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Nov 24, 2018 6:47 AM
(2380 views)

Hello, I was analyzing this simple DOE:

A B Y

33 180 3317

33 180 3653

17 230 6133

17 230 6436

25 205 5939

33 230 12431

17 180 1710

17 180 1806

25 205 5578

33 230 13680

with Standard Least Square and with GenReg.

I noticed that while the estimates are exactly the same, GenReg yields smaller stderr (in italics).

**Standard Least Square:**

Intercept -29469.6125 *1390.0621826 *-21.20 <.0001

A 265.5625 *19.698753398 *13.48 <.0001

B 140.97 *6.3036010872 *22.36 <.0001

(A-25)*(B-205) 6.305 *0.787950*1359 8.00 0.0002

**GenReg (normal, forward selection, min AICc)**

Term Estimate Std Error Wald ChiSquare Prob > ChiSquare Lower 95% Upper 95%

Intercept -29469.6125 *1210.3742588 *592.80177141 <.0001 -31841.90246 -27097.32254

A 265.5625 *15.108244044 *308.96231754 <.0001 235.9508858 295.1741142

B 140.97 *4.834638094 *850.20853436 <.0001 131.49428346 150.44571654

(A-25)*(B-205) 6.305 *0.6043297618 *108.84844181 <.0001 5.1205354322 7.4894645678

Can anyone explain why this is so?

thanks a lot in advance.

Matteo

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I don't see a difference in AICc or BIC between the two platforms, but I definitely see the difference in the standard errors.

In the GenReg platform, if you switch the estimation to Standard Least Squares you will get exactly the same standard errors. You start seeing the differences when that is changed to Stepwise, even though the model is the same.

The answer is due to a different method being used to estimate the standard errors. From the JMP help, Gen Reg is doing this:

Standard Least Squares has a more direct calculation of the standard error.

Dan Obermiller

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Re: stderr in least square vs generalized regression

Hi Matteo, I have the same question. Curious as to why RMSE and AICc / BIC differ between the platforms but parameter estimates are the same!

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I don't see a difference in AICc or BIC between the two platforms, but I definitely see the difference in the standard errors.

In the GenReg platform, if you switch the estimation to Standard Least Squares you will get exactly the same standard errors. You start seeing the differences when that is changed to Stepwise, even though the model is the same.

The answer is due to a different method being used to estimate the standard errors. From the JMP help, Gen Reg is doing this:

Standard Least Squares has a more direct calculation of the standard error.

Dan Obermiller

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