# Correlation Matrix for the Compound Symmetry Structure Compute the correlation matrix for a the compound symmetry structure. ```r corLevCompSymm(par, nlevels, levels, lowerSQRT = FALSE, compGrad = TRUE, cov = FALSE, impl = c("C", "R")) ``` ## Arguments - `par`: Numeric vector of length `1` if `cov` is `TRUE` or with length `2` else. The first element is the correlation coefficient and the second one (when it exists) is the variance. - `nlevels`: Number of levels. - `levels`: Character representing the levels. - `lowerSQRT`: Logical. When `TRUE` the (lower) Cholesky root $L$ of the correlation matrix $C$ is returned instead of the correlation matrix. - `compGrad`: Logical. Should the gradient be computed? - `cov`: Logical. If `TRUE` the matrix is a covariance matrix (or its Cholesky root) rather than a correlation matrix and the last element in `par` is the variance. - `impl`: A character telling which of the C and R implementations should be chosen. ## Returns A correlation matrix (or its Cholesky root) with the optional `gradient` attribute. ## Note When `lowerSQRT` is `FALSE`, the implementation used is always in R because no gain would then result from an implementation in C. ## Examples ```r checkGrad <- TRUE lowerSQRT <- FALSE nlevels <- 12 set.seed(1234) par <- runif(1L, min = 0, max = pi) ##============================================================================ ## Compare R and C implementations for 'lowerSQRT = TRUE' ##============================================================================ tR <- system.time(TR <- corLevCompSymm(nlevels = nlevels, par = par, lowerSQRT = lowerSQRT, impl = "R")) tC <- system.time(T <- corLevCompSymm(nlevels = nlevels, par = par, lowerSQRT = lowerSQRT)) tC2 <- system.time(T2 <- corLevCompSymm(nlevels = nlevels, par = par, lowerSQRT = lowerSQRT, compGrad = FALSE)) ## time rbind(R = tR, C = tC, C2 = tC2) ## results max(abs(T - TR)) max(abs(T2 - TR)) ##=========================================================================== ## Compare the gradients ##=========================================================================== if (checkGrad) { library(numDeriv) ##======================= ## lower SQRT case only ##======================== JR <- jacobian(fun = corLevCompSymm, x = par, nlevels = nlevels, lowerSQRT = lowerSQRT, impl = "R", method = "complex") J <- attr(T, "gradient") ## redim and compare. dim(JR) <- dim(J) max(abs(J - JR)) nG <- length(JR) plot(1:nG, as.vector(JR), type = "p", pch = 21, col = "SpringGreen3", cex = 0.8, ylim = range(J, JR), main = paste("gradient check, lowerSQRT =", lowerSQRT)) points(x = 1:nG, y = as.vector(J), pch = 16, cex = 0.6, col = "orangered") } ``` ## Author(s) Yves Deville

corLevCompSymm function