Comments on: Deming Regression

By: Jon Peltier

Jon Peltier — Wed, 02 Dec 2009 16:01:00 +0000

Hi Bill -

The confidence interval information isn’t buried in the calculations. I didn’t implement the algorithms for these quantities.

By: Bill Harris

Bill Harris — Wed, 02 Dec 2009 15:35:43 +0000

Jon, very helpful for slope intercept and correlation, but I need the 95% CIs for the slope and intercept to know if the slope is sig diff from 1.0 and if the intercept is sig diff from 0. Is that information buried somewhere in here? Thx

By: Jan Karel Pieterse

Jan Karel Pieterse — Thu, 08 Oct 2009 04:24:58 +0000

Jon: Yes, that is an important distinction. Good post by the way.

By: Jon Peltier

Jon Peltier — Wed, 07 Oct 2009 10:43:51 +0000

JK -

The DOE suggestion is a good one for two machines used in production. In another scenario, consider that the two machines are used for measurement of some property. This regression is useful for comparing the measurements of the two machines.

By: Jan Karel Pieterse

Jan Karel Pieterse — Wed, 07 Oct 2009 07:50:43 +0000

If I understand this problem correctly, what we’re trying to determine here is the effect of using two machines on product characteristics.
Unlike continuous process variables which you can control by e.g. turning a dial or entering a setpoint, the effect of machine is a qualitative variable.
The statistics needed to determine the effect of a machine differ from those to determine the effect of a “normal” process variable.
By using a Design of Experiments (DoE) software package, you can set up an experiment scheme which lets you determine the machine effects and (more importantly) the interactions between various process settings and the machine effects.

So if your goal is to determine machine effects, consider buying DoE (Design of Experiments) software and (even more important) taking a DoE course. Let me take this further:

I’d strongly advice ANY (yes, ANY) researcher, process engineer, …, anyone doing tests, to take a DoE course.

By: DaleW

DaleW — Wed, 07 Oct 2009 02:46:33 +0000

Jon – It’s a nice utility. And it would be really cool if it could be generalized to do X v. Y orthogonal regression in the absence of that special replicated pair structure you require for Deming regression now.

From additional reading, the key to this problem seems to be having a decent estimate of the ratio of random error in Y to random error in X. While not elegant, one option is to simply ask the user for his best estimate of the variance ratio of these errors, with a default of 1 (which can sometimes be appropriate when X and Y are the same units — that’s what the other Excel VBA code I mentioned assumes but doesn’t document).

A variance ratio of 0 is the same as reverse OLS regression; a variance ratio approaching infinity is the same as Ordinary Least Squares regression. Those are easy with Excel. Orthogonal regression is for the intermediate cases where both X and Y have residual error. It would be good to add X-Y orthogonal regression to your growing list of solutions that are readily available without leaving Excel . . . ?

By: Jon Peltier

Jon Peltier — Tue, 06 Oct 2009 01:48:12 +0000

Jeff – I guess the test would be to use machine A as X and machine B as Y and do the analysis, then reverse the machines and repeat it. I actually looked at it as two variables which were dependent on independent variables which are not shown in the analysis (such as inputs into the machines, raw materials, operating conditions).

Dale – Tune in tomorrow. I’ve built a little tool to carry out the analysis more easily.

By: DaleW

DaleW — Tue, 06 Oct 2009 00:40:38 +0000

Hi, Jon. When I used this somewhat more robust linear regression technique it was going by the name of orthogonal regression, which I now see is a superset of two variable linear Deming regression. Your example is a special case where X and Y might be expected to have similar values in the same units, but of course Deming regression can be handy whenever BOTH X and Y are known to have significant measurement error, and we want to estimate the underlying linear relationship.

Anyway, I’d downloaded and modified and stashed away a workbook from 2005 by sj00 that performed this using VBA, but it would trust the coding and documentation of the PTS version much more. Thanks for bringing more numerical methods to Excel!

By: jeff weir

jeff weir — Mon, 05 Oct 2009 22:14:46 +0000

Hi Jon. I was initially uncertain how regression analysis would be relevant in your example above of the regression of one machine output on another…I didn’t think there was a dependent variable i.e. how would the output of one machine (your Y value) be dependent on the output of another (your X value) given that these machines are independent from one another.

However, after a bit of internet reading, I see that Deming Regression is often used to evaluate a manufacturer’s claims regarding a product, or to judge acceptability of say different clinical chemistry methods.

You learn something every post, as the saying goes…

By: Jan Karel Pieterse

Jan Karel Pieterse — Mon, 05 Oct 2009 10:15:30 +0000

Nice post Jon.

As a (former) process engineer I can relate to subjects like this one.
Of course if you’d want to do this research properly (no pun intended), you’d set up an experiment using Design of Experiments, factoring in the machine as a qualitative variable in the design.