@amoeba After our conversation on Meta CV I erased the Q&A post altogether; the moderators wanted to be nice, but the post doesn't belong in CV. Thank you for explaining the rules of "CW" and "on-hold". I have great appreciation for both moderators, and remember your help on other posts. I hope you see that my only interest was in having the information I had worked on available for reference. What I did is simply print my answer to a pdf - that simple, and proceeded to erase. Cheers!

@Antoni I can assure you that all of the moderators appreciate positive effort directed toward the site. We want good contributions from enthusiastic participants (it's the point of the site after all), but they do need to fit with the rules of the site. I agree with the point @amoeba made in your deleted meta post: "the real question here should be how to edit this thread so that it becomes on-topic". We'd prefer to fix posts than delete them, unless they seem un-rescuable.

@Glen_b Not a problem. I just wanted to keep the info on the response somehow for myself - you know how it is with the latex... Finally I just printed the answer and saved it in my computer. I hope I have explained myself well enough to dispel any thoughts of me wanting to preserve this post against the rules of the site. Frankly, the post wasn't good - I gave it my best shot at modifying the Q and the A several times, and I ran out of ideas. Cheers!

@l'ombradel'atzavara interesting name change. Is that name choice based on the novel?

@Glen_b Not really. Having the real name there is just a bit stressful... you know... communication is imperfect, everybody means well, but words have cutting edges online, and I can only control what comes out of my keyboard. I'm going to take a step back and re read Borges perhaps. CV stackexchange is wonderful but I don't know enough math to get so involved. Cheers, Glen. You and William are doing a great mitzvah teach so many people.

@l'ombradel'atzavara I certainly understand the impetus to use a different name and no judgement was implied; I was just curious about the specific choice. Many people choose not to give their complete personal details for a variety of reasons (myself included; back in the early 1990s I used to use my full name for everything, but switched to a couple of related pseudonyms for the more robust fora I participate in, and for my first name elsewhere).

I don't think I've used my full name online for (at least for almost everything) since about 1999.

I'd have used "Glen" without the "_b" but there was already a "Glen" here when I signed up and I figured a duplicate would be a bad idea. The intent was to signal a second Glen, though we have a number of Glen names so that didn't quite convey the intended sense in the end.

(You've made some good contributions. We all have things to learn. I could point you to some of my poorer posts - at least the ones not already deleted - and that might make you feel like you had company. I've had some good lessons from chl, cardinal, Scortchi, whuber and others on my own failings - fortunately uniformly kind ones. I value such encounters, but then I can always benefit from a little humility, and dealing with a lot of smart people can be humbling.)

@Glen_b Glen, Great talking to you. The site has been great, and participants are incredible people. Using my real name is my preference, but it is also more exposed. I didn't anticipate any controversy on a post on Meta I erased yesterday, for instance. I'm still not sure of things like CW, chat rooms, the community blog, the rules for erasing questions.

@l'ombradel'atzavara You didn't break any rules at all by deleting the question. I just couldn't figure out what was wrong with it, since it seemed fine to me. I figured it might be useful.

hello all

Anyone knows of a numerical routine/library that computes Kummer's confluent hypergeometric function for complex argument?

in C++ or C?

@l'ombradel'atzavara I didn't have a chance to see your meta post unfortunately, but just in case you aren't aware, you can click "edit" on a question and just save the plain text in order to render it later on anything that runs MathJax. I do this all the time to copy equations from questions into comments, or render things from questions in markdown / website with mathjax. Sorry if that's not what you were talking about re: saving questions / LaTex, just thought I would chime in.

Sorry, the formatting didn't save there, but I hope you get the idea.

@ChrisC Thanks a lot Chris. This is very useful!

@amoeba re this q, yes, on closer inspection it's a shame that this is one of the very top results if you search google for "varimax". (Not just on our site - I mean the whole internet! The Stack Exchange guys are very good at SEO, but it is a double-edged sword.)

I am toying still with the idea of including some sample data into the question, to make it more concrete. Let me know if you think this is sensible. (I am particularly tempted to replicate the example on p.165 of this pdf as it seems a particularly good demonstration)

Let me know if you think that's sensible.

Sure, @Silverfish, I think including a concrete example into the thread would be excellent (even though it seems that it should rather belong to an answer rather than the question -- on the other hand, I guess it depends on how you frame the Q)

@amoeba Yes that was something I was weighing up. "Here's an example, what does it mean?"

versus "Explain, possibly using an example (of your choice)"

Is this dataset included in R?

There's a bit of a trade-off. Canonical suggests "general". But the kind of reader coming for a canonical question is likely to prefer "concrete" to "abstract", even though "abstract" is closely related to "general". And yes, it's included

The data set seems to provide a reasonable demonstration of the principles, including interpretability, and is widely available. Which would make it a good choice, I think.

It's a pity that the raw data are not available, only the corr matrix

@amoeba It would certainly be "nicer" to have complete data. To what extent would that be harmful in this context?

Not harmful at all. It's just that with raw data one could e.g. draw biplots, and it can be helpful, but for specifically the discussion of factor rotations it's not crucial (and perhaps even an unnecessary complication)

I was just trying to think whether there would be any knock-on effects. Biplots is a good example. But since the core material is still demonstrable I think it'd be ok

Looked at this correlation table. It's kind of funny, actually. All the variables are positively correlated (not surpringly), meaning that the first factor / PC can be expected to be similar to the global average (probably age) and the second will be height-weight, i.e. "fatness". Now, according to varimax this is a bad solution and it should be rotated ...

to get "lankiness" and "stockiness". Now an older girl is simultaneously lankier and stockier. Is this really conceptually simpler?

@amoeba It might be nicer to have something with both positive and negative correlations. But also where the rotated solution is somehow "clearer" conceptually

Well, I think it's a good example because it shows that "interpretability" is in the eye of the beholder.

(Perhaps there is a more convincing case for varimax, but I don't know any.)

utdallas.edu/~herve/Abdi-rotations-pretty.pdf

Another pdf, sorry. Has entirely fake data about wines. I thought that made the interpretability argument rather better.

I don't like fake data :)

I only like fake data if it's to prove a mathematical point.

By the way, you seem to be going quite deep into this! In the end you will probably be the best person to answer your own question.

I wouldn't have a good facility with the algebra if I were to write a mathematical solution! But I think it's a shame that the current questions we have on this topic are so poor.

If I recall correctly, the first factor in (E)FA is "more important" than the second factor, but with a slightly different sense to what happens in PCA (communality rather than total variance explained)

I suppose what I see as the heart of the question about interpreting rotations, is in what sense my "new factors" are the "same" as my "old factors".

Yes, it's "shared variance" as opposed to "total variance", but as I have been arguing in various threads, most of the times they are very close

I am not sure that all factor extraction methods and routines/libraries will sort factors by explained [shared] variance, but this can always be done.

My new "factor 1" clearly doesn't refer to the same latent factor as my "old factor 1" - we can see that from any example where the rotation is by a substantial amount, because it changes our interpretation quite radically (that's why I quite liked the first one I showed you, rotating by about 30 degrees makes quite a difference)

I agree that this is at the heart, yes. That's important to explain very clearly.

but on the other hand, their are still some similarities between the latent factors before and after rotation - if we use varimax, my new latent factor are still orthogonal, like my original ones were

and (if my understanding is correct), then jointly I can still explain just as much from "new factor 1 and factor 2" as I could with "old factor 1 and factor 2"

That's correct.

Presumably, my new factor 1 is no longer "as important" as my old factor 1, which is in some sense something that I've "lost"

but I haven't lost anything jointly so my other factor(s) must have "made up for it"

I think that's the right way to see it, yes. You trade some explained variance for "interpretability".

@amoeba That's speaking very roughly but I'm trying to think "What's the maximal take-away that a non-technical person with a social science or similar background could get from such a question?"

If I can ask a question that hits all these points, then that's much better than anything we've got at the moment. And hopefully would be clearer than e.g. Wikipedia's rather broader article.

And for a technical person, there's room for a more mathematical answer that addresses these points by explaining them on an algebraic level.

Just indicate that the answers should aim to explain both the mathematical side of it AS WELL AS to provide some intuition at what's going on and why. I think you don't necessarily need to write a massive question explicitly listing all the things you want to be covered in the answers (as I think your tendency sometimes is: to write great but very long questions)

If I can pitch that right it's got a good chance of being, for our purposes, "canonical".

I was intending this to be a short one

Sometimes the shorter ones take most planning!

I guess in the end the canonicalness depends on the answers

Great question without any or with lousy answers is not something you want to refer other people to

Quite so :) Though some questions are more "answerable" than others!

Cheers for the discussion. It has helped me formulate a better, particularly sharper, focus. Will likely post tomorrow or soon after. Have a good night!

You too. See you

The identifiability tag didn't have a wiki or excerpt. It's a bit hard to figure out what to put there (perhaps why there wasn't one). I tried to throw something together--not sure how well it worked. If anyone wants to take a look, it might help to get another set of eyeballs on it.