# repeated measurements

#### leo nidas

##### New Member
Hi there,

I am struggling to understand the way we analyze longitudinal data and I've gone through the net and some books but still have some questions.

Let's consider a very simple example because only through an example I might get a chance..

We have two subjects, the first one has been measured three times, in three distinct time points, and the other one, two times.

So

[y11 y12 y13 y21 y22]'=[1 1 1 1 1; x11 x12 x13 x14 x15]' + [b0 b1]' +[e11 e12 e13 e14 e15]

where y11, y12, y13 are the three measurements of the first subject, and
y21 y22 are the two measurements of the second subject.

Similarly x11, x12, x13 are the time points of the measurements etc.

I want to suppose the the subjects are independent, while the measuremets within a subject are not, and have some correlation let ρ. (i.e. The working correlation matrix has exchangeable stucture right?)

So this is wht I think is the right thing:

bhat=(X'WX)^-1*X'*W*y,

where W=V^-1,

where V=diag(V1,V2),

where V1=s^2*
[1 ρ ρ
ρ 1 ρ
1 1 ρ]

V2=s^2*
[1 ρ
ρ 1]

and the ρ is esimated using e(ij)=( y(ij)-yhat(ij) )/ s

by r=1/((N-p)*s^2)*Σ(e(ij)e(ij)) for j different from k.

Am I correct?

Could someone please use the same example with (whatever) numbers so as to compare results?

Another question is that shouldn't the ρ included in the V1 be different from the ρ of the V2? If so, I can use the above formula to estimate ρ1 and ρ2. If not, how can I estimate the ρ?The results that the above formula will not gine different ρ for each subject?