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

[Cameron McIntosh <cnm100@hotmail.com>]

This paper might also be of interest:

Wu, C.-H. (2007). An empirical study on the transformation of likert-scale data to numerical scores. Applied Mathematical Sciences, 1(58), 2851-2862.
http://www.m-hikari.com/ams/ams-password-2007/ams-password57-60-2007/wuchienhoAMS57-60-2007.pdf

Cam

> Date: Mon, 3 Sep 2012 15:44:30 -0500
> To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu
> From: richardwilliams.ndu@gmail.com
> Subject: Re: st: RE: Mean test in a Likert Scale
> 
> 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
> 
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
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