Finding Correlations in Data with Uncertainty: Classical Solution

August 13, 2013

(This article was first published on Exegetic Analytics » R, and kindly contributed to R-bloggers)

Following up on my previous post as a result of an excellent suggestion from Andrej Spiess. The data are indeed very heteroscedastic! Andrej suggested that an alternative way to attack this problem would be to use weighted correlation with weights being the inverse of the measurement variance.

Let’s look at the synthetic data first.

> library(weights)
> wtd.cor(synthetic$mu.x, synthetic$mu.y, weight = 1 / synthetic$sigma.y**2)
      correlation    std.err  t.value    p.value
V1.V1   0.1945633 0.09908485 1.963603 0.05240988

This is in excellent agreement with the bootstrap results. Now the original experimental data.

> wtd.cor(original$mu.x, original$mu.y, weight = 1 / original$sigma.y**2)
      correlation    std.err  t.value      p.value
V1.V1   0.2407686 0.04606181 5.227076 2.656016e-07

Here the agreement with the bootstrap result is not as good. I’m not quite sure why, but suspect that it might have something to do with the fact that the original data are quite severely skewed so that assumptions about normality would probably be voilated.

To leave a comment for the author, please follow the link and comment on their blog: Exegetic Analytics » R. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)