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Re: st: RE: Mean test in a Likert Scale

From   Richard Williams <>
Subject   Re: st: RE: Mean test in a Likert Scale
Date   Mon, 03 Sep 2012 15:44:30 -0500

At 11:00 AM 9/3/2012, Maarten Buis wrote:
On Mon, Sep 3, 2012 at 4:54 PM, Yuval Arbel wrote:
> Nick and Maarten, Note, that Kmenta's message is to prefer models with
> less restrictions.

As always, there is no such thing as a free lunch. Less restrictions
typically cost statistical power, and if the restriction works well
for a particular applications, not using it will be a waste. Moreover,
such statements are in practice used to prefer models with less known
restrictions over models with well known restrictions. For example, I
have seen it used to prefer an -oprobit- over an -ologit- because
-ologit- implies the proportional odds assumption and -oprobit-
implies an equivalent assumption with a less memorable name.

I had a fairly prominent econometrician make that argument to me once. My response was that both ologit and oprobit require what has been called the parallel lines or parallel regressions assumption to be met. It just so happens that, with ologit, if parallel lines holds then proportional odds will hold too. But it isn't like ologit has an additional hurdle to clear; it is just that if it clears the parallel lines hurdle, it simultaneously clears the proportional odds hurdle too.

> Moreover, are you suggesting we can deal in the same manner with
> quantitative values and ordinal variables? if our independent
> variables are  what subjects marked on a questionnaire on a scale
> between 1 to 5 is  the statistical treatment within a regression
> analysis framework should be identical to an independent variable
> measured in US dollars?

No, all I am saying is that I do not rule out that there exists an
application where treating a ordinal variable as having a linear
effect works well enough and that it is worth checking whether that is
the case, as you can safe a lot of power that way. Moreover, an amount
in dollars may not be as cardinal as one might hope; often respondents
round their answers considerably even if asked to provide exact

Maybe this has already been mentioned, but pages 421-422 of Long & Freese (2006) show how to test whether an ordinal independent variable can be treated as though it were interval. See

Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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