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

From   Yuval Arbel <>
Subject   Re: st: RE: Mean test in a Likert Scale
Date   Thu, 6 Sep 2012 11:55:56 +0300

Maarteen, I didn't quite follow the statement you made regarding free
lunch and restricted models. I thought the less restrictive the model
is the more powerful it is. It is well known, for example, that
estimation of unrestricted models always yield higher R-squares and
higher log-likelihood - so the LR statistics (or F-Statistics) for
testing the validity of a restriction imposed on a model have to be

On Mon, Sep 3, 2012 at 11:21 PM, Cameron McIntosh <> wrote:
> 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.
> Cam
>> Date: Mon, 3 Sep 2012 15:44:30 -0500
>> To:;
>> From:
>> 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
>> -------------------------------------------
>> Richard Williams, Notre Dame Dept of Sociology
>> OFFICE: (574)631-6668, (574)631-6463
>> HOME: (574)289-5227
>> EMAIL: Richard.A.Williams.5@ND.Edu
>> WWW:
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Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
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