# Thread: Regression Analysis thoughts - Could I model my data this particular way?

1. ## Regression Analysis thoughts - Could I model my data this particular way?

Hello,

Looking for a guidng hand with a regression problem that I have managed to create. Apologies for my lack of statistical knowledge, but if you need any more information in order to give advice please let me know.

I have run an experiment with one group of participants (n=20). Each participant visits the lab on four separate occasions.

On each visit, a participant completes a leg exercise session with a tourniquet placed around their leg. The parameters of the exercise itself remain exactly the same on each visit, I only manipulate the pressure of the tourniquet on the leg (first visit = no pressure, then 30mmHg pressure on the second visit, 50mmHg pressure on the next visit and 70mmHg on the last visit.) I record the mean change in leg blood-flow that each participant experiences during each particular exercise session. I also take a range of physical measurements for each participant (body weight, leg length etc.) on their first visit.

I've already used simple linear OLS regression to display the linear relationship between a particular physical characteristic (thigh circumference) and the mean change in blood flow at each of the four tourniquet pressures that I used (0, 30, 50, 70). However, I'd be interested in trying to roll everything together and build a model that could predict the mean change in leg blood-flow, by inputting the thigh circumference of a participant and ANY cuff pressure between the value of 0-70mmHg, not just the four pressures that I tested.

I understand that multiple regression would be inappropriate to achieve this using my dataset as I do not have true independence of observations. I have tried a GLM repeated measures and this gives me a separate slope and intercept for each of the four tourniquet pressures I investigated. That's ok, but I'm hoping to get the stats/model to reflect that tourniquet pressure is not a categorical variable by nature, it's continuous (I just pre-selected four pressures to actually test at). Thus giving me one slope for 'Tourniquet Pressure' in the model.

Could anyone give any pointers as to an appropriate way to achieve this? I appreciate my sample size is hardly enormous as the study was not initially designed to achieve this, but it would be good (if possible) to consider any potential usefulness/viability of such a model so that I could develop this into a future larger study.

Much Thanks,
Phil

2. ## Re: Regression Analysis thoughts - Could I model my data this particular way?

You may be able to use a multilevel model, where measurements are clustered in participant and then treat the pressure amount as a continuous variable in then model. This would likely give you the answer you want.

Multilevel models are much more tricky to learn than OLS.

Also, you would be trying to interpolate data for values not measured, which can lead to bias if the relationship between pressure and flow don't have a dose-response relationship that is linear.

Lastly, given your sample size the model may not support too many covariates before it becomes overfitted and not generalizable.

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