# Dimension reduction This function provides several methods to estimate the central space or central mean space of y on x. It returns the matrix of central space or central mean space for different dimensions and contains other information used for dimension selection by `mave.dim`. ```r mave( formula, data, method = "CSOPG", max.dim = 10, screen = NULL, subset, na.action = na.fail ) mave.compute( x, y, method = "CSOPG", max.dim = 10, screen = nrow(x)/log(nrow(x)) ) ``` ## Arguments - `formula`: the model used in regression - `data`: the data - `method`: This parameter specify which method will be used in dimension reduction. It provides five methods, including "csMAVE","csOPG","meanOPG","meanMAVE","KSIR" by default, method = 'csOPG' * 'meanOPG' and 'meanMAVE' estimate dimension reduction space for conditional mean * 'csMAVE' and 'csOPG' estimate the central dimension reduction space * 'KSIR' is a kernel version of sliced inverse regression (Li, 1991). It is fast, but with poor accuracy. - `max.dim`: the maximum dimension of dimension reduction space. The default is 10. In practice, max.dim will be equal to min(max.dim,ncol(x),screen). - `screen`: specify the number of variables retained after screening method. The default is n/log(n). When this number is smaller than max.dim, then max.dim will change to the value of screen - `subset`: an optional vector specifying a subset of observations to be used in the fitting process. - `na.action`: a function which indicates what should happen when the data contain NAs. The default is na.action, which wil stop calculations. If na.action is set to be na.omit, the incomplete cases will be removed. - `x`: The n by p design matrix. - `y`: The n by q respond matrix. ## Returns dr is a list which contains: * dir: dir[[d]] is the central space with d-dimension d = 1, 2, ..., p reduced direction of different dimensions * y: the value of response * idx: the index of variables which survives after screening * max.dim: the largest dimensions of CS or CMS which have been calculated in mave function * ky: parameter used for DIM for selection * x: the original training data ## Examples ```r x <- matrix(rnorm(400*5),400,5) b1 <- matrix(c(1,1,0,0,0),5,1) b2 <- matrix(c(0,0,1,1,0),5,1) eps <- matrix(rnorm(400),400,1) y <- x%*%b1 + (x%*%b2)*eps #finding central space based on OPG method #dr.csopg <- mave.compute(x,y, method = 'csopg') #or dr.csopg <- mave(y ~ x, method = 'csopg') #dr.meanopg <- mave.compute(x,y, method = 'meanopg') #or dr.meanopg <- mave(y ~ x, method = 'meanopg') #find central mean space based on ksir method dr.ksir <- mave(y~x,method='ksir') #or #dr.ksir <- mave.compute(x,y,method='ksir') #See more examples about screening and mutiple responses in the vignette #Using screening for high dimensional data #x <- matrix(rnorm(100*50),100,50) #y1 = as.matrix(x[,1])+rnorm(100)*.2 #y2 = as.matrix(x[,2]+x[,3])*as.matrix(x[,1]+x[,5])+rnorm(100)*.2 #y = cbind(y1,y2) #dr.sc = mave(y~x,method='CSOPG',max.dim=5,screen=20) #dr.sc.dim = mave.dim(dr.sc) #print the directions of central space with the selected variables #dr.sc.dim$dir[[3]][dr.sc$idx,] ``` ## References Li K C. Sliced inverse regression for dimension reduction[J]. Journal of the American Statistical Association, 1991, 86(414): 316-327. Xia Y, Tong H, Li W K, et al. An adaptive estimation of dimension reduction space[J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2002, 64(3): 363-410. Xia Y. A constructive approach to the estimation of dimension reduction directions[J]. The Annals of Statistics, 2007: 2654-2690. Wang H, Xia Y. Sliced regression for dimension reduction[J]. Journal of the American Statistical Association, 2008, 103(482): 811-821. ## See Also `mave.dim` for dimension selection, `predict.mave` for prediction using the dimension reduction space, `coef.mave` for accessing the basis vectors of dimension reduction space of given dimension, `plot.mave` for plot method for mave class