# Within/Between Multivariate Analysis

I am interested in analysing two dependent variables, let's say Alpha and Beta.

I tested 40 participants, divided into two different treatment groups: Group A (n = 20) and Group B (n = 20)

Within each group, I measured Alpha and Beta six times (time variable, t1 to t6)

I would like to analyse these data both considering:

1. The time variable,
2. The difference between group (how Alpha and Beta change over time and differs between groups).

While always interested in comparing the two groups (point #2), I would like to create a model which takes the time variable into account in two different ways: 1a) A level considering the within-subject aspect (how Alpha and Beta change over multiple time-points for each participants >> We could see each subject as a cluster of data > Orange Clustering); 1b) A level considering within time-points among all subject of the same group (how at each time Alpha and Beta evolve over the time points > We could see each time point as a cluster > Yellow Clustering). Please refer to the attached file for a clearer overview! {Image Caption: In green we have group A and in blue Group B. Each row is a participant and each coloumn is one time-point. Each participant's graph represent a point taking Alpha and Beta measurements for each time-point. Both of the levels of analysis I would be interested in are in Orange (clustering each data for each participant across time) and in Yellow (clustering data for each time point across participants. While always interested in comparing Group A to Group B.}

I explored some possibilities such as Linear Mixed Models, Hierarchical Models and Doubly Multivariate Analysis, but I am still not sure which is the most comprehensive for my desired analysis.