The following is a random intercept and slope model for a lo

The following is a random intercept and slope model for a longitudinal study. There are N subjects and each subject’s response is measured at J time points. For i = 1,...,N and j = 1,...,J, Y_ij = + _0i + t_ij + t_ij1i + _ij

where t_ij = time of measurement j for subject i, and and are fixed parameters.

The models assumptions are for i = 1,...,N and j = 1,...,J,

E(_ij) ~ N(0,²)

_0i ~ N

_{1i ~} N

E(_0i) = 0

E(_1i) = 0

var(_0i) = ²₀

var(1i) = ²₁

cov(_0i,_1i )=²₀₁

and (11,...NJ) are independent of all _0i and all _1i. The distribution of (_0i,_1i) is bivariate normal.

What is the intraclass correlation?

Solution

intra class correlation r(0i,1i)=cov(0i,1i)/square root of (var(0i)var(1i)=201/(2021)^1/2