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Multivariate Ordinal Logistic Fit: are p values returned by Effect Likelihood Tests Type 3 errors?

Hi JMP Community,

 

I ran a simple ordinal logistic fit analysis with one nominal variable (treatment), and two continuous variables (FACTOR A and FACTOR (see below).

A colleague asked me if the p values returned by the Effect Likelihood Ratio Tests are Type 3 errors instead of Type 1 errors. Based on my limited understanding of Type 3 error, I'm not sure that it is correct. Could you shed some light on this topic?

 

Effect Likelihood Ratio Tests

Source	Nparm	DF	L-R ChiSquare	Prob>ChiSq
treatment	2	2	45.6793484	<.0001*
FACTOR A	1	1	0.03728633	0.8469
FACTOR B	1	1	2.06649958	0.1506

 

Treatment:

• Control + MTX
• Drug X + MTX
• Drug X alone

FACTOR A: continuous baseline biomarker A

FACTOR B: continuous baseline biomarker B

Response: ordinal (0 – 1)

Thank you,

Thierry

Re: Multivariate Ordinal Logistic Fit: are p values returned by Effect Likelihood Tests Type 3 error

I am guessing that your colleague is talking about Type I versus Type III Sums of Squares. Type I Sum of Squares means that the tests are sequential, meaning that the order of your model makes a difference on the significance. Type III Sum of Squares means that all of the sums of squares are calculated so that the order is not important. 

 

Your analysis is not using Sum of Squares, so there is no Type I or Type III to worry about. To prove this, you could refit your model changing the order of the terms to show that the p-values remain the same regardless of the ordering of the terms.

Re: Multivariate Ordinal Logistic Fit: are p values returned by Effect Likelihood Tests Type 3 error

As far as I am aware, Type III errors are not a statistical term - that is, there is no hypothesis test that sheds any light on this type of error.  It is an error of finding an effect, but it is due to a different cause than the hypothesized cause represented by that variable.  Thus, it is heavily dependent on context and subject matter knowledge - which I don't have for the case you are describing.  I think your colleague is really suggesting that the significant p-values you have found are really capturing the effect of some other variables than the one you have in the model.