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I'm using the R package rqpd to perform quantile regression on panel data with penalized fixed effects and running into singularity issues. The issue can be "fixed" by simply decreasing the ztol parameter which determines when numerically small numbers should be considered to be zero. When I decrease the value from its default 1e-5 to 1e-10 everything checks out, but this feels a bit arbitrary. So my question is what sort of values for ztol are adequate? Is there a way to judge that say 1e-9 is still appropriate but 1e-10 is taking things a little to far?

I'm conscious that another possible cause of singularity in quantile regression is binned data, but my dependent variable is only binned across the entire panel, not for individual groups for which fixed effects are introduced (see chart). Judging from the source code of rqpd() it looks like the test for singularity is run across the whole panel, so I tried jittering the dependent variable anyway, but with ztol=1e-5 and reasonable jitter factors there was still singularity.

Any help/views would be much appreciated - thanks!

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patalt
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  • As an aside, inefficiency of quantile regression and lack of ability to model a variety of correlation patterns in longitudinal data may be cause for considering semiparametric models. See this. – Frank Harrell Mar 24 '22 at 11:57

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I have since reached out to Roger Koenker and received a prompt response. The answer is twofold where the first part reflects Koenker's response: 1) singularity of $X'X$ may be due to multicollinearity, in which case decreasing ztol may lead to convergence, but does not tackle the problem of linear dependencies in and of itself; 2) if 1) is not a reason for concern, then decreasing ztol should not be problematic though as per Koenker (2004) estimation will become more computationally expensive since the number of non-zero elements increases.

patalt
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