Causal Inference cheat sheet for data scientists

Being able to make causal claims is a key business value for any data science team, no matter their size.
Quick analytics (in other words, descriptive statistics) are the bread and butter of any good data analyst working on quick cycles with their product team to understand their users. But sometimes some important questions arise that need more precise answers. Business value sometimes means distinguishing what is true insights from what is incidental noise. Insights that will hold up versus temporary marketing material. In other terms causation.

When answering these questions, absolute rigour is required. Failing to understand key mechanisms could mean missing out on important findings, rolling out the wrong version of a product, and eventually costing your business millions of dollars, or crucial opportunities.
Ron Kohavi, former director of the experimentation team at Microsoft, has a famous example: changing the place where credit card offers were displayed on generated millions in revenue for the company.

The tech industry has picked up on this trend in the last 6 years, making Causal Inference a hot topic in data science. Netflix, Microsoft and Google all have entire teams built around some variations of causal methods. Causal analysis is also (finally!) gaining a lot of traction in pure AI fields. Having an idea of what causal inference methods can do for you and for your business is thus becoming more and more important.

The causal inference levels of evidence ladder

Hence the causal inference ladder cheat sheet! Beyond the value for data scientists themselves, I’ve also had success in the past showing this slide to internal clients to explain how we were processing the data and making conclusions.

The “ladder” classification explains the level of proof each method will give you. The higher, the easier it will be to make sure the results from your methods are true results and reproducible – the downside is that the set-up for the experiment will be more complex. For example, setting up an A/B test typically requires a dedicated framework and engineering resources.
Methods further down the ladder will require less effort on the set-up (think: observational data), but more effort on the rigour of the analysis. Making sure your analysis has true findings and is not just commenting some noise (or worse, is plain wrong) is a process called robustness checks. It’s arguably the most important part of any causal analysis method. The further down on the ladder your method is, the more robustness checks I’ll require if I’m your reviewer 🙂

I also want to stress that methods on lower rungs are not less valuable – it’s almost the contrary! They are brilliant methods that allow use of observational data to make conclusions, and I would not be surprised if people like Susan Athey and Guido Imbens, who have made significant contributions to these methods in the last 10 years, were awarded the Nobel prize one of these days!

The causal inference levels of evidence ladder – click on the image to enlarge it

Rung 1 – Scientific experiments

On the first rung of the ladder sit typical scientific experiments. The kind you were probably taught in middle or even elementary school. To explain how a scientific experiment should be conducted, my biology teacher had us take seeds from a box, divide them into two groups and plant them in two jars. The teacher insisted that we made the conditions in the two jars completely identical: same number of seeds, same moistening of the ground, etc.
The goal was to measure the effect of light on plant growth, so we put one of our jars near a window and locked the other one in a closet. Two weeks later, all our jars close to the window had nice little buds, while the ones we left in the closet barely had grown at all.
The exposure to light being the only difference between the two jars, the teacher explained, we were allowed to conclude that light deprivation caused plants to not grow.

Sounds simple enough? Well, this is basically the most rigorous you can be when you want to attribute cause. The bad news is that this methodology only applies when you have a certain level of control on both your treatment group (the one who receives light) and your control group (the one in the cupboard). Enough control at least that all conditions are strictly identical but the one parameter you’re experimenting with (light in this case). Obviously, this doesn’t apply in social sciences nor in data science.

Then why do I include it in this article you might ask? Well, basically because this is the reference method. All causal inference methods are in a way hacks designed to reproduce this simple methodology in conditions where you shouldn’t be able to make conclusions if you followed strictly the rules explained by your middle school teacher.

Rung 2 – Statistical Experiments (aka A/B tests)

Probably the most well-known causal inference method in tech: A/B tests, a.k.a Randomized Controlled Trials for our Biostatistics friends. The idea behind statistical experiments is to rely on randomness and sample size to mitigate the inability to put your treatment and control groups in the exact same conditions. Fundamental statistical theorems like the law of large numbers, the Central Limit theorem or Bayesian inference gives guarantees that this will work and a way to deduce estimates and their precision from the data you collect.

Arguably, an Experiments platform should be one of the first projects any Data Science team should invest in (once all the foundational levels are in place, of course). The impact of setting up an experiments culture in tech companies has been very well documented and has earned companies like Google, Amazon, Microsoft, etc. billions of dollars.

Of course, despite being pretty reliable on paper, A/B tests come with their own sets of caveats. This white paper by Ron Kohavi and other founding members of the Experiments Platform at Microsoft is very useful.

Rung 3 – Quasi-Experiments

As awesome as A/B tests (or RCTs) can be, in some situations they just can’t be performed. This might happen because of lack of tooling (a common case in tech is when a specific framework lacks the proper tools to set up an experiment super quickly and the test becomes counter-productive), ethical concerns, or just simply because you want to study some data ex-post. Fortunately for you if you’re in one of those situations, some methods exist to still be able to get causal estimates of a factor. In rung 3 we talk about the fascinating world of quasi-experiments (also called natural experiments).

A quasi-experiment is the situation when your treatment and control group are divided by a natural process that is not truly random but can be considered close enough to compute estimates. In practice, this means that you will have different methods that will correspond to different assumptions about how “close” you are to the A/B test situation. Among famous examples of natural experiments: using the Vietnam war draft lottery to estimate the impact of being a veteran on your earnings, or the border between New Jersey and Pennsylvania to study the effect of minimum wages on the economy.

Now let me give you a fair warning: when you start looking for quasi-experiments, you can quickly become obsessed by it and start thinking about clever data collection in improbable places… Now you can’t say you haven’t been warned 😜 I have more than a few friends who were lured into attracted by a career in econometrics for the sheer love of natural experiments.

Most popular methods in the world of quasi-experiments are: differences-in-differences (the most common one, according to Scott Cunnigham, author of the Causal Inference Mixtape), Regression Discontinuity Design, Matching, or Instrumental variables (which is an absolutely brilliant construct, but rarely useful in practice). If you’re able to observe (i.e. gather data) on all factors that explain how treatment and control are separated, then a simple linear regression including all factors will give good results.

Rung 4 – The world of counterfactuals

Finally, you will sometimes want to try to detect causal factors from data that is purely observational. A classic example in tech is estimating the effect of a new feature when no A/B test was done and you don’t have any kind of group that isn’t receiving the feature that you could use as a control:

Slightly adapted from CausalImpact‘s documentation

Maybe right new you’re thinking: wait… are you saying we can simply look at the data before and after and be allowed to make conclusions? Well, the trick is that often it isn’t that simple to make a rigorous analysis or even compute an estimate. The idea here is to create a model that will allow to compute a counterfactual control group. Counterfactual means “what would have happened hadn’t this feature existed”. If you have a model of your number of users that you have enough confidence in to make some robust predictions, then you basically have everything

There is a catch though. When using counterfactual methods, the quality of your prediction is key. Without getting too much into the technical details, this means that your model not only has to be accurate enough, but also needs to “understand” what underlying factors are driving what you currently observe. If a confounding factor that is independent from your newest rollout varies (economic climate for example), you do not want to attribute this change to your feature. Your model needs to understand this as well if you want to be able to make causal claims.

This is why robustness checks are so important when using counterfactuals. Some cool Causal Inference libraries like Microsoft’s doWhy do these checks automagically for you 😲 Sensitivity methods like the one implemented in the R package tipr can be also very useful to check some assumptions. Finally, how could I write a full article on causal inference without mentioning DAGs? They are a widely used tool to state your assumptions, especially in the case of rung 4 methods.

(Quick side note: right now with the unprecedented Covid-19 crisis, it’s likely that most prediction models used in various applications are way off. Obviously, those cannot be used for counterfactual causal analysis)

Technically speaking, rung 4 methods look really much like methods from rung 3, with some small tweaks. For example, synthetic diff-in-diff is a combination of diff-in-diff and matching. For time series data, CausalImpact is a very cool and well-known R package. causalTree is another interesting approach worth looking at. More generally, models carefully crafted with domain expertise and rigorously tested are the best tools to do Causal Inference with only counterfactual control groups.

Hope this cheat sheet will help you find the right method for your causal analyses and be impactful for your business! Let us know about your best #causalwins on our Twitter, or in the comments!

Comment expliquer la baisse de participation aux municipales 2020 ?

Dimanche dernier, le 15 mars 2020, la France a organisé le premier tour des élections municipales, après avoir annoncé une fermeture des écoles puis des restaurants et commerces non essentiels. La participation à ce scrutin s’établit à 44,64 %, en chute de 20 points par rapport à 2014, date des précédentes élections municipales (voir une très belle carte du Monde ici, assez illustrative de la situation)

Ce rapide billet ne s’attardera pas sur la question de savoir s’il fallait ou non organiser ces élections (le second tour est, lui, reporté à plus tard) ; nous cherchons ici à identifier quels sont les facteurs explicatifs de la baisse de participation aux municipales, et si ces facteurs peuvent avoir favorisé un ou plusieurs partis politiques.

Un sondage “jour de vote” réalisé par IFOP [modifié : je parlais dans la version initiale par erreur d’un sondage IPSOS ; celui-ci est consultable ici, et qui donne d’autres résultats encore, avec une plus forte participation à droite qu’à gauche sur l’échiquier politique] (consultable ici) montrait une importance du paramètre Covid-19 sur les raisons de ne pas aller voter (plus de 50% des sondés n’ayant pas voté jugeant que c’était une des raisons déterminantes), mais aussi une disparité entre les différentes familles politiques, avec une plus forte abstention chez les électeurs d’EELV (60 %) et une plus faible abstention chez les partisans d’En Marche (37 %).

Une analyse fine des résultats, bureau de vote par bureau, permet d’identifier les bureaux de vote pour lesquels l’évolution de l’abstention a été la plus forte entre 2014 et 2020 (on se limite au même scrutin des municipales), et, une fois ces bureaux de vote identifiés, analyser les résultats politiques obtenus au premier tour de l’élection présidentielle de 2017. Comme toujours, les données sont sur (ici pour les municipales 2020), merci à eux !

Le graphique ci-après résume les résultats obtenus :

On constate que les résultats ne sont pas les mêmes que ceux du sondage du jour du vote. Il semblerait que le vote Macron ou Le Pen, au premier tour en 2017, soit un bon indicateur d’une plus forte abstention aux municipales 2020. Cela ne veut cependant pas dire que les électeurs ayant choisi ces deux candidats sont plus sensibles au risques liées au Covid-19 ; peut-être est-ce plutôt lié à une séquence politique qui, pour les municipales 2020, n’était pas favorable à En Marche par exemple, même en l’absence de pandémie.

Méthodologie : les données relatives aux premiers tours des élections municipales de 2014 et 2020 ainsi que celles de la présidentielle 2017 sont agrégées au niveau du bureau de vote (on exclut ici les bureaux de vote ayant disparu, ayant fusionné ou ayant été créés). On calcule ensuite sur les un peu plus de 60 000 bureaux restants un différentiel de participation entre 2014 et 2020, qu’on régresse sur le taux parmi les votants pour chacun des candidats au premier tour de la présidentielle 2017.

Data analysis of the French football league players with R and FactoMineR

This year we’ve had a great summer for sporting events! Now autumn is back, and with it the Ligue 1 championship. Last year, we created this data analysis tutorial using R and the excellent package FactoMineR for a course at ENSAE (in French). The dataset contains the physical and technical abilities of French Ligue 1 and Ligue 2 players. The goal of the tutorial is to determine with our data analysis which position is best for Mathieu Valbuena 🙂

The dataset

A small precision that could prove useful: it is not required to have any advanced knowledge of football to understand this tutorial. Only a few notions about the positions of the players on the field are needed, and they are summed up in the following diagram:

Positions of the fooball players on the field
Positions of the fooball players on the field

The data come from the video game Fifa 15 (which is already 2 years old, so there may be some differences with the current Ligue 1 and Ligue 2 players!). The game features rates each players’ abilities in various aspects of the game. Originally, the grade are quantitative variables (between 0 and 100) but we transformed them into categorical variables (we will discuss why we chose to do so later on). All abilities are thus coded on 4 positions : 1. Low / 2. Average / 3. High / 4. Very High.

Loading and prepping the data

Let’s start by loading the dataset into a data.frame. The important thing to note is that FactoMineR requires factors. So for once, we’re going to let the (in)famous stringsAsFactors parameter be TRUE!

> frenchLeague <- read.csv2("french_league_2015.csv", stringsAsFactors=TRUE)
> frenchLeague <-, 2, factor))

The second line transforms the integer columns into factors also. FactoMineR uses the row.names of the dataframes on the graphs, so we’re going to set the players names as row names:

row.names(frenchLeague) <- frenchLeague$name
frenchLeague$name <- NULL

Here’s what our object looks like (we only display the first few lines here):

> head(frenchLeague)
                     foot position league age height overall
Florian Thauvin      left       RM Ligue1   1      3       4
Layvin Kurzawa       left       LB Ligue1   1      3       4
Anthony Martial     right       ST Ligue1   1      3       4
Clinton N'Jie       right       ST Ligue1   1      2       3
Marco Verratti      right       MC Ligue1   1      1       4
Alexandre Lacazette right       ST Ligue1   2      2       4

Data analysis

Our dataset contains categorical variables. The appropriate data analysis method is the Multiple Correspondance Analysis. This method is implemented in FactoMineR in the method MCA. We choose to treat the variables “position”, “league” and “age” as supplementary:

> library(FactoMineR)
> mca <- MCA(frenchLeague, quali.sup=c(2,3,4))

This produces three graphs: the projection on the factorial axes of categories and players, and the graph of the variables. Let’s just have a look at the second one of these graphs:

Projection of the players on the first two factorial axes (click to enlarge)
Projection of the players on the first two factorial axes (click to enlarge)

Before trying to go any further into the analysis, something should alert us. There clearly are two clusters of players here! Yet the data analysis techniques like MCA suppose that the scatter plot is homogeneous. We’ll have to restrict the analysis to one of the two clusters in order to continue.

On the previous graph, supplementary variables are shown in green. The only supplementary variable that appears to correspond to the cluster on the right is the goalkeeper position (“GK”). If we take a closer look to the players on this second cluster, we can easily confirm that they’re actually all goalkeeper. This absolutely makes a lot of sense: in football, the goalkeeper is a very different position, and we should expect these players to be really different from the others. From now on, we will only focus on the positions other than goalkeepers. We also remove from the analysis the abilities that are specific to goalkeepers, which are not important for other players and can only add noise to our analysis:

> frenchLeague_no_gk <- frenchLeague[frenchLeague$position!="GK",-c(31:35)]
> mca_no_gk <- MCA(frenchLeague_no_gk, quali.sup=c(2,3,4))

And now our graph features only one cluster.


Obviously, we have to start by reducing the analysis to a certain number of factorial axes. My favorite method to chose the number of axes is the elbow method. We plot the graph of the eigenvalues:

> barplot(mca_no_gk$eig$eigenvalue)


Graph of the eigenvalues

Around the third or fourth eigenvalue, we observe a drop of the values (which is the percentage of the variance explained par the MCA). This means that the marginal gain of retaining one more axis for our analysis is lower after the 3rd or 4th first ones. We thus choose to reduce our analysis to the first three factorial axes (we could also justify chosing 4 axes). Now let’s move on to the interpretation, starting with the first two axes:

> plot.MCA(mca_no_gk, invisible = c("ind","quali.sup"))

Projection of the abilities on the first two factorial axes
Projection of the abilities on the first two factorial axes

We could start the analysis by reading on the graph the name of the variables and modalities that seem most representative of the first two axes. But first we have to keep in mind that there may be some of the modalities whose coordinates are high that have a low contribution, making them less relevant for the interpretation. And second, there are a lot of variables on this graph, and reading directly from it is not that easy. For these reasons, we chose to use one of FactoMineR’s specific functions, dimdesc (we only show part of the output here):

> dimdesc(mca_no_gk)
$`Dim 1`$category
                      Estimate       p.value
finishing_1        0.700971584 1.479410e-130
volleys_1          0.732349045 8.416993e-125
long_shots_1       0.776647500 4.137268e-111
sliding_tackle_3   0.591937236 1.575750e-106
curve_1            0.740271243  1.731238e-87
finishing_4       -0.578170467  7.661923e-82
shot_power_4      -0.719591411  2.936483e-86
ball_control_4    -0.874377431 5.088935e-104
dribbling_4       -0.820552850 1.795628e-117

The most representative abilities of the first axis are, on the right side of the axis, a weak level in attacking abilities (finishing, volleys, long shots, etc.) and on the left side a very strong level in those abilities. Our interpretation is thus that axis 1 separates players according to their offensive abilities (better attacking abilities on the left side, weaker on the right side). We procede with the same analysis for axis 2 and conclude that it discriminates players according to their defensive abilities: better defenders will be found on top of the graph whereas weak defenders will be found on the bottom part of the graph.

Supplementary variables can also help confirm our interpretation, particularly the position variable:

> plot.MCA(mca_no_gk, invisible = c("ind","var"))

Projection of the supplementary variables on the first two factorial axis
Projection of the supplementary variables on the first two factorial axis

And indeed we find on the left part of the graph the attacking positions (LW, ST, RW) and on the top part of the graph the defensive positions (CB, LB, RB).

If our interpretation is correct, the projection on the second bissector of the graph will be a good proxy for the overall level of the player. The best players will be found on the top left area while the weaker ones will be found on the bottom right of the graph. There are many ways to check this, for example looking at the projection of the modalities of the variable “overall”. As expected, “overall_4” is found on the top-left corner and “overall_1” on the bottom-right corner. Also, on the graph of the supplementary variables, we observe that “Ligue 1” (first division of the french league) is on the top-left area while “Ligue 2” (second division) lies on the bottom-right area.

With only these two axes interpreted there are plenty of fun things to note:

  • Left wingers seem to have a better overall level than right wingers (if someone has an explanation for this I’d be glad to hear it!)
  • Age is irrelevant to explain the level of a player, except for the younger ones who are in general weaker.
  • Older players tend to have more defensive roles

Let’s not forget to deal with axis 3:

> plot.MCA(mca_no_gk, invisible = c("ind","var"), axes=c(2,3))

Projection of the variables on the 2nd and 3rd factorial axes
Projection of the variables on the 2nd and 3rd factorial axes

Modalities that are most representative of the third axis are technical weaknesses: the players with the lower technical abilities (dribbling, ball control, etc.) are on the end of the axis while the players with the highest grades in these abilities tend to be found at the center of the axis:

Projection of the supplementary variables on the 2nd and 3rd factorial axes
Projection of the supplementary variables on the 2nd and 3rd factorial axes

We note with the help of the supplementary variables, that midfielders have the highest technical abilities on average, while strikers (ST) and defenders (CB, LB, RB) seem in general not to be known for their ball control skills.

Now we see why we chose to make the variables categorical instead of quantitative. If we had kept the orginal variables (quantitative) and performed a PCA on the data, the projections would have kept the orders for each variable, unlike what happens here for axis 3. And after all, isn’t it better like this? Ordering players according to their technical skills isn’t necessarily what you look for when analyzing the profiles of the players. Football is a very rich sport, and some positions don’t require Messi’s dribbling skills to be an amazing player!

Mathieu Valbuena

Now we add the data for a new comer in the French League, Mathieu Valbuena (actually Mathieu Valbuena arrived in the French League in August of 2015, but I warned you that the data was a bit old ;)). We’re going to compare Mathieu’s profile (as a supplementary individual) to the other players, using our data analysis.

> columns_valbuena <- c("right","RW","Ligue1",3,1
> frenchLeague_no_gk["Mathieu Valbuena",] <- columns_valbuena

> mca_valbuena <- MCA(frenchLeague_no_gk, quali.sup=c(2,3,4), ind.sup=912)
> plot.MCA(mca_valbuena, invisible = c("var","ind"), col.quali.sup = "red", col.ind.sup="darkblue")
> plot.MCA(mca_valbuena, invisible = c("var","ind"), col.quali.sup = "red", col.ind.sup="darkblue", axes=c(2,3))

Last two lines produce the graphs with Mathieu Valbuena on axes 1 and 2, then 2 and 3:

Axes 1 and 2 with Mathieu Valbuena as a supplementary individual
Axes 1 and 2 with Mathieu Valbuena as a supplementary individual (click to enlarge)

Axes 2 and 3 with Mathieu Valbuena as a supplementary individual
Axes 2 and 3 with Mathieu Valbuena as a supplementary individual (click to enlarge)

So, Mathieu Valbuena seems to have good offensive skills (left part of the graph), but he also has a good overall level (his projection on the second bissector is rather high). He also lies at the center of axis 3, which indicates he has good technical skills. We should thus not be surprised to see that the positions that suit him most (statistically speaking of course!) are midfield positions (CAM, LM, RM). With a few more lines of code, we can also find the French league players that have the most similar profiles:

> mca_valbuena_distance <- MCA(frenchLeague_no_gk[,-c(3,4)], quali.sup=c(2), ind.sup=912, ncp = 79)
> distancesValbuena <-$ind$coord)
> distancesValbuena[912, ] <- mca_valbuena_distance$ind.sup$coord

> euclidianDistance <- function(x,y) {
 return( dist(rbind(x, y)) )

> distancesValbuena$distance_valbuena <- apply(distancesValbuena, 1, euclidianDistance, y=mca_valbuena_distance$ind.sup$coord)
> distancesValbuena <- distancesValbuena[order(distancesValbuena$distance_valbuena),]

> names_close_valbuena <- c("Mathieu Valbuena", row.names(distancesValbuena[2:6,]))

And we get: Ladislas Douniama, Frédéric Sammaritano, Florian Thauvin, N’Golo Kanté and Wissam Ben Yedder.

There would be so many other things to say about this data set but I think it’s time to wrap this (already very long) article up 😉 Keep in mind that this analysis should not be taken too seriously! It just aimed at giving a fun tutorial for students to discover R, FactoMineR and data analysis.