R help - Aug 2009 - lm.fit algo

Hi, everyone,

This is a little silly, but I cant figure out the algorithm behind
lm.fit function used in the context of promax rotation algorithm:

The promax function is:

promax <- function(x, m = 4)
{
    if(ncol(x) < 2) return(x)
    dn <- dimnames(x)
    xx <- varimax(x)
    x <- xx$loadings
    Q <- x * abs(x)^(m-1)
    U <- lm.fit(x, Q)$coefficients
    d <- diag(solve(t(U) %*% U))
    U <- U %*% diag(sqrt(d))
    dimnames(U) <- NULL
    z <- x %*% U
    U <- xx$rotmat %*% U
    dimnames(z) <- dn
    class(z) <- "loadings"
    list(loadings = z, rotmat = U, crap = x, coeff = Q)
}

And the line I'm having trouble with is:

U <- lm.fit(x, Q)$coefficients

I'm trying to rewrite this routine in Java and got stuck on the lm.fit part.

Thanks,
~Pavlo

Hi,

On Aug 17, 2009, at 5:09 PM, Pavlo Kononenko wrote:
> Hi, everyone,
>
> This is a little silly, but I cant figure out the algorithm behind
> lm.fit function used in the context of promax rotation algorithm:
>
> The promax function is:
>
> promax <- function(x, m = 4)
> {
>    if(ncol(x) < 2) return(x)
>    dn <- dimnames(x)
>    xx <- varimax(x)
>    x <- xx$loadings
>    Q <- x * abs(x)^(m-1)
>    U <- lm.fit(x, Q)$coefficients
>    d <- diag(solve(t(U) %*% U))
>    U <- U %*% diag(sqrt(d))
>    dimnames(U) <- NULL
>    z <- x %*% U
>    U <- xx$rotmat %*% U
>    dimnames(z) <- dn
>    class(z) <- "loadings"
>    list(loadings = z, rotmat = U, crap = x, coeff = Q)
> }
>
> And the line I'm having trouble with is:
>
> U <- lm.fit(x, Q)$coefficients
Isn't this doing a least squares regression using the predictor  
variables in x and the (I guess) real valued numbers in vector Q?

x is a matrix of n (observations) by p (predictors)

The $coefficients is just taking the vector of coefficients/weights  
over the predictors  -- this would be a vector of length p -- such that

x %*% t(t(U)) ~ Q

  * t(t(U)) is ugly, but I just want to say get U to be a column vector
  * ~ is used as "almost equals")

You'll need some numerical/scientific/matrix library in java, perhaps  
this could be a place to start:

http://commons.apache.org/math/userguide/stat.html#a1.5_Multiple_linear_regression

Hope that helps,
-steve

--
Steve Lianoglou
Graduate Student: Computational Systems Biology
   |  Memorial Sloan-Kettering Cancer Center
   |  Weill Medical College of Cornell University
Contact Info: http://cbio.mskcc.org/~lianos/contact