# Re: [R] Cronbach's alpha

From: A. Beaujean <abeaujean_at_gmail.com>
Date: Wed 24 Jan 2007 - 22:41:29 GMT

Even if the grouping of variables has been fixed by "domain knowledge", it does not mean there is unidimensionality in your items (at least for the sample of folks you have). For example, math reasoning and math fluency could both be "conceptually "put into a single math test, but, assuming a random sample of folks and enough items, it would really be measuring two different areas (which then could attenuate the overall alpha).

You are right that alpha is similar to latent variable modeling. Here is a reference you might find useful.

Miller, M. B. (1995). Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling, 2(3), 255-273

I am not sure if the R IRT package can do item-level factor analysis, but the TESTFACT program does (it is the one I have had to use in the past). Also, the R "psych" package can compute McDonald's omega estimates the general factor saturation of a test.

Best,

Alex

On 1/24/07, Weiwei Shi <helprhelp@gmail.com> wrote:
>
> Hi, there:
>
> I read that article (thanks Chucks, etc to point that out). Now I
> understand how those negatives are generated since my research subject
> "should" have negative convariance but they "are" measuring the same
> proper to go ahead to use this measurement.
>
> To clear my point , I describe my idea here a little bit. My idea is
> to look for a way to assign a "statistic" or measurement to a set of
> variables to see if they "act" cohesively or coherently for an event.
> Instead of using simple correlation, which describes var/var
> correlation; I wanted to get a "total correlation" so that I can
> compare between setS of variables. Initially I "made" that word but
> google helps me find that statistic exists! So I read into it and post
> my original post on "total correlation". (Ben, you can find total
> correlation from wiki).
>
> I was suggested to use this alpha since it measures a "one latent
> construct", in which matches my idea about one event. I have a feeling
> it is like factor analysis; however, the grouping of variables has
> been fixed by domain knowledge.
>
> Sorry if it is off-list topic but I feel it is very interesting to go
>
> Thanks,
>
> Weiwei
>
>
>
> On 1/24/07, Doran, Harold <HDoran@air.org> wrote:
> > Hi Dave
> >
> > We had a bit of an off list discussion on this. You're correct, it can
> > be negative IF the covariance among individual items is negative AND if
> > that covariance term is larger than the sum of the individual item
> > variances. Both of these conditions would be needed to make alpha go
> > negative.
> >
> > Psychometrically speaking, this introduces some question as to whether
> > the items are measuring the same latent trait. That is, if there is a
> > negative covariance among items, but those items are thought to measure
> > a common trait, then (I'm scratching my head) I think we have a
> > dimensionality issue.
> >
> >
> >
> > > -----Original Message-----
> > > From: r-help-bounces@stat.math.ethz.ch
> > > [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Dave Atkins
> > > Sent: Wednesday, January 24, 2007 4:08 PM
> > > To: R-help@stat.math.ethz.ch
> > > Subject: Re: [R] Cronbach's alpha
> > >
> > >
> > > Harold & Weiwei--
> > >
> > > Actually, alpha *can* go negative, which means that items are
> > > reliably different as opposed to reliably similar. This
> > > happens when the sum of the covariances among items is
> > > negative. See the ATS site below for a more thorough explanation:
> > >
> > > http://www.ats.ucla.edu/STAT/SPSS/library/negalpha.htm
> > >
> > > Hope that helps.
> > >
> > > cheers, Dave
> > > --
> > > Dave Atkins, PhD
> > > Assistant Professor in Clinical Psychology Fuller Graduate
> > > School of Psychology
> > > Email: datkins@fuller.edu
> > > Phone: 626.584.5554
> > >
> > >
> > > Weiwei
> > >
> > > Something is wrong. Coefficient alpha is bounded between 0 and 1, so
> > > negative values are outside the parameter space for a reliability
> > > statistic. Recall that reliability is the ratio of "true
> > > score" variance
> > > to "total score variance". That is
> > >
> > > var(t)/ var(t) + var(e)
> > >
> > > If all variance is true score variance, then var(e)=0 and the
> > > reliability is var(t)/var(t)=1. On the other hand, if all variance is
> > > measurement error, then var(t) = 0 and reliability is 0.
> > >
> > > Here is a function I wrote to compute alpha along with an
> > > example. Maybe
> > > try recomputing your statistic using this function and see if you get
> > > the same result.
> > >
> > > alpha <- function(columns){
> > > k <- ncol(columns)
> > > colVars <- apply(columns, 2, var)
> > > total <- var(apply(columns, 1, sum))
> > > a <- (total - sum(colVars)) / total * (k/(k-1))
> > > a
> > > }
> > >
> > > data(LSAT, package='ltm')
> > > > alpha(LSAT)
> > > [1] 0.2949972
> > >
> > >
> > > Harold
> > >
> > > > -----Original Message-----
> > > > From: r-help-bounces at stat.math.ethz.ch
> > > > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of
> > > Weiwei Shi
> > > > Sent: Wednesday, January 24, 2007 1:17 PM
> > > > To: R R
> > > > Subject: [R] Cronbach's alpha
> > > >
> > > > Dear Listers:
> > > >
> > > > I used cronbach{psy} to evaluate the internal consistency and
> > > > some set of variables gave me alpha=-1.1003, while other,
> > > > alpha=-0.2; alpha=0.89; and so on. I am interested in knowing
> > > > how to interpret 1. negative value 2. negative value less than -1.
> > > >
> > > > I also want to re-mention my previous question about how to
> > > > evaluate the consistency of a set of variables and about the
> > > > total correlation (my 2 cent to answer the question). Is
> > > > there any function in R to do that?
> > > >
> > > > Thank you very much!
> > > >
> > > >
> > > >
> > > > --
> > > > Weiwei Shi, Ph.D
> > > > Research Scientist
> > > > GeneGO, Inc.
> > > >
> > > > "Did you always know?"
> > > > "No, I did not. But I believed..."
> > > > ---Matrix III
> > > >
> > > > ______________________________________________
> > > > R-help at stat.math.ethz.ch mailing list
> > > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > > http://www.R-project.org/posting-guide.html
> > > > and provide commented, minimal, self-contained, reproducible code.
> > > >
> > > --
> > > Dave Atkins, PhD
> > > Assistant Professor in Clinical Psychology
> > > Fuller Graduate School of Psychology
> > > Email: datkins@fuller.edu
> > > Phone: 626.584.5554
> > >
> > > ______________________________________________
> > > R-help@stat.math.ethz.ch mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > http://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible code.
> > >
> >
> > ______________________________________________
> > R-help@stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
>
> --
> Weiwei Shi, Ph.D
> Research Scientist
> GeneGO, Inc.
>
> "Did you always know?"
> "No, I did not. But I believed..."
> ---Matrix III
>
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

```--
***************
A. Alexander Beaujean, Ph.D.
http://myprofile.cos.com/abeaujean
http://www.baylor.edu/soe/faculty/index.php?id=38476

"General impressions are never to be trusted. Unfortunately when they are of
long standing they become fixed rules of life, and assume a prescriptive
right not to be questioned. Consequently those who are not accustomed to
original inquiry entertain a hatred and a horror of statistics. They cannot
endure the idea of submitting their sacred  impressions to cold-blooded
verification. But it is the triumph of scientific men to rise superior to
such superstitions, to devise tests by which the value of beliefs may be
ascertained, and to feel sufficiently masters of themselves to discard
contemptuously whatever may be found untrue." --Sir Francis Galton, FRS

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