Ready-to-hand Dean Eckles on people, technology & inference

The Atlantic reports on the data deluge and its value for innovation.¹ I particularly liked how Erik Brynjolfsson and Andrew McAfee, who wrote the Atlantic piece, highlight the value of experimentation for addressing causal questions — and that many of the questions we care about are causal.²

In writing about experimentation, they report that Hal Varian, Google’s Chief Economist, estimates that Google runs “100-200 experiments on any given day”. This struck me as incredibly low! I would have guessed more like 10,000 or maybe more like 100,000.

The trick of course is how one individuates experiments. Say Google has an automatic procedure whereby each ad has a (small) random set of users who are prevented from seeing it and are shown the next best ad instead. Is this one giant experiment? Or one experiment for each ad?

This is a bit of a silly question.³

But when most people — even statisticians and scientists — think of an experiment in this context, they think of something like Google or Amazon making a particular button bigger. (Maybe somebody thought making that button bigger would improve a particular metric.) They likely don’t think of automatically generating an experiment for every button, such that a random sample see that particular button slightly bigger. It’s these latter kinds of procedures that lead to thinking about tens of thousands of experiments.

That’s the real deluge of experiments.

1. I don’t know that I would call much of it ‘innovation’. There is some outright innovation, but a lot of that is in the general strategies for using the data. There is much more gained in minor tweaking and optimization of products and services. [↩]
2. Perhaps they even overstate the power of simple experiments. For example, they do not mention the fact that many times the results these kinds of experiments often change over time, so that what you learned 2 months ago is no longer true. [↩]
3. Note that two single-factor experiments over the same population with independent random assignment can be regarded as a single experiment with two factors. [↩]

Sometimes an approximate method is in some important sense better than the “exact” one — and not just because it is easier or faster.

In statistical inference, a standard example here is the Agresti-Coull confidence interval for a binomial proportion: the “exact” interval from inverting the binomial test is conservative — giving overly wide intervals with more than the advertised coverage — but the standard (approximate) Wald interval is too narrow.¹ The Agresti-Coull confidence interval, which is a modification of the Wald interval that can be justified on Bayesian grounds, has better performance than either.²

Even knowing this, like many people I suspect, I am a sucker for the “exact” over the approximate. The rest of this post gives another example of “approximate is better than exact” that Art Owen and I recently encountered in our work on bootstrapping big data with multiple dependencies.

The bootstrap is a computational method for estimating the sampling uncertainty of a statistics.³ When using bootstrap resampling or bagging, one normally draws observations without replacement from the sample to form a bootstrap replicate. Each replicate then consists of zero or more copies of each observation. If one wants to bootstrap online — that is, one observation at a time — or generally without synchronization costs in a distributed processing setting, machine learning folks have used the Poisson approximation to the binomial. This approximate bootstrap works as follows: for each observation in the sample, take a Poisson(1) draw and include that many of that observation in this replicate.

Since this is a “lossy” approximation, investigators have sometimes considered and advocated “lossless” alternatives (Lee & Clyde, 2004). The Bayesian bootstrap, in which each replicate is a n-dimensional draw from the Dirichlet, can be done exactly online: for each observation, take a Exp(1) draw and use it as the weight for that observation for this replicate.⁴ Being a sucker for methods labeled “lossless” or “exact”, I implemented this method in Hive at Facebook, and used it instead of the already available Poisson method. I even chortled to others, “Now we have an exact version implemented to use instead!”

But is this the best of all possible distributions for bootstrap reweighting? Might there be some other, better distribution (with mean 1 and variance 1)? In particular, what distribution minimizes our uncertainty about the variance of the mean, given the same number of bootstrap replicates?

We examined this question (Owen and Eckles, 2011, section 3.3) and found that the Poisson(1) weights give a sharper estimate of the variance than the Exp(1) weights: the lossy approximation to the standard resampling bootstrap is better than the exact Bayesian reweighting bootstrap. Interestingly, both of these are beat by using “double-or-nothing” U{0, 2} weights — that is, something close to half-sampling.⁵ Furthermore, the Poisson(1) and U{0, 2} versions are more general, since they don’t require using weighting (observations can duplicated) and, when using them as weights, they don’t require using floating point numbers.⁶

1. The Wald interval also gives zero-width intervals when observations are all either y=1 or y=0. [↩]
2. That is, it contains the true value closer to 100 * (1 – alpha)% of the time than the others. This example is a favorite of Art Owen’s. [↩]
3. Hesterberg et al. (PDF) is a good introduction to the bootstrap. Efron (1979) is the first paper on the bootstrap. [↩]
4. In what sense is this “exact” or “lossless”? This online method is exactly the same as the offline Bayesian bootstrap in which one takes a n-dimensional draw from the Dirichlet. On the other hand, the Poisson(1) method is often seen as an online approximation to the offline bootstrap. [↩]
5. Why is this? See the paper, but the summary is that U{0, 2} has the lowest kurtosis, and Poisson(1) has lower kurtosis than Exp(1). [↩]
6. This is especially useful if one is doing factorial weighting, as we do in the paper, where multiplication of weights for different grouping factors is required. [↩]

Some comments on problems with investigating psychological processes using estimates of average (i.e. marginal) effects. Hence the play on words in the title.

Social psychology makes a lot of being theoretical. This generally means not just demonstrating an effect, but providing evidence about the psychological processes that produce it. Psychological processes are, it is agreed, intra-individual processes. To tell a story about a psychological process is to posit something going on “inside” people. It is quite reasonable that this is how social psychology should work — and it makes it consistent with much of cognitive psychology as well.

But the evidence that social psychology uses to support these theories about these intra-individual processes is largely evidence about effects of experimental conditions (or, worse, non-manipulated measures) averaged across many participants. That is, it is using estimates of marginal effects as evidence of conditional effects. This is intuitively problematic. Now, there is no problem when using experiments to study effects and processes that are homogenous in the population. But, of course, they aren’t: heterogeneity abounds. There is variation in how factors affect different people. This is why the causal inference literature has emphasized the differences among the average treatment effect, (average) treatment effect on the treated, local average treatment effect, etc.

Not only is this disconnect between marginal evidence and conditional theory trouble in the abstract, we know it has already produced many problems in the social psychology literature.¹ Baron and Kenny (1986) is the most cited paper published in the Journal of Personality and Social Psychology, the leading journal in the field. It paints an rosy picture of what it is like to investigate psychological processes. The methods of analysis it proposes for investigating processes are almost ubiquitous in social psych.² The trouble is that this approach is severely biased in the face of heterogeneity in the processes under study. This is usually described as problem of correlated error terms, omitted-variables bias, or adjusting for post-treatment variables. This is all true. But, in the most common uses, it is perhaps more natural to think of it as a problem of mixing up marginal (i.e. average) and conditional effects.³

What’s the solution? First, it is worth saying that average effects are worth investigating! Especially if you are evaluating a intervention or drug that might really be used — or if you are working at another level of analysis than psychology. But if psychological processes are your thing, you must do better.

Social psychologists sometimes do condition on individual characteristics, but often this is a measure of a single trait (e.g., need for cognition) that cannot plausibly exhaust all (or even much) of the heterogeneity in the effects under study. Without much larger studies, they cannot condition on more characteristics because of estimation problems (too many parameters for their N). So there is bound to be substantial heterogeneity.

Beyond this, I think social psychology could benefit from a lot more within-subjects experiments. Modern statistical computing (e.g., tools for fitting mixed-effects or multilevel models) makes it possible — even easy — to use such data to estimate effects of the manipulated factors for each participant. If they want to make credible claims about processes, then within-subjects designs — likely with many measurements of each person — are a good direction to more thoroughly explore.

1. The situation is bad enough that I (and some colleagues) certainly don’t even take many results in social psych as more than providing a possibly interesting vocabulary. [↩]
2. Luckily, my sense is that they are waning a bit, partially because of illustrations of the method’s bias. [↩]
3. To translate to the terms used before, note that we want to condition on unobserved (latent) heterogeneity. If one doesn’t, then there is omitted variable bias. This can be done with models designed for this purpose, such as random effects models. [↩]

Psychologists have posited numerous psychological traits and described causal roles they ought to play in determining human behavior. Most often, the canonical measure of a trait is a questionnaire. Investigators obtain this measure for some people and analyze how their scores predict some outcomes of interest. For example, many people have been interested in how psychological traits affect persuasion processes. Traits like need for cognition (NFC) have been posited and questionnaire items developed to measure them. Among other things, NFC affects how people respond to messages with arguments for varying quality.

How useful are these traits for explanation, prediction, and adaptive interaction? I can’t address all of this here, but I want to sketch an argument for their irrelevance to adaptive interaction — and then offer a tentative rejoinder.

Interactive technologies can tailor their messages to the tastes and susceptibilities of the people interacting with and through them. It might seem that these traits should figure in the statistical models used to make these adaptive selections. After all, some of the possible messages fit for, e.g., coaching a person to meet their exercise goals are more likely to be effective for low NFC people than high NFC people, and vice versa. However, the standard questionnaire measures of NFC cannot often be obtained for most users — certainly not in commerce settings, and even people signing up for a mobile coaching service likely don’t want to answer pages of questions. On the other hand, some Internet and mobile services have other abundant data available about their users, which could perhaps be used to construct an alternative measure of these traits. The trait-based-adaptation recipe is:

1. obtain the questionnaire measure of the trait for a sample,
2. predict this measure with data available for many individuals (e.g., log data),
3. use this model to construct a measure for out-of-sample individuals.

This new measure could then be used to personalize the interactive experience based on this trait, such that if a version performs well (or poorly) for people with a particular score on the trait, then use (or don’t use) that version for people with similar scores.

But why involve the trait at all? Why not just personalize the interactive experience based on the responses of similar others? Since the new measure of the trait is just based on the available behavioral, demographic, and other logged data, one could simply predict responses based on those measure. Put in geometric terms, if the goal is to project the effects of different message onto available log data, why should one project the questionnaire measure of the trait onto the available log data and then project the effects onto this projection? This seems especially unappealing if one doesn’t fully trust the questionnaire measure to be accurate or one can’t be sure about which the set of all the traits that make a (substantial) difference.

I find this argument quite intuitively appealing, and it seems to resonate with others.¹ But I think there are some reasons the recipe above could still be appealing.

One way to think about this recipe is as dimensionality reduction guided by theory about psychological traits. Available log data can often be used to construct countless predictors (or “features”, as the machine learning people call them). So one can very quickly get into a situation where the effective number of parameters for a full model predicting the effects of different messages is very large and will make for poor predictions. Nothing — no, not penalized regression, not even a support vector machine — makes this problem go away. Instead, one has to rely on the domain knowledge of the person constructing the predictors (i.e., doing the “feature engineering”) to pick some good ones.

So the tentative rejoinder is this: established psychological traits might often make good dimensions to predict effects of different version of a message, intervention, or experience with. And they may “come with” suggestions about what kinds of log data might serve as measures of them. They would be expected to be reusable across settings. Thus, I think this recipe is nonetheless deserves serious attention.

1. I owe some clarity on this to some conversations with Mike Nowak, Maurits Kaptein, and others. [↩]

Some reflections on how “quantitative” social psychology is and how this matters for its application to design and decision-making — especially in industries touched by the Internet.

In many ways, contemporary social psychology is dogmatically quantitative. Investigators run experiments, measure quantitative outcomes (even coding free responses to make them amenable to analysis), and use statistics to characterize the collected data. On the other hand, social psychology’s processes of stating and integrating its conclusions remain largely qualitative. Many hypotheses in social psychology state that some factor affects a process or outcome in one direction (i.e., “call” either beta > 0 or beta < 0). Reviews of research in social psychology often start with a simple effect and then note how many other variables moderate this effect. This is all quite fitting with the dominance of null-hypothesis significance testing (NHST) in much of psychology: rather than producing point estimates or confidence intervals for causal effects, it is enough to simply see how likely the observed data is given there there is no effect.¹ Of course, there have been many efforts to change this. Many journals require reporting effect sizes. This is a good thing, but these effect sizes are rarely predicted by social psychological theory. Rather, they are reported to aid judgments of whether a finding is not only statistically significant but substantively or practically significant, and the theory predicts the direction of the effect.

Not only is this process of reporting and combining results not quantitative in many ways, but it requires substantial inference from the particular settings of conducted experiments to the present settings. This actually helps to make sense of the practices described above: many social psychology experiments are conducted in conditions and with populations that are so different from those in which people would like to apply the resulting theories, that expecting consistency of effect sizes is implausible.² This is not to say that these studies cannot tell us a good deal about how people will behave in many circumstances. It's just that figuring out what they predict and whether these predictions are reliable is a very messy, qualitative process.

Thus, when it comes to making decisions -- about a policy, intervention, or service -- based on social-psychological research, this process is largely qualitative. Decision-makers can ask, which effects are in play? What is their direction? With interventions and measurement that are very likely different from the present case, how large were the effects?³

Sometimes this is the best that social science can provide. And such answers can be quite useful in design. The results of psychology experiments can often be very effective when used generatively. For example, designers can use taxonomies of persuasive strategies to dream up some ways of producing desired behavior change.

Nonetheless, I think all this can be contrasted with some alternative practices that are both more quantitative and require less of this uneasy generalization. First, social scientists can give much more attention to point estimates of parameters. While not without its (other) flaws, the economics literature on financial returns to education has aimed to provide, criticize, and refine estimates of just how much wages increase (on average) with more education.⁴

Second, researchers can avoid much of the messiest kinds of generalization altogether. Within the Internet industry, product optimization experiments are ubiquitous. Google, Yahoo, Facebook, Microsoft, and many others are running hundreds to thousands of simultaneous experiments with parts of their services. This greatly simplifies generalization: the exact intervention under consideration has just been tried with a random sample from the very population it will be applied to. If someone wants to tweak the intervention, just try it again before launching. This process still involves human judgment about how to react to these results.⁵ An even more extreme alternative is when machine learning is used to fine-tune, e.g., recommendations without direct involvement (or understanding) by humans.

So am I saying that social psychology — at least as an enterprise that is useful to designers and decision-makers — is going to be replaced by simple “bake-off” experiments and machine learning? Not quite. Unlike product managers at Google, many decision-makers don’t have the ability to cheaply test a proposed intervention on their population of interest.⁶ Even at Google, many changes (or new products) under consideration are too difficult to build to them all: one has to decide among an overabundance of options before the most directly applicable data could be available. This is consistent with my note above that social-psychological findings can make excellent inspiration during idea generation and early evaluation.

1. To parrot Andrew Gelman, in social phenomena, everything affects everything else. There are no betas that are exactly zero. [↩]
2. It's also often implausible that the direction of the effect must be preserved. [↩]
3. Major figures in social psychology, such as Lee Ross, have worked on trying to better anticipate the effects of social interventions from theory. It isn’t easy. [↩]
4. The diversity of the manipulations used by social psychologists ostensibly studying the same thing can make this more difficult. [↩]
5. Generalization is not avoided. In particular, decision-makers often have to consider what would happen if an intervention tested with 1% of the population is launched for the whole population. There are all kinds of issues relating to peer influence, network effects, congestion, etc., here that don’t allow for simple extrapolation from the treatment effects identified by the experiment. Nonetheless, these challenges obviously apply to most research that aims to predict the effects of causes. [↩]
6. However, Internet services play a more and more central role in many parts of our life, so this doesn’t just have to be limited to the Internet industry itself. [↩]