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Low rank fixed effect design matrix LMER package

2 messages · suraj keshri, Ben Bolker

Original
suraj keshri
# 
Hi,

I'm trying to implement some pieces of LMER algorithm in Python. I'm facing
low rank fixed effect design matrix issue. One way to take care of low rank
is to detect linearly dependent columns using ideas from SVD/QR
decomposition and remove it. My design matrix is very big and sparse.
Therefore, instead of doing SVD of the design matrix (X), I do SVD of X^T *
X. However, one has to decide a threshold for the singular values. When I
look at the singular values of X^T*X, the range is very large (1e+12 to
1e-4). In this situation, how does one decide the threshold so that X^T*X
is invertible (after removing linearly dependent columns)? How does LMER
package solve this problem?

Thank you so much for any help!!


Suraj
Ben Bolker
# 
The place to start looking is line 222 of 
https://github.com/lme4/lme4/blob/master/R/modular.R . We call the 
Matrix::rankMatrix() and stats::qr() functions with a default tolerance 
of 1e-7.  The comment in the code at that point specifies

## Perform the qr-decomposition of X using LINPACK method,
## as we need the "good" pivots (and the same as lm()):
## FIXME: strongly prefer rankMatrix(X, method= "qr.R")

   Hope that helps.

   Ben Bolker
On 16-02-10 08:39 PM, suraj keshri wrote: