The number of degrees of freedom (0) is not positive. Factor analysis may not be appropriate.

[Art Kendall]

What do other list members think of the idea of factoring items for each anticipated construct separately?

In my experience, beginners often start with items they hope will cohere into separate scales. Exploratory FA can help to see whether the items "bunch together" as anticipated.  In my experience, in these situations there are often items that split across factors. Sometimes the differences between the  "obtained scoring key" and the "hoped scoring key" are very informative.

The OP never posted neither the meanings of the attitudes that were intended nor the items that were intended to measure those attitudes.

Also we do not yet know whether this is the first effort to measure these attitudes or whether the OP is just checking whether the scoring key from previous research is reasonable with the current set of respondents.

In addition we do not know where the FA fits into the overall research effort.


We also do not yet know the total number of items, the number of scales, how the items came about, the listwise number of cases, etc.

In any case the Kaiser criterion is only for machine efficiency, based on the idea that one would not be interested in a factor that accounted only as much variance as an average item.
 
YMMV, but after parallel analysis came about, I went back to FAs from earlier decades in which I had used the consensus of several stopping rules (other than KAISER). For my work the number of factors was close to that where the the obtained eigenvalue was one more than the 95th percentile for that eigenvalue from parallel analysis. (For each factor subtract the parallel analysis eigenvalue from the obtained eigenvalue.

Even without the above information, the OP should consider the practicalities of obtaining more cases so that there are many more cases than the total scale items in the instrument

[Rich Ulrich]

Art,

Did you miss the early messages? There are 3 variables (11-point items) and N=220.

Two items correlate at 0.71, which is probably close to the maximum possible, given

single-item reliabilities for "attitudes".  

I've never seen d.f. come up in my factor analyses, but I've never factored 3 items.

Also, I've never used the ML method, and I wonder if the problem goes away without it.

I wonder if the analysis did proceed up to the Rotation before the error message?

I can say, however, with "min-eigen" of 1, there will be only two factors at most, so there is

not much to rotate.  With a positive manifold (all r's positive), the first raw component

will be the sum of all items; the second will be the bi-polar contrast of the two vars with

highest r  versus the other variable.

--

Rich Ulrich

---

From: SPSSX(r) Discussion <[hidden email]> on behalf of Art Kendall <[hidden email]>
Sent: Friday, May 19, 2017 8:27:59 AM
To: [hidden email]
Subject: Re: The number of degrees of freedom (0) is not positive. Factor analysis may not be appropriate.

 

What do other list members think of the idea of factoring items for each
anticipated construct separately?

In my experience, beginners often start with items they hope will cohere
into separate scales. Exploratory FA can help to see whether the items
"bunch together" as anticipated.  In my experience, in these situations
there are often items that split across factors. Sometimes the differences
between the  "obtained scoring key" and the "hoped scoring key" are very
informative.

The OP never posted neither the meanings of the attitudes that were intended
nor the items that were intended to measure those attitudes.

Also we do not yet know whether this is the first effort to measure these
attitudes or whether the OP is just checking whether the scoring key from
previous research is reasonable with the current set of respondents.

In addition we do not know where the FA fits into the overall research
effort.


We also do not yet know the total number of items, the number of scales, how
the items came about, the listwise number of cases, etc.

In any case the Kaiser criterion is only for machine efficiency, based on
the idea that one would not be interested in a factor that accounted only as
much variance as an average item.
 
YMMV, but after parallel analysis came about, I went back to FAs from
earlier decades in which I had used the consensus of several stopping rules
(other than KAISER). For my work the number of factors was close to that
where the the obtained eigenvalue was one more than the 95th percentile for
that eigenvalue from parallel analysis. (For each factor subtract the
parallel analysis eigenvalue from the obtained eigenvalue.

Even without the above information, the OP should consider the
practicalities of obtaining more cases so that there are many more cases
than the total scale items in the instrument




-----
Art Kendall
Social Research Consultants
--
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[Art Kendall]

I did notice that there are only three variables.

I was trying to suggest that not including all of the items from all of the constructs, in my mind, a questionable approach.

I also have never factored 3 items.  

Did you see my previous post? I asked if other list members found this an unusual thing to do.  Perhaps I should have used stronger language.

The .71 and .72 correlations make me ask a lot of questions, as I did in my previous post.

I really would like to see the wording of those items.

[Mike]

Okay, just a minor point.  In structural equation modeling, it is
traditional to think of the enterprise as consisting of two parts:

(1) The measurement model:  under the assumption that one
is analyzing relationships among latent variables (factors)
instead of empirical variables, one has to specify how the
empirical variable relate to the latent variable(s).  Confirmatory
factor analsis (CFA) is one way to establish how the empirical
variables relate/load on the latent variables.  More on this
shortly.

(2) The structural model: this specifies the set of relationships
among the latent variables.  This is sort of like multiple regression
except OLS multiple regression (and other types) don't allow
for errors in the predictors (though one could pre-process them
to eliminate the errors).

Back to the measurement model, latent variables may have few
empirical indicators with the classic case being three empirical
variables to one latent variable/factor.  With CFA, one can impose
constraints on loadings, variances, and covariances which frees
up degrees of freedom and make the df > 0 -- exploratory factor
analysis provide df= 0 ("just identified") which makes it an inferior
method of analysis.

For support on this point, see the following:

Reilly, T. (1995). A necessary and sufficient condition for
identification of confirmatory factor analysis models of
factor complexity one. Sociological Methods & Research, 23(4),
421-441.
http://dx.doi.org/10.1177/0049124195023004002

The abstract follows:

 After specification of a structural equation model and
before estimation of parameters, the identification status
of the model must be determined. For the measurement portion
of the model, however, there are very few rules to help the
researcher verify whether the model is identified or not.
This article introduces a necessary and sufficient identification
rule for models of factor complexity one. The rule is easy
to understand, is easy to apply, and applies to portions as
well as to the whole model. Moreover, it provides a diagnostic
tool that helps with identification questions. Many examples are given.

See Figure 1 on page 429 for the model relevant to the present
discussion.

And remember, YMMV.

-Mike Palij
New York University
[hidden email]


----- Original Message ----
On Friday, May 19, 2017 4:30 PM, Art Kendall wrote:

>I did notice that there are only three variables.
>
> I was trying to suggest that not including all of the items from all
> of the
> constructs, in my mind, a questionable approach.
>
> I also have never factored 3 items.
>
> Did you see my previous post? I asked if other list members found this
> an
> unusual thing to do.  Perhaps I should have used stronger language.
>
> The .71 and .72 correlations make me ask a lot of questions, as I did
> in my
> previous post.
>
> I really would like to see the wording of those items.

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[Art Kendall]

It is conceivable that there are constructs/latents that can be measured with only 3 empirical /items.

I would usually recommend writing more than three candidate items to measure an attitudinal construct. It could turn out that only three actually work out as hoped.

Attitudes, are a little more "squishy".  I still would like to see more detail about the actual situation.

"Attitudes" is often used with varying degrees of rigor in definition.

[Mike]

Whether or not an "attitude" can be represent by 3 or N >>> 3
empirical variables depends upon one's theory of that "attitude",
indeed, if one actually believed that a construct called "attitude"
actually exists.  Remember that the major contribution of social
psychologists in the 1960s was the "power of the situation" as
represented by the Stanley Milgram's "obedience to authority"
studies, Phil Zimbardo's "Stanford Prison Experiment" (SPE),
Latane and Darley's "bystander apathy" research, and other
research that showed that situational variables exerted greater
influence over behavior than measures of attitude or personality
(see Zimbardo's account of the SPE, specifically, the attitude and
personality measures taken before subjects were randomly assigned
to "guard" or "prisoner" roles).  I think present day social
psychologists
may rely more upon "priming" effects than traditional measures
of attitude, as represented by the "implicit association" test,
for example, see:
http://psycnet.apa.org/index.cfm?fa=buy.optionToBuy&uid=2009-08950-006

But I can understand the old school orientation that an attitude
needs many empirical indicators, such as Bob Altemeyer's
"Right Wing Authoritarianism" (RWA) scale which can be used
as measure of one's tendency to submit to authority (roots of
the RWA scale go back to Adorno et al's "Authoritarian Personality",
Milgram's work, and other sources). The RWA has 32 items of
which only 30 are analyzed, 15 are "pro-trait" (measured on
a 9 point rating scale, where increasing numbers reflect higher
degrees of RWA) and 15 "con-trait" items (measured on a
9 point scale where lower numbers reflect higher degrees of
RWA; this is done to control for response bias -- contrait items
have to have their value "reflected" to make their numbers
consistent with protrait items).  Then again, there may be benefits to
a shorter instrument; see:
http://www.sciencedirect.com/science/article/pii/S0191886905001170

Again, YMMV.

-Mike Palij
New York University
[hidden email]



----- Original Message -----
On Friday, May 19, 2017 6:00 PM, Art Kendall wrote:

> It is conceivable that there are constructs/latents that can be
> measured with
> only 3 empirical /items.
>
> I would usually recommend writing more than three candidate items to
> measure
> an attitudinal construct. It could turn out that only three actually
> work
> out as hoped.
>
> Attitudes, are a little more "squishy".  I still would like to see
> more
> detail about the actual situation.
>
> "Attitudes" is often used with varying degrees of rigor in definition.

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[Art Kendall]

I remain agnostic about the appropriateness of factoring only items of one construct and have only 3 items for an "attitude".  I would need to hear more detail.
----

Across the sciences there is a trade off between model complexity and simplicity. Constructs should not be multiplied beyond necessity. Avoiding undue complexity is an important part of the scientific thinking.

In the early 70's in many parts of social psychology, the person environment interaction idea became more explicit.  This was sometimes called the Aptitude-Treatment Interaction approach.  Earlier work looked at characteristics of a person in explaining behavior.(nature?) Then situations/contexts/environments were found to have influences. (Nurture?)  The newer approach implicitly said that good explanations had to consider 3 sets of constructs on the predictor side. P things about the person. E things about the environment. And P*E things about the person in the environment.  

There have been significant advances by moving to more complex explanations. Some examples follow.
Traditional thinking had masculity and femininity as opposite ends of a construct. Studies using bipolar meaures gave muddy and/or contradictory results. In the 70s, Bem used exploratory FA to find that a two factor solution fit the data on self described possession of sterotypical traits. People placed them selve along 2 axes. One could be (high,high), (low, low) (low, high) (high,low)etc.

Also in the early 70s, Lorr found that inconsistent results about liberalism-conservatism were likely due to using a single measure.  It turned out that there were 3 factors underlying a large set of candidate L-C items. General L-C (bipolar), equalitarianism (unipolar), and sexual freedom (unipolar).

In other domains, poverty has been found to be a better explainer when a set of measures are used. A curvilinear model gives a better fit between performance and anxiety than a linear one.

Using items in FA from possibly related constructs, or having a large candidate item pool has sometimes proven useful in advancing understanding.


The word “attitudes” is often used loosely. It might be perceptions, cognitve styles, preferences, etc. etc. This is why I asked what the items were and what constructs were being used/distinguished.


_____
The construction of measures can take place in different phases of a research program.  A small (pilot?) study might be only to try to establish a measure of a construct.  


P.S. I don’t know what areas of social psych you are interested in, but you or your students might want to know to know about the Society for Terrorism Research meeting at NYU.
I’ll be there. I don’t know about Phil Zimbardo, but we are both on the Advisory Board.
http://www.societyforterrorismresearch.org/str-11th-annual-international-conference