Suppose I can observe $Y_{ijt}$, $i = 1,2,..., n$ , $j = 1,2,3$ and $t = $ 3 weeks, 1 months, half a year and one year.
I am interested in whether
- $E(Y|j=1,k) = E(Y|j = 2,k)= E(Y|j=3,k)$
- $E(Y|j, k) = \alpha_j + \beta_j k $
At first, I thought it was a simple question that I can simply use ANOVA for different periods of time in the first case, and for the second I can run simple linear regression at given $j = 1,2,3$. Yet I realized that for each individual $i$ at given time period $t = k$, $Y_{i1k}$, $Y_{i2k}$ , $Y_{i3k}$ are likely correlated, which render ANOVA ineffective. I am what kind of model should I build to tackle these two questions that I want to tackle?