Linear Mixed Models

#1
Hi guys, would much appreciate your input here.

I intend to quantify the relative impact of one variable (with 3 intrinsic grades on a scale from 1-3) on the dependent variable that lies between 0 and 1 (it is a ratio). My patient sample is extremely small (3 patients). However, of each patient, several measures were taken at different time points (total number of dat a points is 21).

I was told that linear mixed models would be a great way to basically compare means between the groups and say whether there is a difference in-between the grouping or not.

However, the estimated marginal means are estimated to lie above 1, which is impossible (maximum value for my dependent variable would be 1).

If the estimated mean is above one, is it correct to just adjust it to 1?

Is there a better way to achieve what I want to show?


Would much appreciate your help!

Thank you!
 
#2
If there are 3 patients only, you should not be using mixed effects models (i.e. fixed effects + random effects). You should be using a fixed effects panel model, which is equivalent to regular regression with dummy variables for patients. Since the dependent variable belongs to [0,1], you should be using logistic regression (logit model), probit regression (probit model) or something similar.
 
#4
If there are 3 patients only, you should not be using mixed effects models (i.e. fixed effects + random effects). You should be using a fixed effects panel model, which is equivalent to regular regression with dummy variables for patients. Since the dependent variable belongs to [0,1], you should be using logistic regression (logit model), probit regression (probit model) or something similar.
Thank you for your input.

My dependent variable can take any value between 0 and 1 and is a ratio variable. My influencer variable can take the value 0,1,2,3.

The way i understand, probit model and logit models are for binary/ordinal/interval scaled dependent variables? Or am i mistaken?

And in what model can i best account for repeated measures of the patients (therefore interdependency of the measured values of the dependent variable)?

Thanks for your help! I hope you can clarify that for me. I would much appreciate it!!

Best