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Many regression-like statistical methods use the general approach of mapping from a set of 'raw', actually observed variables to a larger set of variables that are the actual space of inputs to the regression, via (for example)

  • basis expansion ([orthogonal] polynomial, spline, etc.)
  • conversion of categorical variables to dummy variables according to some contrast scheme

For example, if I started with a Wilkinson-Rogers/R formula ~ poly(x,2) + f (where x is numeric and f is a factor/categorical variable),

  1. x and f would be my [???] variables
  2. (Intercept), poly(x, 2)1, poly(x, 2)2, fB (the columns of my model matrix) would be my [???] variables

I have a vague memory that I've used "input" for #1 and "predictor" for #2 in the past, but I don't know where I got that from or whether I've gotten it reversed from the original source. Can anyone point me to clear/useful/established terminology that distinguishes between these two types of (covariates/features/(independent|explanatory|predictor) variables) ?

(Slightly related to Regression terminology, predictor vs IV vs?)

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From Schielzeth 2010 Methods in Ecology and Evolution ("Simple means to improve the interpretability of regression models"):

Throughout the paper, I will make an important distinction between input variables and predictors. Input variable are the variables that were measured (possibly transformed), while predictors are the terms that are entered in the model (Gelman & Hill 2007). Hence, predictors encompass the main effects, but also polynomials of input variables and interaction terms.

And ultimately from Gelman and Hill 2007 Applied Regression Modeling (via Google Books), p. 37:

We refer to the $X$-variables in the regression as predictors or "predictor variables" ... we use the term inputs for the information on the units that goes into the $X$-variables. Inputs are not the same as predictors. For example, consider the model that includes the interaction of maternal education and maternal IQ:

$$ \textrm{kid.score} = 58 + 16 \cdot \textrm{mom.hs} + 0.5 \cdot \textrm{mom.iq} - 0.2 \cdot \textrm{mom.hs} \cdot \textrm{mom.iq} + \textrm{error} $$

This regression has four predictors — maternal high school, maternal IQ, maternal high.school × IQ, and the constant term — but only two inputs, maternal education and IQ.

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