Hi,
For my thesis project, I want to fit a quadratic model on each individual separately. For example, I have variable X1 and X2 (e.g., price1 and price 2) and variable Y1 and Y2 (e.g., Reaction Time1 and Reaction time 2), and 75 participants. Each participant conducted X1 and X2, and it is expected that the RT distribution is a quadratic distribution. Moreover, the expectation is that the peak of the distribution in X2 is on a different spot than on X1.
I want to estimate for each participant their RT distribution on X1 and X2 separately, and compare the outcome parameters with a statistical test.
Does anyone know how to analyze this problem in SPSS or in R?
Thank you very much!
I am sorry but you goal doesn't make sense. Sample sizes of one don't work in regression. Consult with your advisor unless s/he suggested this. In that case consult a STATISTICAL consultant. Best wishes, David Booth
As Professor Booth says, your model makes little sense if you have only one observation for each of your 75 respondents.
If you want a regression model for each respondent then you need multiple observations from each individual respondent. 3 observations will give you an answer, but you would want around 10 to get a reliable answer (regression model)
Your question makes total sense, and this usually is a good place to ask for advice.
The model you want to build would be called a multi-level polynomial regression. Multi-level means you are estimating on population level and participant level, simultaneously. As Hume F. Winzar (repeatedly) pointed out, a within-subject repeated measures design is required for participant-level estimates. It is unclear from your question, if you have that or not. If you have it, I describe (multi-level) polynomial regression with R in two chapters of my book:
https://schmettow.github.io/New_Stats/mpm.html#prm
https://schmettow.github.io/New_Stats/mlm.html#universality
Note that I am using a Bayesian regression engine, which allows me to derive estimates for the stationary points of polynomial models. That is very useful, because polynomial coefficients themselves often have no meaningful interpretation.
If you need further statistical advice, your university has a quite capable (Bayesian) Statistics department (prof. Wagenmakers).
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