In a previous article, we showed the use of partial pooling, or hierarchical/multilevel models, for level coding high-cardinality categorical variables in vtreat. In this article, we will discuss a little more about the how and why of partial pooling in R.
We will use the lme4 package to fit the hierarchical models. The acronym “lme” stands for “linear mixed-effects” models: models that combine so-called “fixed effects” and “random effects” in a single (generalized) linear model. The lme4 documentation uses the random/fixed effects terminology, but we are going to follow Gelman and Hill, and avoid the use of the terms “fixed” and “random” effects.
The varying coefficients [corresponding to the levels of a categorical variable] in a multilevel model are sometimes called random effects, a term that refers to the randomness in the probability model for the group-level coefficients….
The term fixed effects is used in contrast to random effects – but not in a consistent way! … Because of the conflicting definitions and advice, we will avoid the terms “fixed” and “random” entirely, and focus on the description of the model itself…
– Gelman and Hill 2007, Chapter 11.4
We will also restrict ourselves to the case that vtreat considers: partially pooled estimates of conditional group expectations, with no other predictors considered.
One of the services that the R package vtreat provides is level coding (what we sometimes call impact coding): converting the levels of a categorical variable to a meaningful and concise single numeric variable, rather than coding them as indicator variables (AKA "one-hot encoding"). Level coding can be computationally and statistically preferable to one-hot encoding for variables that have an extremely large number of possible levels.
By default, vtreat level codes to the difference between the conditional means and the grand mean (catN variables) when the outcome is numeric, and to the difference between the conditional log-likelihood and global log-likelihood of the target class (catB variables) when the outcome is categorical. These aren’t the only possible level codings. For example, the ranger package can encode categorical variables as ordinals, sorted by the conditional expectations/means. While this is not a completely faithful encoding for all possible models (it is not completely faithful for linear or logistic regression, for example), it is often invertible for tree-based methods, and has the advantage of keeping the original levels distinct, which impact coding may not. That is, two levels with the same conditional expectation would be conflated by vtreat‘s coding. This often isn’t a problem — but sometimes, it may be.
So the data scientist may want to use a level coding different from what vtreat defaults to. In this article, we will demonstrate how to implement custom level encoders in vtreat. We assume you are familiar with the basics of vtreat: the types of derived variables, how to create and apply a treatment plan, etc.
The R package seplyr has a neat new feature: the function seplyr::expand_expr() which implements what we call “the string algebra” or string expression interpolation. The function takes an expression of mixed terms, including: variables referring to names, quoted strings, and general expression terms. It then “de-quotes” all of the variables referring to quoted strings and “dereferences” variables thought to be referring to names. The entire expression is then returned as a single string.
The development version of my new R package seplyr is performing in practical applications with dplyr0.7.*much better than even I (the seplyr package author) expected.
I think I have hit a very good set of trade-offs, and I have now spent significant time creating documentation and examples.
I wish there had been such a package weeks ago, and that I had started using this approach in my own client work at that time. If you are already a dplyr user I strongly suggest trying seplyr in your own analysis projects.
vtreat is an Rdata.frame processor/conditioner that prepares real-world data for predictive modeling in a statistically sound manner. It prepares variables so that data has fewer exceptional cases, making it easier to safely use models in production. Common problems vtreat defends against include: infinity, NA, too many categorical levels, rare categorical levels, and new categorical levels (levels seen during application, but not during training). vtreat::prepare should be your first choice for real world data preparation and cleaning.
Nina Zumelrecently mentioned the use of Laplace noise in “count codes” by Misha Bilenko (see here and here) as a known method to break the overfit bias that comes from using the same data to design impact codes and fit a next level model. It is a fascinating method inspired by differential privacy methods, that Nina and I respect but don’t actually use in production.
Nina Zumel introduced y-aware scaling in her recent article Principal Components Regression, Pt. 2: Y-Aware Methods. I really encourage you to read the article and add the technique to your repertoire. The method combines well with other methods and can drive better predictive modeling results.
From feedback I am not sure everybody noticed that in addition to being easy and effective, the method is actually novel (we haven’t yet found an academic reference to it or seen it already in use after visiting numerous clients). Likely it has been applied before (as it is a simple method), but it is not currently considered a standard method (something we would like to change).