Reid Landes
2008-Feb-08 16:35 UTC
[R] User specified correlation structure (e.g., 2-banded Toeplitz)
Dear All: I am trying to fit a special case of a 2-banded Toeplitz correlation structure. A 2-banded Toeplitz has ones on the diagonal, a correlation, RHO1, on the first off-diagonal, and a correlation, RHO2, on the second off-diagonal, with zeros on all subsequent off-diagonals. After reading relevant sections in Mixed-Effects Models in S and S-PLUS (Pinheiro & Bates, 2000) and searching on the R-help archives, I've figured out how to get the 2-banded Toeplitz, but not the desired special case. In the example below, the initial value RHO1 = 0 and RHO2= -0.3. The output matrix below is an example of the special case I'd like to fit -- a 2-banded Toeplitz constraining RHO1=0. Fitting the 2-banded Toeplitz structure to the ``Orthodont'' example dataset provided in R-Help, we estimate RHO1 also (since the example matrix below contains INITIAL values). ---------------------Start R-code & output ------------------------------- #This intilizes a 2-banded Toeplitz structure cs1ARMA <- corARMA(value = c(0,-.3), form = ~ 1 | Subject, p = 2, q = 0) cs1ARMA <- Initialize(cs1ARMA, data = Orthodont) corMatrix(cs1ARMA)$M01 [,1] [,2] [,3] [,4] [1,] 1.0 0.0 -0.3 0.0 [2,] 0.0 1.0 0.0 -0.3 [3,] -0.3 0.0 1.0 0.0 [4,] 0.0 -0.3 0.0 1.0> TOEP2 <- gls(distance ~ Sex * I(age - 11), Orthodont,+ correlation = corARMA(value = c(0,-.3), form = ~ 1 | Subject, p = 2, q = 0), + weights = varIdent(form = ~ 1 | age)) #-- Selected output follows----- Correlation Structure: ARMA(2,0) Formula: ~1 | Subject Parameter estimate(s): Phi1 Phi2 0.3269544 0.4897645 --------------------- End R-code & output -------------------------------- I cannot figure out how to restrict RHO1 = 0, while allowing estimation of RHO2. Maybe an answer lies in specifying a different ``position vector'' other than the default: corARMA(..., form = ~ 1 | Subject ...). (See p226 of Pinheiro & Bates, 2000 for explanation of a position vector.) But I'm not totally sure if I understand the position vector and I know I don't know how it works in R. Then again, there is likely a completely different way to solve this problem. Any help will be appreciated! Reid