# Multivariate repeated measures, binary and continuous

#### robsncoppers

##### New Member
Hello all. I am working with a data set of multivariate repeated measurements. Specifically, subjects performed an exercise they were taught up to three times each and recorded heart rate variability (HRV) and whether they felt a particular sensation (details omitted). Whether they reported feeling the sensation was recorded as a binary variable, yes or no. Subjects also recorded baseline HRV at rest before being taught the exercise.

My purpose is twofold, (i) to quantify the change from baseline HRV and (ii) to determine whether the sensation corresponds to the change in HRV.

To solve (i) I am treating the baseline HRV values as fixed covariates in a linear regression of the HRV values. This works well enough. But to solve (ii) I am uncertain how to move forward. First I thought I might use a hierarchical model, conditioning the binary response on the HRV values, but I don't want to imply that causation between the two dependent variables. I only want to quantify correlation. That made me wonder about multivariate generalized linear models, but I couldn't find much about binomial-normal multivariate models. I also wonder whether a simple solution, using some non-parametric test for correlation isn't the best idea. But would this ignore relevant information in the regression analysis used to solve (i)?

If anyone has any thoughts or helpful links, I would appreciate it!

Have a nice day!

#### Phaedrus

##### New Member
If you are thinking in modeling the probability of your particular sensation (1=present 0=not present) taking into account some predictors (such as HRV or the change in HRV) you could take a look at logistic regression (although I am sure you have already done this). An open paper that reviews this is this one (click here).

#### robsncoppers

##### New Member
Phaedrus, yes, I have considered that. But because I am interested in the change in HRV and I have repeated measures on it, I consider it to be a dependent variable much like the binary response. I feel as though using one or the other (the change in HRV or the binary response) as an independent variable in the regression implies causation when really I don't know whether one causes the other. thanks for replying!

#### bugman

##### Super Moderator
Well, you could use a GLM with your binary variable as your response and HRV as a covariate. Generalised Estiamting Equations may be useful for the longitudinal aspect of the study, but I haven' t really used them.