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

[Richard Williams <richardwilliams.ndu@gmail.com>]

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
> answers.

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

http://www.stata.com/bookstore/regression-models-categorical-dependent-variables/index.html

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Richard Williams, Notre Dame Dept of Sociology
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