# Generalized or mixed-response reduced-rank regression Peforms either rank constrained maximum likelihood estimation or singular value penalized estimation. ```r mrrr( Y, X, is.pca = NULL, offset = NULL, ctrl.id = c(), family = list(gaussian(), binomial()), familygroup = NULL, maxrank = min(ncol(Y), ncol(X)), penstr = list(), init = list(), control = list() ) ``` ## Arguments - `Y`: response matrix - `X`: covariate matrix - `is.pca`: If TRUE, mixed principal component analysis with X=I - `offset`: matrix of the same dimension as Y for offset - `ctrl.id`: indices of unpenalized predictors - `family`: a list of family functions as used in `glm` - `familygroup`: a list of family indices of the responses - `maxrank`: integer giving the maximum rank allowed. Usually this can be set to min(n,p,q) - `penstr`: a list of penalty structure of SVD, contains penstr$penaltySVD is the penalty of SVD, penstr$lambdaSVD is the regularization parameter - `init`: a list of initial values of kappaC0, kappaS0, C0, and S0 - `control`: a list of controling parameters for the fitting ## Returns S3 `mrrr` object, a list containing - **obj**: the objective function tracking - **converged**: TRUE/FALSE for convergence - **coef**: the estimated coefficient matrix - **outlier**: the estimated outlier matrix - **nrank**: the rank of the fitted model ## Details The model fitting process can be fine tuned through argument `control`. The available elements for `control` include * epsilon: positive convergence tolerance epsilon; the iterations converge when |new - old | / (old + 0.1) \< epsilon. treated as zero. * sv.tol: tolerance for singular values. * maxit: integer giving the maximal number of iterations. * trace:: logical indicating if tracing the objective is needed. * conv.obj:: if TRUE, track objective function. * equal.phi:: if TRUE, use a single dispersion parameter for Gaussian responses. * plot.obj:: if TRUE, plot obj values along iterations; for checking only * plot.cv:: if TRUE, plot cross validation error. * gammaC0:: adaptive scaling to speed up computation. Similarly, the available elements for arguments `penstr` specifying penalty structure of SVD include * penaltySVD: penalty for reducing rank * lambdaSVD: tuning parameter. For penaltySVD = rankCon, this is the specified rank. ## Examples ```r library(rrpack) simdata <- rrr.sim3(n = 100, p = 30, q.mix = c(5, 20, 5), nrank = 2, mis.prop = 0.2) Y <- simdata$Y Y_mis <- simdata$Y.mis X <- simdata$X X0 <- cbind(1, X) C <- simdata$C family <- simdata$family familygroup <- simdata$familygroup svdX0d1 <- svd(X0)$d[1] init1 = list(kappaC0 = svdX0d1 * 5) offset = NULL control = list(epsilon = 1e-4, sv.tol = 1e-2, maxit = 2000, trace = FALSE, gammaC0 = 1.1, plot.cv = TRUE, conv.obj = TRUE) fit.mrrr <- mrrr(Y_mis, X, family = family, familygroup = familygroup, penstr = list(penaltySVD = "rankCon", lambdaSVD = 2), control = control, init = init1) summary(fit.mrrr) coef(fit.mrrr) par(mfrow = c(1, 2)) plot(fit.mrrr$obj) plot(C ~ fit.mrrr$coef[- 1 ,]) abline(a = 0, b = 1) ```

mrrr function