229 – Random Effect/Mixed Models
On the Reproducibility of Latent Variables
William D. Heavlin
Google Inc.
Latent variables are typically constructed to explain variance and optimize validity, then later refined to enhance reproducibility. Here we promote reproducibility to a first-order property. Our example uses the ratings of NFL quarterbacks. Emphasizing reproducibility corresponds to a shift in purpose - from describing recent passer performance to predicting its future level. The NFL passer rating is a weighted sum of four ratios: the numerators consist of counts of completed passes, yardage, touchdowns, and interceptions; the denominator is the number of attempted passes. Our objective function maximizes the correlation between past and future passer ratings by the choice of weights. At our disposal are two classes of weights: (a) weights on the four ratios and (b) weights on recent and less recent games. The algorithm itself we term Spokane, for symmetric, positive canonical correlation.