What statistical test do I run if I had one response variable assessed by 3 doses (2 mg, 10 mg, 20 mg) and 2 types of a diet (A, B) at 10 different time points (1-10)? To summarize, I had 6 groups (A2, A10, A20, B2, B10, B20) of 10 individuals that were measured for a certain response variable (say 'Y') in a 10 week study (each were measured per week).
You could try a 3 (dose) by 2 (diet) by 10 (within-subject: time) repeated-measure ANOVA, but I would be worried with only 10 people in each cell only a quite strong effect would be detectable. Do you hypothesize a linear dose-response relationship? Do you similarly hypothesize that the change in your dependent variable over time is linear? If so, you could probably conduct a hierarchical linear regression where participant number is dummy coded as categorical (and each participant has 10 rows). Then have column for dose, time, and your dependent variable. Then you would choose the order to put them into the regression, as well as if to put in the interactions, based on your hypotheses. Hope that helps some with your project, David. ~ Kevin
Just a note on terminology. In the statistical dialect I am most familiar with, hierarchical linear regression means ordinary least squares linear regression with explanatory variables entered in steps (or blocks), with the data analyst (as opposed to an algorithm) determining the order of entry. I think Kevin is recommending what I would call a multilevel model, but which a lot of others call a hierarchical linear model or a linear mixed model.
By the way, I agree with Kevin in recommending that type of model. If you use traditional repeated measures ANOVA, any subject with even 1 missing data point is excluded from the analysis (unless you impute something for the missing values). A multilevel model, on the other hand, uses all available data for each subject, and does not exclude those with some missing data points. It also allows more flexibility in how you model the error structure.
David, if you're not familiar with these types of models, the book by Jos Twisk gives a very accessible introduction; and the book by Singer & Willett explains very nicely how these models work when the clustering involves occasions (or time points) clustered within subjects. HTH.
https://www.cambridge.org/core/books/applied-multilevel-analysis/7755169EDD3B2304B041773D48F2BA6F
http://www.oupcanada.com/catalog/9780195152968.html
https://stats.idre.ucla.edu/other/examples/alda/
Thank you to the both of you, Kevin and Bruce, for your elaborate descriptions and suggestions. My dependant variable would be body weight, where I would expect a linear growth over time, but only to a certain extent. I guess there would more likely be a logarithmic growth rather than a linear growth, so would this change my model?
David
Hello David. In a preliminary exploratory model, you could treat time as a categorical variable. This allows the mean for each level of time to fall where it may, with no forcing the means to fall on a straight line, a quadratic function, etc. You can then plot those means and see what kind of function makes sense when you do your actual analysis, with time treated as a continuous variable. IIRC, Singer & Willett describe this strategy in their book, Applied Longitudinal Data Analysis. HTH.
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