topic Re: How to calculate UCL from Mahalanobis Distance in Discussions

How to calculate UCL from Mahalanobis Distance

PhamBao — Fri, 09 Jun 2023 00:54:58 GMT

Hi all,
Currently, I am using JMP 12 version
Do you know how to calculate UCL distance from Mahalanobis Distance chart?

If you guy know how to get it, could you please show me the formula?

Sincerely

Re: How to calculate UCL from Mahalanobis Distance

jthi — Sat, 24 Sep 2022 08:45:25 GMT

Click the "?" from JMP toolbar and then click on Mahalanobis Distances, this will open Help page Outlier Analysis . From here you can find Mahalanobis Distance and find its documentation Mahalanobis Distance Measures and finally

Re: How to calculate UCL from Mahalanobis Distance

PhamBao — Mon, 26 Sep 2022 08:41:59 GMT

Hi Jthi,

got it -- I already find the document due to your instruction.

However, do you know whether we can get syntax / code to calculate UCL

Thanks

Re: How to calculate UCL from Mahalanobis Distance

Mark_Bailey — Mon, 26 Sep 2022 14:40:05 GMT

This example illustrates how to calculate UCL with JSL.

Names Default to Here( 1 );

alpha = 0.05;	// typical decision level for type I error risk
n = 1600;		// about the number in your plot
p = 5; 			// guess of the number of variables used to compute distance

ucl = Sqrt( (((n-1)^2)/n) * Beta Distribution( 1-alpha, p/2, (n-p-1)/2 ) );

Re: How to calculate UCL from Mahalanobis Distance

PhamBao — Thu, 29 Sep 2022 13:47:21 GMT

Hi,
Thank for your instruction
I try to follow your instruction but the result is not correct.
I will display the script below and image

Based on your instruction, does p =2 and n = 85

Multivariate(
	Y(:DELTAMINIZ, :CARRIER_X),
	Estimation Method("Row-wise"),
	Matrix Format("Square"),
	Scatterplot Matrix(Density Ellipses(1), Shaded Ellipses(0), Ellipse Color(3)),
	Jackknife Distances(1)
);

Re: How to calculate UCL from Mahalanobis Distance

Mark_Bailey — Thu, 29 Sep 2022 14:09:46 GMT

What is the UCL shown if you click the red triangle next to Multivariate and select Outlier Analysis > Mahalanobis Distance?

My apologies! I used the wrong function. I also added the calculation of the jack-knife UCL. Please use this modified script instead of the one that I posted earlier.

Names Default to Here( 1 );

alpha = 0.05;	// typical decision level for type I error risk
n = 31;		// about the number in your plot
p = 7; 			// guess of the number of variables used to compute distance

m ucl = Sqrt( (((n-1)^2)/n) * Beta Quantile( 1-alpha, p/2, (n-p-1)/2 ) );

j ucl = Sqrt( (((n-2)*(n^2))/((n-1)^3))*((m ucl^2)/(1-((n*(m ucl^2))/((n-1)^2)))) );

Show( m ucl, j ucl );

Re: How to calculate UCL from Mahalanobis Distance

PhamBao — Sun, 02 Oct 2022 03:31:40 GMT

It works like a gem. Appreciate !

Re: How to calculate UCL from Mahalanobis Distance

PhamBao — Sun, 02 Oct 2022 05:26:13 GMT

Hi Mark_Bailey,

I use Jackknife method to detect outlier, but I found 1 case that I really need your advice.
You can refer to the images below.
Based on the right chart, all the data points on 8th carrier_x should be outliers. However, when I use Jackknife method with default settings, this method only points out 1 outlier instead 4.

I believe that not enough data points leads to the result

Do you have any suggestion / method that I can catch outliers more efficiently?

Re: How to calculate UCL from Mahalanobis Distance

jthi — Sun, 02 Oct 2022 06:24:02 GMT

Maybe the four episode outliers blog post series can help you or at least give some ideas

Re: How to calculate UCL from Mahalanobis Distance

PhamBao — Mon, 03 Oct 2022 06:51:56 GMT

Appreciate Jthi for your recommendation

Re: How to calculate UCL from Mahalanobis Distance

Mark_Bailey — Mon, 03 Oct 2022 14:57:06 GMT

I believe you are misusing the outlier analysis. It applies to linear correlations. You have a non-linear relationship between two variables. I would not expect it to correctly identify outliers and non-outliers in such a case.

Re: How to calculate UCL from Mahalanobis Distance

PhamBao — Fri, 07 Oct 2022 14:24:59 GMT

Hi Mark

Appreciate for your input. You are correct. Both variables are non-linear. Which method can I use to detect outliers from non-linear variables.

Sincerely,