John,
A few points:
(1) One way to think about factor analysis is that it is a
technique to explain the mathematical basis for correlations,
specifically, being able to reduce a correlation matrix to a
smaller matrix where the rows and columns are independent
(though one may be satisfied with a smaller factor matrix with
correlated factors). With the development of confirmatory factor
analysis, we can test whether a single factor or multifactor
model best accounts for a correlation matrix. Structural
equation modeling (SEM) allows for much more complex
factor models. That being said, there are a number of problems
in getting adequate fit of models to data as well as problems
of interpretation. The key point is that this is all in terms of
mathematics and does not necessarily have any psychological
relevance.
(2) The original conception of "g" depended upon getting
a large first eigenvalue or factor from an unrotated factor
matrix. The model of the data can be said to be
X = common variance + error variance
where common variance is "g" when talking about measues
of mental abilities. However, an unrotated factor matrix can
be difficult to interpret because, well, it may not represent the
structure in the data. That is, instead of a single factor, several
factors may be required. Rotation of the factors while maintaining
orthogonal relations among them (i.e., uncorrelated factors)
often reveals several factors. Varimax rotation attempts to
maximize the loading of a variable on one factor while minimizing
the loadings on other factors. This, of course, undermines
the whole "general intelligence" position. This was promoted
by Thurstone with his primary mental abilities approach and
others (e.g., Guilford; Gardner and his "multiple intelligences"
approach is a johnny-come-lately) and this would researchers
to focus on tests based on several specific factors (e.g., verbal
ability, math ability, spatial, etc.) instead of a single factor.
(3) If one allows the factors to be correlated after they are
extracted, one can come up with a correlation matrix for the
factors which can be further factor analyzed. Proponents of
"g" would argue that "general intelligence" was a "higher order"
factor in order to save their theory -- but now "g" is even further
away from the actual data it is supposed to explain. "g"
is now a "second order" factor but some situations might have
it as a "third order" factor (a large number of variables and
subjects are required to get these higher order factors).
"g" has strayed far from its original meaning and it is no longer
clear what it means, especially when is refering to second-order
or higher unitary factors. In this sense, "g" is an artfact because
it comes about the continual factor analyses of correlation
matrices -- from the original correlation matrix of empirical
variables to the derived correlation matrices for factors.
If one believes in his/her heart that "g" exists as a meaningful
entity, I'm sure that this seems like a reasonable thing to do.
If one does not believe in "g", this seems like grasping at
straws.
(4) This is a special time of year because the different strains
of Christianity celebrate Easter at the same time; see:
http://www.almanac.com/content/when-easter
The main distinction is whether one follows the "modern"
Gregorian calendar or the "old" Julian calendar (they are based
on lunar cycles and not all have transitioned from the old
calendar to the new old; however, Russia was late in making
the transition which explains why the October revolution is
celebrated in November). Roman Catholics follow the
Gregorian calendar while the Orthodox Christians tend to
follow the Julian calendar which means that the holidays
are usually out of sync. However, Byzantine rite Catholics
historically have followed the Julian calendar though in
recent years some have changed to observing the holiday
on the Gregorian calendar. For some background on this
see:
http://www.crisismagazine.com/2011/we-are-non-roman-catholics
Bringing this back to the original point of this thread, one
could use the metaphor that "g" is like the Catholic Church,
that is, an overarching conception that governs all sub-units
even those that don't recognize its authority because it can
be argued that they are all derived from Roman Catholicism.
The different varieties of Catholics and Christians are like
specific abilities, representing different components that
operate in a common system. So, from this perspective,
a "g" enthusiast would focus on the importance of Roman
Catholicism as driving all forms of Christianity while people
who don't care for "g", well, not so much. ;-)
Me, I'm a primary abilities kind of guy. ;-)
-Mike Palij
New York University
[email protected]
----- Original Message -----
On Wednesday, April 09, 2014 12:37 PM, John Kulig wrote:
Mike
I am not sure I get the point about g being an artifact of factor
analysis. I realize we can name factors anything we wish. The loadings
correlate the sub-tests with the hypothetical/latent variable that we
call factor I, II etc .... I also know that there are different methods
of factor analysis, and we can get different results, but if guided by
theory/common sense and the result is a construct that succinctly
summarizes a broad array of empirical findings, then I do not see the
artifact.
I do know that a factor will emerge when it predicts differences. So
(loosely stealing an example from Cronbach/ the pencil is my example)
... a sub-test of vocabulary and a sub-test of pencil sharpening ability
will not see a common factor emerge with homogeneous Ss, even though
there is a skill common to both - willingness to sit and follow
directions. But if we had a more heterogeneous sample of people from
very different cultures, a common factor of "willingness" would emerge
to predict differences. In the later example, the "willingness" would be
a useful construct, label it what you will. As I think about the
neurological underpinnings (jumping from one issue to another) it may be
the case that there are numerous brain functions common to all tasks, or
maybe only some tasks. Like factor analysis, do they predict differences
in the population we get our samples from?
And - jumping again - I suspect Mike and I are in a small group who
celebrate Greek Passover/Easter given his expertise in that area (add
our list to the cross-cultural dudes on tips. UNLESS he is simply an
expert in very diverse fields - OMG! is that g????). Whatever the case,
have a fruitful equinox holiday season!
----- Original Message -----
On Wednesday, April 9, 2014 12:16:17 PM, Mike Palij wrote:
On Wed, 09 Apr 2014 07:50:49 -0700, Jim Clark wrote:
Hi
I'm surprised to see the IQ bashing based on a perhaps simplistic
interpretation of some brain research showing that two different
areas of the brain light up in 16 subjects performing various cognitive
tasks.
[snip]
I think you miss the point: it is the use of IQ/intelligence/"g" as
theoretical concepts for cognitive or brain processing that is
being contested. There are alternative theoretical frameworks
that can be used but some people feel compelled to use
IQ/intelligence/"g". One might prefer a theory that claims that
the Flying Spaghetti Monster fills a person's heads with blue
fairies that when active give off energy that is detected by
neuroimaging techniques (but I'll leave the debunking of
neuroscience results to Tips resident neuroscience debunker
Scott Lilienfeld ;-). Hence, every thought you have is the result
of a busy blue fairy. Now try to falsify that claim. But do so
after you show the evidence for virtual particles. ;-) See
the following article in Scientific American but also read the
comments:
http://www.scientificamerican.com/article/are-virtual-particles-rea/
Then take a look at the Physics FAQ on virtual particles:
http://www.mat.univie.ac.at/~neum/physfaq/topics/virtual
Oh, and I'm glad that no one has shown that the claim that "g"
is an artifact of factor analysis is false. ;-)
Somewhat related, there is an interesting interview with Flynn in
the latest Skeptic magazine.
Interesting interview but it leaves one wondering why anybody let
the Irish immigrate to their country. ;-)
-Mike Palij
New York University
[email protected]
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