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Volken's phunny phactor rotations
Volken's conclusion of "only 23 percent is due to the independent influence of national IQ" is a qualified conclusion. It would be like assuming that the 130-point average IQ of lawyers is largely independent of their positions as lawyers and therefore explains very little -- perhaps in the way of their lifestyle prudence or their investment savvy -- in terms of their incomes, when in fact factor analysis shows that lawyers do not become lawyers in the first place unless their IQs are high enough to allow them to pass the barrister's exams. Again, Volken is simply saying he takes issue with the generalizability of the g-nexus as a force of broad influence upon other factors such as EF and ID. He even states, point blank, his bias at the end of the section quoted above with the loaded phrase neglects the influence structure: "The conclusion of Lynn/Vanhanen ... is therefore fundamentally wrong, since it completely neglects the influence structure of the variables involved."
What is wrong with what Volken is saying here is that just because it is a demonstrable fact that factors can be rotated -- and, yes, they always can be rotated, depending upon the whim of the researcher or his assumption of direction of influence ("influence structure" in Volken's lexiphanicism) -- in such ways so as to make general factors appear very small, neither ipso-facto makes general factors irrelevant in specific cases, nor in general. If that were the case, then at some times a given factor would be relevant and at other times it wouldn't, depending upon who performed the latest factor rotation and why. But that is not the case. General factors are relevant to the degree that they can be maximized by factor rotation, and there is only one number (give or take a few thousandths of a degree of coefficient of congruence) in any given data set that can result when this is done. IOW, general factors are always there. You oftentimes must rotate the factors, however, in order to mathematically see them.
Jensen explains factor rotation in The g Factor.
http://www.questia.com/PM.qst?a=o&d=24373874
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HOW INVARIANT IS g ACROSS DIFFERENT METHODS OF FACTOR ANALYSIS?
This is one of the crucially important questions in our present inquiry. Obviously the simplest way to answer it is to simulate a variety of correlation matrices that are similar to those found for actual mental test data but for which we already know the true factor structure exactly, and then see how accurately different factor analytic models and methods can estimate 7 the "true" factors known to exist in these artificial matrices.
This is just what I did, in collaboration with Dr. Li-Jen Weng, at that time a postdoctoral research scholar at the University of California, Berkeley, and a specialist in factor analysis and mathematical statistics...
Of course, we used no type of factor analysis that is expressly designed to preclude the appearance of a general factor (such as orthogonal rotation of the primary factors). We were concerned here exclusively with the amount of variation in the g factor when it is extracted by the various methods most commonly described in modern textbooks of factor analysis...
The result of this analysis was that every one of the methods of factor analysis estimated the true g so closely that there was hardly any basis for choosing between them. The congruence coefficients between the true g factor and the g factor obtained by the various methods ranged from +997 to +.999, with an average of +.998. This is especially remarkable because some of the artificial matrices were specifically designed to "trick" particular methods into yielding estimates that would deviate markedly from the true values, for example by simulating tests of highly mixed factor composition (e.g., each test having substantial loadings on all of the primary factors)...
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(The g Factor. p81-82)
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This orthogonal simple structure model, it turns out, has proved inappropriate in the abilities domain, and in fact Thurstone (1931) himself early on used oblique rotation of the factor axes to achieve the best possible approximation to simple structure. (Oblique factors are correlated with each other.) He only subsequently advanced orthogonal rotation to avoid some of the complications associated with oblique rotation. But it was apparent that, in the abilities domain, a good fit of the data to a simple structure model could not be achieved with orthogonal rotation, because a general factor permeates all of the primary abilities. Orthogonal rotation would achieve simple structure only if Thurstone's original theory were true. (That is the theory that mental ability consists of a number of distinct, uncorrelated abilities represented by the primary factors, and that there is no general factor in the abilities domain.) But that theory has long since been proven false. Thurstone assiduously attempted to devise tests that would provide factor-pure measures of what he called the primary mental abilities revealed by his method of multiple factor analysis. 3 But it proved impossible to devise a test that was a pure measure of any primary factor.
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(The g Factor. p76-77)
We might note that this second instance is analogous to the Volken instance. Substitute mental ability in the above with sociological outcome, and abilities with sociological factors and we have, "That is the theory that sociological outcome consists of a number of distinct, uncorrelated sociological factors represented by the primary factors, and that there is no general factor in the sociological factors domain."
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Any form of factor analysis that allows the extraction of a general factor has no trouble finding a very robust g in any sizable collection of Guilford's tests despite their assignment to distinct cells of the SOI. Guilford nonetheless argued that the 150 cells were orthogonal, or uncorrelated, primary factors. His empirical demonstration of so many orthogonal factors, however, relied on a technique known as targeted orthogonal rotation. Aptly named Procrustes, this method literally forces tests that were specifically selected or designed to measure the
SOI abilities to have significant loadings only on particular factors, the number and definitions of which are predetermined by the SOI model. This cannot be accepted as evidence that the 150 abilities in different cells of the SOI are not intercorrelated, since Guilford's Procrustes method of orthogonal rotation foreordains uncorrelated factors. In brief, Guilford simply assumed a priori that g does not exist, and he eschewed any type of factor analysis that would allow g to appear.
---
(The g Factor. p117)
This third instance is, again, analogous to what Volken did in his respective factor analysis of sociological factors, especially the last sentence wherein it might be instructive to simply replace Guilford's name with Volken's.
In brief, Volken simply assumed a priori that g does not exist, and he eschewed any type of factor analysis that would allow g to appear.
-Chris
The key phrase here is "the independent effects of [EF and ID]." This calculation doesn't work the way Volken says it works unless he qualifies his methods by assuming that EF and ID are not broadly influenced by national IQ (e.g., calls EF and ID "independent effects"). A major theme in Lynn's and Vanhanen's work is that a massively broad influence of national IQ -- or anything else -- will not be visible unless factors that might otherwise be assumed to be independent are put to the test as possibly non-independent factors. So, again, the Lynn/Vanhanen thesis is contingent upon the g-nexus effect generalizing from within the United States to outside the United States and therefore contributing broadly to variance in social factors outside the United States. And the fact that Volken takes issue with the generalizability of the g-nexus is not contested. Volken clearly takes issue with it -- as instanced by his assumption above of independence of factors -- and that one thing is the major point of his paper.Originally posted by Nereid
Perhaps we don't have the same Volken paper? In the first part, Volken looks at the relative strength of three factors, assumed to be independent (i.e. an unbiased starting point), and finds: "While the total amount of variance explained by all three variables amounts to 63 percent, only 23 percent is due to the independent influence of national IQ. The remaining 40 percent, or roughly two thirds of the total variance, comes into existence due to the independent effects of economic freedom (29 percent of explained variance) and the level of democratization (11 percent of explained variance)."
Volken's conclusion of "only 23 percent is due to the independent influence of national IQ" is a qualified conclusion. It would be like assuming that the 130-point average IQ of lawyers is largely independent of their positions as lawyers and therefore explains very little -- perhaps in the way of their lifestyle prudence or their investment savvy -- in terms of their incomes, when in fact factor analysis shows that lawyers do not become lawyers in the first place unless their IQs are high enough to allow them to pass the barrister's exams. Again, Volken is simply saying he takes issue with the generalizability of the g-nexus as a force of broad influence upon other factors such as EF and ID. He even states, point blank, his bias at the end of the section quoted above with the loaded phrase neglects the influence structure: "The conclusion of Lynn/Vanhanen ... is therefore fundamentally wrong, since it completely neglects the influence structure of the variables involved."
What is wrong with what Volken is saying here is that just because it is a demonstrable fact that factors can be rotated -- and, yes, they always can be rotated, depending upon the whim of the researcher or his assumption of direction of influence ("influence structure" in Volken's lexiphanicism) -- in such ways so as to make general factors appear very small, neither ipso-facto makes general factors irrelevant in specific cases, nor in general. If that were the case, then at some times a given factor would be relevant and at other times it wouldn't, depending upon who performed the latest factor rotation and why. But that is not the case. General factors are relevant to the degree that they can be maximized by factor rotation, and there is only one number (give or take a few thousandths of a degree of coefficient of congruence) in any given data set that can result when this is done. IOW, general factors are always there. You oftentimes must rotate the factors, however, in order to mathematically see them.
Jensen explains factor rotation in The g Factor.
http://www.questia.com/PM.qst?a=o&d=24373874
---
HOW INVARIANT IS g ACROSS DIFFERENT METHODS OF FACTOR ANALYSIS?
This is one of the crucially important questions in our present inquiry. Obviously the simplest way to answer it is to simulate a variety of correlation matrices that are similar to those found for actual mental test data but for which we already know the true factor structure exactly, and then see how accurately different factor analytic models and methods can estimate 7 the "true" factors known to exist in these artificial matrices.
This is just what I did, in collaboration with Dr. Li-Jen Weng, at that time a postdoctoral research scholar at the University of California, Berkeley, and a specialist in factor analysis and mathematical statistics...
Of course, we used no type of factor analysis that is expressly designed to preclude the appearance of a general factor (such as orthogonal rotation of the primary factors). We were concerned here exclusively with the amount of variation in the g factor when it is extracted by the various methods most commonly described in modern textbooks of factor analysis...
The result of this analysis was that every one of the methods of factor analysis estimated the true g so closely that there was hardly any basis for choosing between them. The congruence coefficients between the true g factor and the g factor obtained by the various methods ranged from +997 to +.999, with an average of +.998. This is especially remarkable because some of the artificial matrices were specifically designed to "trick" particular methods into yielding estimates that would deviate markedly from the true values, for example by simulating tests of highly mixed factor composition (e.g., each test having substantial loadings on all of the primary factors)...
---
(The g Factor. p81-82)
---
This orthogonal simple structure model, it turns out, has proved inappropriate in the abilities domain, and in fact Thurstone (1931) himself early on used oblique rotation of the factor axes to achieve the best possible approximation to simple structure. (Oblique factors are correlated with each other.) He only subsequently advanced orthogonal rotation to avoid some of the complications associated with oblique rotation. But it was apparent that, in the abilities domain, a good fit of the data to a simple structure model could not be achieved with orthogonal rotation, because a general factor permeates all of the primary abilities. Orthogonal rotation would achieve simple structure only if Thurstone's original theory were true. (That is the theory that mental ability consists of a number of distinct, uncorrelated abilities represented by the primary factors, and that there is no general factor in the abilities domain.) But that theory has long since been proven false. Thurstone assiduously attempted to devise tests that would provide factor-pure measures of what he called the primary mental abilities revealed by his method of multiple factor analysis. 3 But it proved impossible to devise a test that was a pure measure of any primary factor.
---
(The g Factor. p76-77)
We might note that this second instance is analogous to the Volken instance. Substitute mental ability in the above with sociological outcome, and abilities with sociological factors and we have, "That is the theory that sociological outcome consists of a number of distinct, uncorrelated sociological factors represented by the primary factors, and that there is no general factor in the sociological factors domain."
---
Any form of factor analysis that allows the extraction of a general factor has no trouble finding a very robust g in any sizable collection of Guilford's tests despite their assignment to distinct cells of the SOI. Guilford nonetheless argued that the 150 cells were orthogonal, or uncorrelated, primary factors. His empirical demonstration of so many orthogonal factors, however, relied on a technique known as targeted orthogonal rotation. Aptly named Procrustes, this method literally forces tests that were specifically selected or designed to measure the
SOI abilities to have significant loadings only on particular factors, the number and definitions of which are predetermined by the SOI model. This cannot be accepted as evidence that the 150 abilities in different cells of the SOI are not intercorrelated, since Guilford's Procrustes method of orthogonal rotation foreordains uncorrelated factors. In brief, Guilford simply assumed a priori that g does not exist, and he eschewed any type of factor analysis that would allow g to appear.
---
(The g Factor. p117)
This third instance is, again, analogous to what Volken did in his respective factor analysis of sociological factors, especially the last sentence wherein it might be instructive to simply replace Guilford's name with Volken's.
In brief, Volken simply assumed a priori that g does not exist, and he eschewed any type of factor analysis that would allow g to appear.
-Chris