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After reading about What is the best way to identify outliers in multivariate data? I noticed that some heuristics are hard to adapt to mult-variate analysis. I'm hoping there is a way to at least have a leverage vs residual plot. I have included an assortment of residual analysis plots to show what I mean.

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The first 3 in this series can be adapted for multi-variate regression, they only require fitted, residual series to generate the plots. However the 4th (bottom right) plot seems tricky to adapt to multi-variate regression related plots.

Is there a way to do it? Could I put all of my data into a k*n long series? From which point I would and then proceed to standardize (0 mean, 1 stdv) and then square it add one and divide by n?

Let me know if there that approach has any potential flaws or if there is a better (more logical/sensible) way to reproduce plot #4.

whuber
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Arash Howaida
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    Have you looked into using influence functions to detect multivariate outlier? I exhibited it when looking at the effect on $R^2$ and correlation in an AJMMS article in 1982. Gnanadesikan talks about it in his multivariate book and Barnett and Lewis discuss it in their book on outliers. – Michael R. Chernick Oct 17 '17 at 16:49
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    @MichaelChernick I suppose I would be open to influence in place of leverage, but eventually I would like to get to the bottom of whether or not leverage could ever be computed and graphed for the multi-variat case. Also, if you have the time to include a graph of the influence function that would be helpful. I could then see how it looked among the other diagnostic plots in my original post. – Arash Howaida Oct 18 '17 at 06:15
  • The influence function contours would depend on the parameter you want to consider (possibly $R^2$ in your case). But it could be some other parameter if you choose. – Michael R. Chernick Oct 18 '17 at 06:19
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    I have been continuously reading into the matter and have only come up with a few handful of tidbits. From google searching I came across a tantalizing explanation: "For several x's, h has a matrix expression". Unfortunately there was no worked out example, so I couldn't get to the bottom of it. I will revise the post title to narrow and clarify things. – Arash Howaida Oct 20 '17 at 17:12

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