Interpretation of Hodges-Lehmann's estimate of tau

[blindfreak]

Dear fellow users,

I ran a rank regression with MiniTab and wonder how to interpret the following output:

Rank Regression: Ideal Employ versus ENVTL. IMPAC; ENVTL. MGMT.; ...

The regression equation is
Ideal Employer Rank = 62,3 - 0,434 ENVTL. IMPACT - 0,251 ENVTL. MGMT. +
0,121 DISCLOSURE - 0,000052 Revenue $ mio - 0,000460 Profit $ mio


Coefficient Coefficient
Predictor Rank Least-sq Rank Least-sq
Constant 62,35 60,53 12,82 11,48
ENVTL. IMPACT -0,4337 -0,4139 0,1233 0,1104
ENVTL. MGMT. -0,2509 -0,2359 0,1681 0,1505
DISCLOSURE 0,12094 0,11792 0,07291 0,06529
Revenue $ mio -0,00005237 -0,00005447 0,00002430 0,00002176
Profit $ mio -0,0004601 -0,0004552 0,0002741 0,0002455

Hodges-Lehmann estimate of tau = 8,808 Least-squares S = %2


Unusual observations

Ideal
ENVTL. Employer
Observation IMPACT Rank Pseudo Fit SE Fit Residual
27 24,2 25,00 27,51 14,31 7,44 10,69 X

X denotes an observation whose X value gives it large leverage.

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The H0 hypothesis is that corporate environmental performance does not determine perceived company attractiveness, i.e. I want to show that objective environmental performance values (my independent continuous variables) do have an influence on corporate attractiveness ratings (my dependent variable).

So far, I learned that I have to look at the Hodges-Lehmann estimate of tau in order to reject my H0 (the lower the value, the better). Unfortunately, I don't know which value of tau allows me to reject the H0. Is there something like a general rule, e.g. when the Hodges-Lehmann estimate is lower than 5 then the H0 can be rejected?

Many thanks!
Linus

 

[Stijloor]

A Quick Bump!

Can someone help Linus?

Thank you very much!!

 

[Miner]

I asked Minitab tech support for an explanation yesterday. I should receive a response later today.

 

[Miner]

Per Minitab, the Hodges-Lehmann estimate of Tau is a confidence interval for the y-intercept (the constant term in the model). It is the equivalent of s in the Least Squares Regression.

There is no equivalent to R^2, but you can store the residuals (using RESIDUALS C subcommand), and evaluate the residuals for normality, fit and order. If the residuals are assymetrical, you can use the WINDOW [K] subcommand to use the density function in lieu of the Hodges-Lehmann estimate.

This method is discussed in chapter 3 of Robust Nonparametric Statistical Methods by Thomas P. Hettmansperger and Joseph W. McKean.

 

[Miner]

Since you can store the residuals you could calculate R^2 manually. See Coefficient of determination and the formulae in the Definitions section.