Blog

Apparent circularity in structural causal model accounts of causation

“It may seem strange that we are trying to understand causality using causal models, which clearly already encode causal relationships. Our reasoning is not circular. Our aim is not to reduce causation to noncausal concepts but to interpret questions about causes of specific events in fully specified scenarios in terms of generic causal knowledge…” (Halpern & Pearl, 2005).

“It may seem circular to use causal models, which clearly already encode causal information, to define actual causation. Nevertheless, there is no circularity. The models do not directly represent relations of actual causation. Rather, they encode information about what would happen under various possible interventions” (Halpern & Hitchcock, 2015).

References

Halpern, J. Y., & Pearl, J. (2005). Causes and Explanations: A Structural-Model Approach. Part I: Causes. The British Journal for the Philosophy of Science, 56(4), 843–887.

Halpern, J. Y., & Hitchcock, C. (2015). Graded Causation and Defaults. The British Journal for the Philosophy of Science, 66(2), 413–457.

Neyman–Rubin causal model – potential outcomes in a nutshell

The Neyman–Rubin causal model (see, e.g., Rubin, 2008) has the following elements:

  • Units, physical entities somewhere/somewhen in spacetime such as someone in Camden Town, London, on a Thursday eve.
  • Two or more interventions, where one is often considered a “control”, e.g., cognitive behavioural therapy (CBT) as usual for anxiety, and another is considered a “treatment”, e.g., a new chat bot app to alleviate anxiety. The “control” does not have to be (and almost certainly cannot be) “nothing”.
  • Potential outcomes, which represent outcomes following each intervention (e.g., following treatment and control) for every unit. Alas, only one potential outcome is realised and observed for a unit, depending on which intervention they actually received. This is what makes causal inference such a challenge.
  • Zero or more pre-intervention covariates, which are measured for all units.
  • The causal effect is the difference in potential outcomes between two interventions for a unit, e.g., in levels of anxiety for someone following CBT and following the app intervention. It is impossible to obtain the causal effect for an individual unit since only one potential outcome can be realised.
  • The assignment mechanism is the conditional probability distribution of being in an intervention group, given covariates and potential outcomes. For randomised experiments, the potential outcomes have no influence on the assignment probability. This assignment mechanism also explains which potential outcomes are realised and which are missing data.

Although the causal effect cannot be obtained for individual units, various causal estimates can be inferred if particular assumptions hold, e.g.,

  • Sample average treatment effect on the treated (SATT or SATET), which is an estimate of the mean difference in a pair of potential outcomes (e.g., anxiety following the app minus anxiety following CBT) for those who were exposed to the “treatment” (e.g., the app) in a sample.
  • Sample average treatment effect (SATE), which is an estimate of the mean difference between a pair of potential outcomes for everyone in a sample.

How does this work?

Suppose we run a randomised trial where people are assigned to either CBT or app based on the outcome of a coin toss. From each participant’s two potential outcomes, we only observe one depending on which group they were assigned to. But since we randomised, we know the missing data mechanism. It turns out that under a coin toss randomised trial, a good estimate of the average treatment effect is simply the difference between the means in observed outcomes for those assigned to the app and those assigned to CBT.

We can also calculate p-values in a variety of ways. One is to assume a null hypothesis of no difference in potential outcomes in the treatment and control conditions, i.e., the potential outcomes are identical for each participant but may vary between participants. Under this particular “sharp” null, we do not have a missing data problem since we can just use whatever outcome was observed for each participant to fill in the blank for the unobserved potential outcome. Since we know the assignment mechanism, it is possible to work out the distribution of possible mean differences under the null by enumerating all possible random assignments to groups and calculating the mean difference between treatment and control for each (in practice there may be too many, but we can approximate by taking a random subset). Now calculate a p-value by working out the probability of obtaining the actually observed mean difference or larger against this distribution of differences under the null.

What’s lovely about this potential outcomes approach is that it’s a simple starting point for thinking about a variety of ways for evaluating the impact of interventions. Though working out the consequences, e.g., standard errors for estimators, may be non-trivial.

References

Rubin, D. B. (2008). For objective causal inference, design trumps analysis. Annals of Applied Statistics, 2(3), 808–840.

Russian

I have been learning Russian for over a year now – initially via a course and now on DuoLingo. Here are some observations.

Sometimes Russian is easier than English

Ты ответил на мой вопрос
You answered my question

Ты не ответил на мой вопрос
You did not answer my question

What’s this “did” nonsense in English?

Apples

DuoLingo really wants us to know how to talk about apples:

У меня есть яблоко
I have an apple

Ты хочешь яблоко?
Would you like an apple?

Я ем яблоко
I am eating an apple

Кошка ест яблоко
The cat is eating an apple

Mnemonics

I like the Russian word for “dogs” (plural), «собаки», because it is pronounced “so-backy” which is almost “so barky”

Обуться – to put on one’s shoes
Sounds like “a-boot-sa”

The name of the “soft sign” in Russian, «ь», is pronounced like “murky snack”.

The plural of bank (банк) in Russian sounds like “banky”: банки. (Don’t know why this helps me remember it’s not, e.g., банкы)

Курт в куртке
Kurt in a jacket

Formality:

Ты
You (informal)

Вы
You (formal)

Картошка
Potato (informal 😉 like “spud”)

Картофель
Potato (formal 😉 )

LOLs

The Russian quotation marks – «» – are called “little Christmas trees” (ёлочки).

The @ symbol is called «собака», “dog”.

Another great Russian word is «класс» which sounds like “class”. Conveniently it also seems to mean “class” in Norn Irish, in the sense of “That’s class.”

For an easy Russian song to sing, try this techno track by Russian artist (and fully qualified dentist) Nina Kraviz: “Ivan, Come On! Unlock The Box!” (Иван, давай! Открой коробку!)

Two infinitives you don’t want to confuse:

Писать (sounds like “piss-at”) is “to write”.

Писать (sounds like “peace-it”) is “to piss”.

Same spelling, different stress. I suppose the context helps distinguish, but it depends on the writer.

Ты любишь писать на ветру
You like to write in the wind

A more beautiful source of confusion:

Мой душ.
(My shower, душ is masculine)

Моя душа.
(My soul, душа is feminine)

The prepositional case of both душ and душа is the same: душе.

В душе музыка
(There is music in the shower/soul)

How to say, “I’m a novice” or “newcomer”: Я новичок. Same as a well-known nerve agent.

Length

Sometimes Russian words are shorter than their English equivalent: “about” in Russian is «о».

Sometimes they’re tricky:

“tourist attraction” is «Достопримечательность».

“Pet” is «домашнее животное» (literally, domestic animal).

Logic

Sometimes Russian is logical:

Завтра – tomorrow
Завтрак – breakfast

Would you [informal] like breakfast tomorrow?
Хочешь завтрак завтра?

And:

Сколько?
(How many?)

Не
(Not)

Glue them together:
Несколько (Several)

And:

четыре – four
четвертый – fourth
четверг – Thursday

пять – five
пятый – fifth
пятница – Friday

среди – in the middle of
среда – Wednesday

Or nearly…

два/две – two
второй – second
вторник – Tuesday

And:

Цвет (tsvet) – colour
Свет (svet) – light

Also… Chromatography was invented by Mikhail Tsvet (Михаил Цвет)

Gender

Past tense singular (except polite 2nd person) conjugations in Russian depend on gender, even 1st person:

Я танцевал
I [masc] danced

Я танцевала
I [fem] danced

Present tense fine:

Я танцую
I dance

Cute

Apparently it is very common to exclaim «блин!» in Russian, e.g., if you drop something or stub your toe. It means “pancake”.

Why would anyone say «немного» when the word «чуть-чуть» exists, sounds like “choot choot” and means the same (“a little”)?

Я только чуть-чуть говорю по-русски
I only speak a little Russian

More grammar

The verb “to be” is usually implicit in Russian present tense:

I am Andi
Я Энди (I Andi)

There’s no explicit verb “to have” in any tense. Instead you use an explicit… wait for it… “to be” with the preposition “by”:

I have a book
У меня есть книга
(By me is book)

Precision

Sometimes Russian is less ambiguous than English:

Он любит свою жену
He loves his wife
x loves x’s wife

Он любит его жену
He loves his wife
x loves y’s wife

x=y possible but xy implied

Balls

Football (game)
футбол

Ball
мяч

Football (ball for playing football)
футбольный мяч (Footbally ball?)

Initialisms

BBC is written «Би-би-си», like spelling it out as “bee-bee-sea”.

The Russian for USA, США, is pronounced like “se sha”. Which makes me wonder why the English isn’t “You-sa”, analagously to “Nato”.

Going

Она идёт на работу
She is going to work [on foot]

Она едет на работу
She is going to work [by some mode of transport like a bus]

Снег идёт
It’s snowing

Words I confuse

деревня – village
дерево – wood/tree
дверь – door

лошадь – horse
площадь – (town) square

Говорить – to speak
Готовить – to cook/prepare

Красивый – pretty
Красный – red

Я устал – I am tried (present tense), but with the «л» it looks like “I was tired” and is literally something like “I became tired (and stayed that way)”

The grammar of the void

В магазине не было чая
In the shop there was no tea

(Genitive – «не было» is always same, irrespective of gender of object because it’s referring to the gender of the void, is how I understand it; other explanations are available)

В магазине был чай
In the shop there was tea

(Nominative – «был» agrees with masc. «чай» and whatever else there actually is)

Cases

Here’s a glimpse of the mess:

Студент
Student (nominative singular)

Студенты
Students (nominative plural)

Много студентов
Many students (genitive plural)

Spacetime

длинный – long (space)
долгий – long (time)

это длинная колбаса
This is a long sausage

Это долго объяснять
This will take a long time to explain

Pronouns

I ran out of steam copy and pasting these; here are a few of them:

1st person 2nd person 3rd person (masc.) 3rd person (fem.) 3rd person (neut.).
English I, Me You He, Him She, Her It
Nominative Case Я Ты Он Она Оно
Accusative Case Меня Тебя Его Её Его
Genitive Case Меня Тебя Его Её Его
Dative Case Мне Тебе Ему Ей Ему
Instrumental Case Мной Тобой Им Ей Им
Prepositional Case Мне Тебе Нём Ней Нём
1st person 2nd person 3rd person
English We, Us You They, Them
Nominative Case Мы Вы Они
Accusative Case Нас Вас Их
Genitive Case Нас Вас Их
Dative Case Нам Вам Им
Instrumental Case Нами Вами Ими
Prepositional Case Нас Вас Них
1st Person 2nd Person
Masc. Fem. Neut. Plural Masc. Fem. Neut. Plural
English My, Mine Your, Yours
Nominative Case Мой Моя Моё Мои Твой Твоя Твоё Твои
Accusative Case
(animate)
Мой
Моего
Мою Моё Мои
Моих
Твой
Твоего
Твою Твоё Твои
Твоих
Genitive Case Моего Моей Моего Моих Твоего Твоей Твоего Твоих
Dative Case Моему Моей Моему Моим Твоему Твоей Твоему Твоим
Instrumental Case Моим Моей Моим Моими Твоим Твоей Твоим Твоими
Prepositional Case Моём Моей Моём Моих Твоём Твоей Твоём Твоих
1st Person 2nd Person
Masc. Fem. Neut. Plural Masc. Fem. Neut. Plural
English Our Your, Yours
Nominative Case Наш Наша Наше Наши Ваш Ваша Ваше Ваши
Accusative Case
(animate)
Наш
Нашего
Нашу Наше Наши
Наших
Ваш
Вашего
Вашу Ваше Ваши
Ваших
Genitive Case Нашего Нашей Нашего Наших Вашего Вашей Вашего Ваших
Dative Case Нашему Нашей Нашему Нашим Вашему Вашей Вашему Вашим
Instrumental Case Нашим Нашей Нашим Нашими Вашим Вашей Вашим Вашими
Prepositional Case Нашем Нашей Нашем Наших Вашем Вашей Вашем Ваших
English Myself, himself, herself.
Nominative Case
Accusative Case Себя
Genitive Case Себя
Dative Case Себе
Instrumental Case Себой
Prepositional Case Себе
Masc. Fem. Neut. Plural
English My own, his own, her own
Nominative Case Свой Своя Своё Свои
Accusative Case
(animate)
Свой
Своего
Свою Своё Свои
Своих
Genitive Case Своего Своей Своего Своих
Dative Case Своему Своей Своему Своим
Instrumental Case Своим Своей Своим Своими
Prepositional Case Своём Своей Своём Своих

That’s half-way down the page over here.

 

Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations

Neat paper by Tennant, P. W. G. et al. (2020): Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations in the International Journal of Epidemiology.

Picture

Recommendations from the paper

  1. The focal relationship(s) and estimand(s) of interest should be stated in the study aims
  2. The DAG(s) for each focal relationship and estimand of interest should be available
  3. DAGs should include all relevant variables, including those where direct measurements are unavailable
  4. Variables should be visually arranged so that all constituent arcs flow in the same direction
  5. Arcs should generally be assumed to exist between any two variables
  6. The DAG-implied adjustment set(s) for the estimand(s) of interest should be clearly stated
  7. The estimate(s) obtained from using the unmodified DAG-implied adjustment set(s)—or nearest approximation thereof—should be reported
  8. Alternative adjustment set(s) should be justified and their estimate(s) reported separately

Social Sciences under Attack in the UK (1981-1983)

Interesting paper by Michael Posner, who was chair of the UK Social Science Research Council (SSRC) when it was under attack by the Conservative Thatcher government in the early 1980s.

Secretary of State Sir Keith Joseph considered dismantling SSRC and asked for an independent review into its utility by an established biologist.

SSRC survived, though one notable change was made…

“Joseph opted for a public, but very light punishment: a change of name. I told him that I could persuade scores of academics to accept a name change if he would promise, on the record, the continuing independence of the SSRC. He agreed, and the SSRC was duly renamed the « Economic and Social Research Council » (ESRC). The significance of this change was the omission of the word « science », which Joseph had insisted upon and which many of us at the council and in academia found it difficult to accept.”

Read more over here.

The aim of critical realist philosophy

“The aim of critical realist philosophy is, when the practice is adequate, to provide a better or more adequate theory of the practice; and, when it is not, to transform the practice in the appropriate way. That is to say the aim of critical realist philosophy is enhanced reflexivity or transformed practice (or both). […]

“Since there is only one world, the theories and principles of critical realist philosophy should also apply to our everyday life. If they do not, then something is seriously wrong. This means that our theories and explanations should be tested in everyday life, as well as in specialist research contexts.”

—Bhaskar, Roy (2013) The consequences of the revindication of philosophical ontology for philosophy and social theory. In: Archer, Margaret and Maccarini, Andrea, (eds.) Engaging with the world. (pp. 11-21). Routledge: London.