[R] lm.fit algo

[Pavlo Kononenko]

Thank you, Steve!

2009/8/18 Steve Lianoglou <mailinglist.honeypot at gmail.com>:
> 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
>
>