similar to: Gram-Schmidt orthonormal factorization

Hi, Why the qr() produces a negative Q compared with Gram-Schmidt? (note example below, except Q[2,3]) Here is an example, I calculate the Q by Gram-Schmidt process and compare the output with qr.Q() a <- c(1,0,1) b <- c(1,0,0) c <- c(2,1,0) x <- matrix(c(a,b,c),3,3) ########################## # Gram-Schmidt ########################## A <- matrix(a,3,1) q1 <-

It is not clear to me that one can. If the singular value decomposition of A is the triple product P d Q', then the singular value decomposition of A'A=S is Q d^2 Q'. The information about the orthonormal matrix P is lost, is it not? ********************************************************** Cliff Lunneborg, Professor Emeritus, Statistics & Psychology, University of Washington,

Hi. I have been looking at the PCAproj function in package pcaPP (R 2.4.1) for robust principal components, and I'm trying to interpret the results. I started with a data matrix of dimensions RxC (R is the number of rows / observations, C the number of columns / variables). PCAproj returns a list of class princomp, similar to the output of the function princomp. In a case where I can

Dear R community: I want to simulate a regression matrix which is generated from an orthonormal matrix X of dimension 30*10 with different between-column pairwise correlation coefficients generated from uniform distribution U(-1,1). Thanks in advance! Rui [[alternative HTML version deleted]]

Dear R community: I am trying to do a simulation study mentioned by Fu (1998), Journal of Computational and Graphical Statistics, Volume7, Number 3, Page 397-416. In order to give a clear statement of quesion I copy the following paragraph from the article: We compare the bridge model with the OLS, the lasso and the ridge in a simulation of a linear regression model of 30 observations and 10

Hi: I've been reading "Computational Methods for Multilevel Modeling" by Pinheiro and Bates, the idea of embedding the technique in my own c-level code. The basic idea is to rewrite the joint density in a form to mimic a single least squares problem conditional upon the variance parameters. The paper is fairly clear except that some important level of detail is missing. For

General goal: Write R code to find the inverse matrix of an nxn positive definite symmetric matrix. Use solve() to verify your code works. Started with a 3x3 matrix example to build the code, but something dosen't seem to be working. I just don't know where I am going wrong. ##Example matrix I found online A<-c(4,1,-1,1,2,1,-1,1,2) m<-matrix(A,nrow=3,ncol=3) ##Caculate the eigen

Hey, R-listers, I have a question about determining the orthogonal basis vectors. In the d-dimensinonal space, if I already know the first r orthogonal basis vectors, should I be able to determine the remaining d-r orthognal basis vectors automatically? Or the answer is not unique? Thanks for your attention. Fred

Hello List, I would like to orthonormalize vectors contained in a matrix X taking into account row weights (matrix diagonal D). ie, I want to obtain Z=XA with t(Z)%*%D%*%Z=diag(1) I can do the Gram-Schmidt orthogonalization with subsequent weighted regressions. I know that in the case of uniform weights, qr can do the trick. I wonder if there is a way to do it in the case of non uniform

Hi all! I'm fairly new to R and not too experienced with regression. Because of one or both of those traits, I'm not seeing why some terms are being dropped from my model when doing a regression using lm(). I am trying to do a regression on some experimental data d, which has two numeric predictors, p1 and p2, and one numeric response, r. The aim is to compare polynomial models in p1

Dear R list users, the singluar value decomposition of a symmetric matrix M is UDV^(T), where U = V. La.svd(M) gives as output three elements: the diagonal of D and the two orthogonal matrices u and vt (which is already the transpose of v). I noticed that the transpose of vt is not exactly u. Why is that? thank you for your attention and your help Stefano AVVISO IMPORTANTE: Questo messaggio di

Suppose one wanted to consider random variables X_1,...X_n and from each subtract off the piece which is correlated with the previous variables in the list. i.e. make new variables Z_i so that Z_1=X_1 and Z_i=X_i-cov(X_i,Z_1)Z_1/var(Z_1)-...- cov(X_i,Z__{i-1})Z__{i-1}/var(Z_{i-1}) I have code to do this but I keep getting a "non-conformable array" error in the line with the covariance.

I've just released the latest R-Forge versions of heplots 0.9-3 and candisc 0.5-18 to CRAN. They should appear there within a day or two. == heplots The heplots package provides functions for visualizing hypothesis tests in multivariate linear models (MANOVA, multivariate multiple regression, MANCOVA, etc.). They represent sums-of-squares-and-products matrices for linear hypotheses and for

Hi R-Helpers: I?m trying to use the function GLMM from lme4 package, (R-1.8.1, Windows 98),and I get the following error: > pd5 = GLMM(nplant~sitio+ + fert+ + remo+ + sitio:fert+ + remo:sitio+ + remo:fert+ + remo:fert:sitio + data=datos, + family=binomial, +

Hi all, A good new year for everybody. Could somebody help me on a question? The Singular Value Decomposition of a matrix A gives A = U * D * t(V) I A is a M X N matrix, U is the left singular matrix (M X N), D is a diagonal singular values matrix (N X N) and V is the transpose right singular ortogonal matrix (N X N). By taking the first l columns of V, with gives a (l X l) matrix, i know

Dear all, Can any one tell me how can i perform Orthogonal Polynomial Regression parameter estimation in R? -------------------------------------------- Here is an "Orthogonal Polynomial" Regression problem collected from Draper, Smith(1981), page 269. Note that only value of alpha0 (intercept term) and signs of each estimate match with the result obtained from coef(orth.fit). What

Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given

Hi all, We know that Hermite polynomial is for Gaussian, Laguerre polynomial for Exponential distribution, Legendre polynomial for uniform distribution, Jacobi polynomial for Beta distribution. Does anyone know which kind of polynomial deals with the log-normal, Student抯 t, Inverse gamma and Fisher抯 F distribution? Thank you in advance! David [[alternative HTML version deleted]]

Hi R-Helpers: I?m trying to fit the same linear model to a bunch of variables in a data frame, so I was trying to adapt the codes John Fox, Spencer Graves and Peter Dalgaard proposed and discused yesterday on this e-mail list: for (y in df[, 3:5]) { mod = lm(y ~ Trt*Dose, data = x, contrasts = list(Trt = contr.sum, Dose = contr.sum)) Anova(mod, type = "III") } ## by John Fox or for

Dear all, Does anybody have an idea or suggestion how to construct (plot) 4-dimensional hypercube in R. Thanks in advance for any pointers. Regards, Andrej