Low rank fixed effect design matrix LMER package
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:
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 [[alternative HTML version deleted]]
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