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I am working on a HLM longitudinal analysis. I have four time points spaced unequally - pre-test: 0 months, post-test: 2 months later, follow-up: 6 months later after pre-test, follow-up2: 12 months later after pre-test. I am interested in modeling a linear and a quadratic growth curve. I learned about using contrasts to address the issue of co-linearity occurring when entering a linear and a quadratic term in the level 1 model. However, because my intervals are unequally spaced, I am unsure that I am using the right contrasts. Using SPSS, ANOVA contrasts, I attempted to specify the metric and obtained the following contrast coefficients: linear -- time=0, -.546; time=2, -.327; time=6, .109; time=12, .764. Quadratic -- time=0, .513; time=2, -.171; time=6, -.741; time=12, .399. My question is, are these contrast coefficients correct? I found articles that demonstrate how to specify the coefficients for equally spaced intervals, but not for unequally spaced intervals. Could these coefficients be verified? thank you.
Dear Peter,
First of all I'm just wondering about your experimental setting (0, 2, 6 and 12 months), which suggests suspicion of non-linear, declining effect. Am I right? Maybe it would be better to perform the experiment in constant intervals if you assume linear effect?
But, to the point. In the situation you present here, in my opinion, this is justified to take such contrasts that suit to the spaces between your time points. The sum of the contrasts should be zero, and the contrasts should be integer numbers. In my calculations the contrasts for linear trend should be -5, -3, 1, 7 and for quadratic 7, -3, -11, 7, if I did no mistake in the calculations.
Michal
Cross-posted from https://stats.stackexchange.com/questions/277695/computing-contrasts-for-unequal-intervals
thank you. there is no linear effect, there is a quadratic effect. so you are correct. are there adjustments I should make in HLM?
thank you for your contrast numbers. what is the calculation process? I can't seem to find a calculation process anywhere. I've looked in Hedeker and Gibbons (2006) but they do not offer any process and no websites have helped. can you share your calculation process?
This was a little bit a "home made" work. I will share with you my calculations in a few hours as I am busy know. If it is a quadratic, don't you think it would be good to check quadratic regression in GLM?
Dear Peter,
Sorry, I could not download my calculations yesterday. Here it is for linear and quadratic trend.
I'm also wondering what is your theory behind quadratic trend for your research. In classic quadratic trend there is a minimum typical for parabola. If you assume your data are monotonously increasing in the quadratic manner form the very beginning of your time points, maybe it would be better to modify the trend to the one I attached as version 2.
Please give me a feedback to let me know if you agree with such a concept of trends, and check if I didn't do any mistake in the calculations.
Michal
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