What’s the difference between fixed and random effects?

Gelman (2005, p. 21) to the rescue.

We prefer to sidestep the overloaded terms “fixed” and “random” with a cleaner distinction […]. We define effects (or coefficients) in a multilevel model as constant if they are identical for all groups in a population and varying if they are allowed to differ from group to group.

Gelman A. (2005). Analysis of variance—why it is more important than ever. Annals of Statistics, 33(1), 1–53

Logic is the language of love

“Life, love and romance are all about surprise: the surprise of an unexpected bouquet of flowers, a mysterious stranger met by chance at a party, the unannounced return of an old lover at your doorstep, the confusion of finding the unknown side of an old friend or acquaintance who becomes your partner. The freshness of a relationship kept new even after years.

“Alive equals surprise.

“The logical world … seems to be a world of no surprise, no serendipity, no romance. Axioms generate propositions, one deduction blindly follows another. The game is over almost as soon as it is begun. Where is the romance in that? No chance for the heart to overrule the head, contradiction to conquer cogitation, desperation and devotion to deliver you from derivation.

“Or is there?

“In the 1920s, a mathematician named Goedel proved that in any consistent logical system [the result is a bit weaker than that… AF], there will always be statements whose truth or falsity can’t be proved by the simple mechanical rules of logic. Even if these “undecidable” statements are appended to the list of axioms, as long as this enlarged system remains consistent, there will still be other statements whose proof or refutation lies outside the power of formal reasoning.

“The unknowable and the unpredictable is embedded in even the most simple of things. Romantically speaking, I like to think of this as saying that if we have a guarantee of truth, and thus the possibility of honesty, then from this we must necessarily have surprise, even mystery—and maybe then, just maybe, with a little bit of luck, we must have love. Q.E.D.”

From Logic is the language of love by Daniel Rockmore

How to get someone’s g

“Intelligence”, “IQ”, “g” (due to Spearman), are terms that are bandied around.

The following may be helpful: the gist of how to calculate someone’s g score, which is often used as the measure of someone’s “intelligence”.

For example, that’s the “IQ”/”intelligence” referred to in the recentish BBC article on research linking childhood intelligence and adult vegetarianism (clever children grow into clever vegetarian adults).

  1. Give hundreds or thousands of people a dozen tests of ability.
  2. Zap everyone’s scores with PCA or factor analysis.
  3. g is the first component and usually explains around half the variance.  Here’s an example genre of analysis of g with other facets to psychometric intelligence.
  4. Use the component to calculate a score.  For factor analysis there are many ways to do this, e.g. Thompson’s scores, Bartlett’s weighted least-squares.  The gist is that for each person you compute a weighted sum of their scores, where the weights are a function of how loaded the particular test score was on g.
  5. To get something resembling an IQ score, scale it so it has a mean of 100 and an SD of 15.
  6. Talk about it as if it were a substantive psychological construct, rather than a statistical artefact 😉

What is this mysterious g thing?

Florence Nightingale

A bio of Florence Nightingale, statistician and nurse. Excerpt:

“Nightingale helped to promote what was then a revolutionary idea (and a religious one for her) that social phenomena could be objectively measured and subjected to mathematical analysis. Her work with medical statistics was so impressive that she was elected (in 1858) to membership in the Statistical Society of England. One of the pioneers in the graphic method of presentation of data, she invented colorful polar-area diagrams to dramatize medical data. Although other methods of persuasion had failed, her statistical approach convinced military authorities, Parliament, and Queen Victoria to carry out her proposed hospital reforms.”

[Photo of her Polar Area Diagram (“coxcomb”) from over here.]


More and more I found myself at a loss for words and didn’t want to hear other people talking either. Their conversations seemed false and empty. I preferred to look at the sea, which said nothing and never made you feel alone.

– Paula McLain, The Paris Wife


Love, the warmth of bodies in contact, is the only mercy shown to us in the darkness. But the only union is that of the organs, and it can’t bridge over the cleavage made by speech. Yet they unite in order to produce beings to stand by them in their hopeless isolation. And the generations look coldly into each other’s eyes. If you cram a ship full to bursting with human bodies, they all freeze with loneliness.

– Bertold Brecht, In the Jungle of Cities


… of course natural language is meaningless. Even in my most optimistic moments I can only conclude that conversation merely exists to disguise the fact that we are all going to die… No doubt following this lecture you will all exist mostly in silence.

– Maurice Clint, 2001 or so, Belfast, in a maths lecture


Language only lives in and through human culture, which on the one hand needs mutual understanding but on the other hand makes direct communication impossible. […] People who use language lose their primitive desires which, however sinful, remain close to the self. Frightened by solitude, their only home, they become automata, slaves of the monster-machine of public relations.

– Brouwer, Life, Art, and Mysticism


The more the words,
the less the meaning,
and how does that profit anyone?

– Ecclesiastes 6:11


Out beyond ideas of wrongdoing and rightdoing,
There is a field. I’ll meet you there.

When the soul lies down in that grass,
The world is too full to talk about.
Ideas, language, even the phrase ‘each other’
Doesn’t make any sense.

– Rumi


Vows are spoken
To be broken
Feelings are intense
Words are trivial
Pleasures remain
So does the pain
Words are meaningless
And forgettable

– Depeche Mode, Enjoy the Silence


What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent.

– Ludwig Wittgenstein, Tractatus Logico-Philosophicus


Silence is sexy
Silence is sexy
So sexy
So silence
Silence is sexy
Silence is sexy
So sexy
So sexy

-From Silence is Sexy by Blixa Bargeld of Einstürzende Neubauten


Woke up this morning and my head was in a daze,
Brave new world had dawned upon the human race,
Words are meaningless and everything’s surreal,
Gonna have to reach my friends to find out how I feel,
And if I taste the honey, is it really sweet?
And do I eat it with my hands or with my feet?
Does anybody really listen when I speak or will I have to say it all again next week?

– Shakespears Sister, Hello (Turn Your Radio On)


And it’s not enough
To tell me that you care,
When we both know the words are empty air.

– Calvin Harris, Sweet Nothing


We are spendthrifts with words,
We squander them,
Toss them like pennies in the air—
Arrogant words,
Angry words,
Cruel words,
Comradely words,
Shy words tiptoeing from mouth to ear.

But the slowly wrought words of love
And the thunderous words of heartbreak—
These we hoard.

– Words, by Pauli Murray

Plato’s The Apology of Socrates

On Saturday I saw Yannis Simonides’s moving performance of Plato’s The Apology of Socrates. Here’s a translation (not the one by Yannis). And an excerpt:

“Friends, who would have acquitted me, I would like also to talk with you about this thing which has happened, while the magistrates are busy, and before I go to the place at which I must die. Stay then awhile, for we may as well talk with one another while there is time. You are my friends, and I should like to show you the meaning of this event which has happened to me. […]

… we shall see that there is great reason to hope that death is a good, for one of two things: – either death is a state of nothingness and utter unconsciousness, or, as men say, there is a change and migration of the soul from this world to another. Now if you suppose that there is no consciousness, but a sleep like the sleep of him who is undisturbed even by the sight of dreams, death will be an unspeakable gain. For if a person were to select the night in which his sleep was undisturbed even by dreams, and were to compare with this the other days and nights of his life, and then were to tell us how many days and nights he had passed in the course of his life better and more pleasantly than this one, I think that any man, I will not say a private man, but even the great king, will not find many such days or nights, when compared with the others. Now if death is like this, I say that to die is gain; for eternity is then only a single night. But if death is the journey to another place, and there, as men say, all the dead are, what good, O my friends and judges, can be greater than this? […] What would not a man give if he might converse with Orpheus and Musaeus and Hesiod and Homer? Nay, if this be true, let me die again and again. I, too, shall have a wonderful interest in a place where I can converse with Palamedes, and Ajax the son of Telamon, and other heroes of old, who have suffered death through an unjust judgment; and there will be no small pleasure, as I think, in comparing my own sufferings with theirs. Above all, I shall be able to continue my search into true and false knowledge; as in this world, so also in that; I shall find out who is wise, and who pretends to be wise, and is not. […]”

Need motivation to vote?

This video of Koichi Toyama, part of a 2007 election campaign for the position of Tokyo governor, may help get you down to the polling station.

Choice quotes:

“To all the voters. This nation is horrible.”

“I have no interest whatsoever in political reform or any kind of reform.”

“This nation must be destroyed.”

“I do not have a single constructive proposal!”

“Annihilate everything that exists.”

“I despise each and every one of you.”

“If you think you can change something by voting, you are COMPLETELY wrong.”


“Please give me a phone call.”

(He wasn’t elected.)


Dov Gabbay, logician, fan of psychologism:

‘I got married in 1970. My wife is an artist, and I learned a lot from her; the fact that I can talk about things, for instance. I remember I was going out with her, before we were married, and we were walking from one part of the university to another part. My objective was to get from A to B, she wanted to stop and look at the moon, because it looked very nice. And I thought: “What the hell would I want to look at the moon for, when I want to go to B?” Now, of course, I will look at the moon at all times with her.’

(From an interview with “Ta!”) My reluctance to look at the lunar eclipse suggests I need to meet an artist—pronto 🙂

Ye olde Spearman

A good test of whether someone understands g is if they characterise it as a general factor in intelligence test scores and not as general intelligence (i.e., a substantive rather than statistical construct). But it’s interesting to see what Spearman originally said in his 1904 “General Intelligence,” Objectively Determined and Measured. On p. 272:

“… we reach the profoundly important conclusion that there really exists a something that we may provisionally term “General Sensory Discrimination” and similarly a “General Intelligence,” and further that the functional correspondence between these two is not appreciably less than absolute.”

He goes on to describe this as a “general theorem”, refining it to (p. 273):

Whenever branches of intellectual activity are at all dissimilar, then their correlations with one another appear wholly due to their being all variously saturated with some common fundamental Function (or group of Functions).”

(Enthusiastic emphasis in original.)

There’s a recent argument against this (though perhaps not quite, given Spearman’s parenthetical “group of Functions”), by van der Maas, et al. (2006). The abstract:

“Scores on cognitive tasks used in intelligence tests correlate positively with each other, i.e., they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g-factor, associated with a single quantitative cognitive or biological process or capacity. In this paper we propose a new explanation of the positive manifold based on a dynamical model, in which reciprocal causation or mutualism plays a central role. It is shown that the positive manifold emerges purely by positive beneficial interactions between cognitive processes during development. A single underlying g-factor plays no role in the model. The model offers explanations of important findings in intelligence research, such as the hierarchical factor structure of intelligence, the low predictability of intelligence from early childhood performance, the integration/differentiation effect, the increase in heritability of g, the Jensen effect, and is consistent with current explanations of the Flynn effect.”

Autistic superiority

A blog post by Michelle Dawson, in which she lists researchers who publish data on people with autism who are superior to neurotypicals on some task, reminded me of a quote I’d saved from a BBS commentary paper by Gernsbacker, Dawson, and Mottron (2006):

“Quite compellingly, each of these statistically significant demonstrations of autistic superiority is labeled by its authors as a harmful dysfunction. Autistics’ superior block-design performance is labeled “weak central coherence,” symptomatic of dysfunctional “information processing in autism” (Shah & Frith 1993, p. 1351). Autistics’ superior performance on embedded figures tests is considered “consistent with the cognitive-deficit theory proposed by Hermelin and O’Connor (1970) … due to a central deficiency in information processing” (Shah & Frith 1983, p. 618). Autistics’ superior recognition memory performance is attributed to deleteriously “enhanced attention to shallow aspects of perceived materials” (Toichi et al. 2002, p. 1424); their superior sentence comprehension is described as being “less proficient at semantically and syntactically integrating the words of a sentence” (Just et al. 2004, p. 1816); their superior imperviousness to memory distortions is explained by “representations in the semantic network [that] may be associated in an aberrant manner” (Beversdorf et al. 2000, p. 8736); and their superior resistance to misleading prior context is attributed to their perception being “less conceptual” (Ropar & Mitchell 2002, p. 652).”

Gernsbacker, M.A., Dawson, M., and Mottron. L. (2006). Autism: Common, heritable, but not harmful. Behavioral and Brain Sciences, 29, 413-414.

Edited to add: hadn’t clicked that the Dawson in the author list is the blog’s author! (She is.)