progress in science [ was: rotations and PCA ]
- "progress in science" is the new topic. I comment. On 9 Apr 2001 07:12:08 -0700, [EMAIL PROTECTED] (Robert J. MacG. Dawson) wrote: > Eric Bohlman wrote: >In science, it's not enough to > > say that you have data that's consistent with your hypothesis; you also > > need to show a) that you don't have data that's inconsistent with your > > hypothesis and b) that your data is *not* consistent with competing > > hypotheses. And there's absolutely nothing controversial about that last > > sentence [...] > > Well, I'd want to modify it a little. On the one hand, a certain amount > of inconsistency can be (and sometimes must be) dealt with by saying > "every so often something unexpected happens"; otherwise it would only > take two researchers making inconsistent observations to bring the whole > structure of science crashing down. And on the other hand there are Once upon a time, I spent many hours with the book, "Criticism and the growth of knowledge." Various (top) philosophers comment on Thomas Kuhn's contributions (normal and revolutionary science; paradigms; and so on), and on each other. In real science (I. Lakatos argues), models are strongly resistant to refutation so long as they remain fertile for research and speculation. The pertinent historical model is "phlogiston versus the caloric theory" -- The honored professors on neither side, it seems, ever convinced the other; there was plenty of conflicting data, for decades. But one side won new adherents and new researchers. > _always_ competing hypotheses. [Consider Jaynes' example of the > policeman seeing one who appears to be a masked burglar exiting from the > broken window of a jewellery store with a bag of jewellery; he (the > policeman) does *not* draw the perfectly logical conclusion that this > might be the owner, returning from a costume party, and, having noticed > that the window was broken, collecting his stock for safekeeping.] It is > sufficient to show that your data are not consistent with hypotheses > that are simpler or more plausible, or at least not much less simple or > plausible. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
Eric Bohlman wrote: In science, it's not enough to > say that you have data that's consistent with your hypothesis; you also > need to show a) that you don't have data that's inconsistent with your > hypothesis and b) that your data is *not* consistent with competing > hypotheses. And there's absolutely nothing controversial about that last > sentence [...] Well, I'd want to modify it a little. On the one hand, a certain amount of inconsistency can be (and sometimes must be) dealt with by saying "every so often something unexpected happens"; otherwise it would only take two researchers making inconsistent observations to bring the whole structure of science crashing down. And on the other hand there are _always_ competing hypotheses. [Consider Jaynes' example of the policeman seeing one who appears to be a masked burglar exiting from the broken window of a jewellery store with a bag of jewellery; he (the policeman) does *not* draw the perfectly logical conclusion that this might be the owner, returning from a costume party, and, having noticed that the window was broken, collecting his stock for safekeeping.] It is sufficient to show that your data are not consistent with hypotheses that are simpler or more plausible, or at least not much less simple or plausible. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
Rich Ulrich <[EMAIL PROTECTED]> wrote: > - Intelligence, figuring what it might be, and categorizing it, and > measuring it... I like the topics, so I have to post more. > On Thu, 05 Apr 2001 22:09:33 +0100, Colin Cooper > <[EMAIL PROTECTED]> wrote: >> (2) Gould's implication is that since Spearman found one factor >> (general ability) whilst Thurstone fornd about 9 identifiable factors, >> then factor analysis is a method of dubious use, since it seems to >> generate contradictory models. There are several crucial differences > - I read Gould as being more subtle than that. Definitely. Gould's point was that since the various forms of factor analysis generate models that are consistent with multiple, and contradictory, explanations of intelligence, and these models all resolve the same amount of variance in the raw data, none of the models provide a basis for favoring one theory over the other. Specifically, if a model is consistent with both a theory that says that intelligence is (hereditary, immutable) *and* with a theory that says that intelligence is (environmental, mutable) than that model does not provide any support for a claim that the first theory better explains reality than the second theory (or vice versa, for that matter). In science, it's not enough to say that you have data that's consistent with your hypothesis; you also need to show a) that you don't have data that's inconsistent with your hypothesis and b) that your data is *not* consistent with competing hypotheses. And there's absolutely nothing controversial about that last sentence, except to extreme post-modernists who would claim that it's an inherently white male view of the world, i.e. people who are far, far, to the left of most of Gould's critics. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
- Intelligence, figuring what it might be, and categorizing it, and measuring it... I like the topics, so I have to post more. On Thu, 05 Apr 2001 22:09:33 +0100, Colin Cooper <[EMAIL PROTECTED]> wrote: > In article <[EMAIL PROTECTED]>, > Rich Ulrich <[EMAIL PROTECTED]> wrote: > > > I liked Gould's book. I know that he offended people by pointing to > > gross evidence of racism and sexism in 'scientific reports.' But he > > has (I think) offended Carroll in a more subtle way. Gould is > > certainly partial to ideas that Carroll is not receptive to; I think > > that is what underlies this critique. > > > > ===snip > > I've several problems with Gould's book. > > (1) Sure - some of the original applications of intelligence testing > (screening immigrants who were ignorant of the language using tests > which were grossly unfair to them) were unfair, immoral and wrong. But > why impugn the whole area as 'suspect' because of the > politically-dubious activities of some researchers a century ago? It I think Gould to "impugned" more than just one area. The message, as I read it, was, "Be leery of social scientists who provide self-congratulatory and self-serving, simplistic conclusions." In recent decades, I imagine that economists have been bigger at that than psychologists. Historians have quite a bit of 20th century history-writing to live down, too. > seems to me to be exceptionally surprising to find that ALL abilities - > musical, aesthetic, abstract-reasoning, spatial, verbal, memory etc. > correlate not just significantly but substantially. Here is one URL for references to Howard Gardner, who has shown some facets of independence of abilities (and who you mention, below). http://www.newhorizons.org/trm_gardner.html > (2) Gould's implication is that since Spearman found one factor > (general ability) whilst Thurstone fornd about 9 identifiable factors, > then factor analysis is a method of dubious use, since it seems to > generate contradictory models. There are several crucial differences - I read Gould as being more subtle than that. > between the work of Spearman and Thurstone that may account for these > differences. For example, (a) Spearman (stupidly) designed tests > containing a broad spectrum of abilities: his 'numerical' test, for > example, comprised various sorts of problems - addition, fractions, etc. > Thurstone used separate tests for each: so Thurstone's factors > essentially corresponded to Spearman's tests. (b) Thurstone's work was > with students where the limited range of abilities would reduce the > magnitude of correlations between tests. (c) More recent work (e.g., > Gustafsson, 1981; Carroll, 1993) using exploratory factoring and CFA > finds good evidence for a three-stratum model of abilities: 20+ > first-order factors, half a dozen second-order factors, or a single > 3rd-order factor. > > (3) Interestingly, Gardner's recent work has come to almost exactly the > same conclusions from a very different starting point. Gardner > identiied groups of abilities which, according to the literature, tended > to covary - for example, which tend to develop at the same age, all > change following drugs or brain injury, which interfere with each other > in 'dual-task' experiments and so on. His list of abilities derived in > this was is very similar to the factors identified by Gustaffson, > Carroll and others. - but Gardner has "groups of abilities" that are, therefore, distinct from each other. And also, only a couple of abilities are usually rewarded (or even measured) in our educational system. When I read his book, I thought Gardner was being overly "scholastic" in his leaning, and restrictive in his data, too. > I have a feeling that we're going to get on to the issue of whether > factors are merely arbitrary representations of sets of data or whether > some solutions are more are more meaningful than others - the rotational > indeterminacy problem - but I'm off to bed! Well, how much data can you load into one factor analysis? How much virtue can you assign to one 'central ability'? - I see the problem as philosophical instead of numeric. What you will *identify* as a single factor (by techniques of today) will be more trivial than you want. Daniel Dennett, in "Consciousness Explained," does a clever job of defining consciousness. And trivializing it; what I was interested in (I reflect to myself) was something much grander, something more meaningful. But intelligence and self-awareness are separate topics, and big ones. Julian Jaynes's book was more useful on the bigger picture -- setting a framework, so to speak, and establishing the size of the problem. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE ME
Re: rotations and PCA
In article <[EMAIL PROTECTED]>, Rich Ulrich <[EMAIL PROTECTED]> wrote: > I liked Gould's book. I know that he offended people by pointing to > gross evidence of racism and sexism in 'scientific reports.' But he > has (I think) offended Carroll in a more subtle way. Gould is > certainly partial to ideas that Carroll is not receptive to; I think > that is what underlies this critique. > > ===snip I've several problems with Gould's book. (1) Sure - some of the original applications of intelligence testing (screening immigrants who were ignorant of the language using tests which were grossly unfair to them) were unfair, immoral and wrong. But why impugn the whole area as 'suspect' because of the politically-dubious activities of some researchers a century ago? It seems to me to be exceptionally surprising to find that ALL abilities - musical, aesthetic, abstract-reasoning, spatial, verbal, memory etc. correlate not just significantly but substantially. (2) Gould's implication is that since Spearman found one factor (general ability) whilst Thurstone fornd about 9 identifiable factors, then factor analysis is a method of dubious use, since it seems to generate contradictory models. There are several crucial differences between the work of Spearman and Thurstone that may account for these differences. For example, (a) Spearman (stupidly) designed tests containing a broad spectrum of abilities: his 'numerical' test, for example, comprised various sorts of problems - addition, fractions, etc. Thurstone used separate tests for each: so Thurstone's factors essentially corresponded to Spearman's tests. (b) Thurstone's work was with students where the limited range of abilities would reduce the magnitude of correlations between tests. (c) More recent work (e.g., Gustafsson, 1981; Carroll, 1993) using exploratory factoring and CFA finds good evidence for a three-stratum model of abilities: 20+ first-order factors, half a dozen second-order factors, or a single 3rd-order factor. (3) Interestingly, Gardner's recent work has come to almost exactly the same conclusions from a very different starting point. Gardner identiied groups of abilities which, according to the literature, tended to covary - for example, which tend to develop at the same age, all change following drugs or brain injury, which interfere with each other in 'dual-task' experiments and so on. His list of abilities derived in this was is very similar to the factors identified by Gustaffson, Carroll and others. I have a feeling that we're going to get on to the issue of whether factors are merely arbitrary representations of sets of data or whether some solutions are more are more meaningful than others - the rotational indeterminacy problem - but I'm off to bed! Colin Cooper = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
On Sun, 01 Apr 2001 22:13:18 +0100, Colin Cooper <[EMAIL PROTECTED]> wrote: > ==snip See Stephen Jay Gould's _The Mismeasure of Man_ for more > > details; note that Thurstone adopted varimax rotations because their > > results were consistent with *his* pet theories about intelligence. > Hmm. Gould's book is generally reckoned to be rather partial and not > particularly accurate - see for example JB Carroll's 'editorial review' > of the second edition in 'Intelligence' about 4 years ago. (sorry - > haven't got the exact reference to hand). Comrey & Lee's book is one of A google search on < Carroll Gould Intelligence > immediately hit a copy of the article -- http://www.mugu.com/cgi-bin/Upstream/Issues/psychology/IQ/carroll-gould.html I liked Gould's book. I know that he offended people by pointing to gross evidence of racism and sexism in 'scientific reports.' But he has (I think) offended Carroll in a more subtle way. Gould is certainly partial to ideas that Carroll is not receptive to; I think that is what underlies this critique. After Google-ing Carroll, I see that he is a long-time researcher in "intelligence." To me, it seems that Gould is in touch with the newer stream of hypotheses about intelligence -- ideas that tend to invalidate the basic structures of old-line theorists like Carroll. In the article, Carroll eventually seems to express high enthusiasm for 'new techniques' (compared to what Gould made use of) in factor analysis. I can say, my own experience and reading has not led me to the same enthusiasm. Am I missing something? > the better introductions - Loehlin 'latent variable Models' is good if > you're coming to it from a structural equation modelling background. > > Colin Cooper -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
==snip See Stephen Jay Gould's _The Mismeasure of Man_ for more > details; note that Thurstone adopted varimax rotations because their > results were consistent with *his* pet theories about intelligence. > Hmm. Gould's book is generally reckoned to be rather partial and not particularly accurate - see for example JB Carroll's 'editorial review' of the second edition in 'Intelligence' about 4 years ago. (sorry - haven't got the exact reference to hand). Comrey & Lee's book is one of the better introductions - Loehlin 'latent variable Models' is good if you're coming to it from a structural equation modelling background. Colin Cooper = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
Rich Ulrich <[EMAIL PROTECTED]> wrote: > On Thu, 29 Mar 2001 10:17:09 +0200, "Nicolas Voirin" > <[EMAIL PROTECTED]> wrote: >> OK, thanks. >> >> In fact, it's a "visual" method to see a set of points with the better >> view (maximum of variance). >> It's like to swivel a cube around to see all of its sides ... but this >> in more than 3D. >> When I show points in differents planes (F1-F2, F2-F3, F2-F4 ... for >> example), I make rotations, isn't it ? > I think I would use the term, "projection" onto specific planes, if > you are denoting x,y, and z (for instance) with F1, F2, F3 : > You can look at the x-y plane, the y-z plane, > and so on. > Here is an example in 2 dimensions, which suggests a simplified > version of an old controversy about 'intelligence'-- > tests might provide two scores of Math=110, Verbal= 90. > However, the abilities can be reported, with no loss of detail, as > General= 100, M-versus-V= +20. Historically, Spearman wanted > us all to conclude that "Spearman's g" had to exist as a mental > entity, since its statistical description could be reliably produced. And Thurstone's dissatisfaction with Spearman's theories led him to invent the technique of axial rotation, particularly the varimax criterion (rotate the axes until the variance of the items' projections on the axes is maximized). See Stephen Jay Gould's _The Mismeasure of Man_ for more details; note that Thurstone adopted varimax rotations because their results were consistent with *his* pet theories about intelligence. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
On Thu, 29 Mar 2001 10:17:09 +0200, "Nicolas Voirin" <[EMAIL PROTECTED]> wrote: > OK, thanks. > > In fact, it's a "visual" method to see a set of points with the better > view (maximum of variance). > It's like to swivel a cube around to see all of its sides ... but this > in more than 3D. > When I show points in differents planes (F1-F2, F2-F3, F2-F4 ... for > example), I make rotations, isn't it ? I think I would use the term, "projection" onto specific planes, if you are denoting x,y, and z (for instance) with F1, F2, F3 : You can look at the x-y plane, the y-z plane, and so on. Here is an example in 2 dimensions, which suggests a simplified version of an old controversy about 'intelligence'-- tests might provide two scores of Math=110, Verbal= 90. However, the abilities can be reported, with no loss of detail, as General= 100, M-versus-V= +20. Historically, Spearman wanted us all to conclude that "Spearman's g" had to exist as a mental entity, since its statistical description could be reliably produced. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
OK, thanks. In fact, it's a "visual" method to see a set of points with the better view (maximum of variance). It's like to swivel a cube around to see all of its sides ... but this in more than 3D. When I show points in differents planes (F1-F2, F2-F3, F2-F4 ... for example), I make rotations, isn't it ? I think I have understand the principle, and I don't forget to consult the books you (all) recommended to me. Sincerly, Nico. PS : Excuse me for my english but I'm french (Lyon) and I am not used to write or speak english. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
On Wed, 28 Mar 2001 08:57:36 +0200, "Nicolas V." <[EMAIL PROTECTED]> wrote: > Hi, > > What are "rotations" in PCA ? > What is the difference between "rotated" and "unrotated" PCA ? > Does it exist in others analysis ? = just on 'existence' = Rotations certain exist in other analyses, and for other purposes. Anytime you have a coordinate system, you have potential for drawing in different axes, and then describing locations in terms of the new system. On a map in 2D, you can describe positions as directions, N-E-S-W. But if a river cuts along the diagonal, it could be more sensible to describe cities as "up-river" from the ocean by some amount, and by how far they are from the main tributary. - simplification like that, is the idea behind rotation. Common Factors are usually selected from the full-rank set, and rotated: so the description will be simpler. The full-rank set of PCs is often used as a matter of convenience (vectors are not correlated); and there's no help from rotation if there's no separate description being used. The set of "significant" Factors in canonical correlation might be subjected to rotation, because they are rather like Common Factors; but that is seldom done (in what I read). -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
rotations and PCA
Hi, What are "rotations" in PCA ? What is the difference between "rotated" and "unrotated" PCA ? Does it exist in others analysis ? Thank you, Nico. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
