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TimS comments on Regression To The Mean [Draft][Request for Feedback] - Less Wrong
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Comments (13)
I don't see the relationship between positive reinforcement and regression to the mean. As discussed in this post, positive reinforcement increases the frequency of a particular behavior, not the quality of the behavior. By contrast, regression to the mean tells us facts about the quality of future behavior, not the quantity.
Concretely, I reward my son for voiding in the potty to increase the frequency that he voids in the potty. (Sorry, potty training is on the mind). But I'm not sure what a quality measure would look like in this circumstance. By contrast, we can imagine a soccer goalkeeper who allows no goals for an entire season. Regression to the mean strongly suggests he won't achieve that feat next season. But what behavior is becoming more or less frequent?
I'm not saying that there's no insight in the convergence of the two concepts. But the current draft suggests a conflict that is not clearly demonstrated.
Regression to the mean can work with non-contious variables. Sticking with the potty training example call using the toilet properly a 1 and failing to use it properly a 0. If a baby has a a fairly stable tendency to use the toilet 3 out of 4 time that the situation comes up the baby would have a mean of .75. If you observe a 0 from the baby you should expect the next time to be closer to the mean, which would mean a 1.
Increasingly unrelated to the OP... you could certainly introduce a quality measure to your son's potty training, if you wanted. For example, you could differentially reward for latency, or for predictable schedules, or for whistling more tunefully while sitting on the toilet, or whatever quality standards you wished to impose.
There still wouldn't be any particular relationship to regression to the mean, though.
That's a good point. Reinforcement is pretty narrowly focused on the individual. By contrast, regression to the mean makes a lot more sense if there is a population of data (the rate of goals allowed by other goalkeepers this season or by the specified goalkeeper in prior seasons - but my example is rapidly going to become less useful because of endpoint issues - there's no way to allow fewer than zero goals per season).
I believe that's what he was trying to address by discussing the "random component" - he omits the opposing nonrandom and controllable component. The only situation I was able to find to match this bias was in the workplace, where working harder can compensate for random components to a limited extent, but not sufficiently to erase variability altogether.
Which I guess is what should be emphasized - the distinction between the random and the nonrandom component, and their apparent convergence.