approach here. A simpler analysis may be more powerful and simplerl. If Type is a pre-post measure you can use the change score as Y and include the centred pre score as a covariate.
Thank you all for your answers! Although I tried to be as clear as possible I still have mislead some of you by not specifying that "type" is just not a pre-/post measure but just a different experimental outcome of the same subject.
Your comments were still very helpful and got me further in understanding LMEs. After consorting with the Statistics Department, the correct LME for correcting for interdependencies is:
Y ~ age*sex*type + (age|subjectId)
were subjectId is the random factor telling the model that type is not and independent measure.
Thanks again!
Greetings, David
If age is continuous I'd normally start with something like this:
Y = age + sex*type +(1|subjectid)
working up to models such as:
Y = age + sex*type + (sex|subjectid) + (type|subjectid)
and so on. centering age is a good idea in most cases also.
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