plot.npmr: Visualize the regression coefficient matrix fit by cross-validated NPMR

Description

Plots features (in orange) by their weights on the first two latent variables in the singular value decomposition of the regression coefficient matrix. Plots response classes (as blue arrows) by their loadings on the first two latent variables. Does this for the regression coefficient matrix fit with the value of lambda closest among all those tried to the value of lambda specified.

Usage

# S3 method for npmr
plot(x, lambda, feature.names = TRUE, ...)

Arguments

x: an object of class npmr
lambda: a single regularization parameter value
feature.names: logical. Should the names of the covariates be used in the plot? If FALSE, use standard plotting symbol (pch=1) instead.
...: additional arguments to be passed to plot

Author

Scott Powers, Trevor Hastie, Rob Tibshirani

References

Scott Powers, Trevor Hastie and Rob Tibshirani (2016). ``Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball.'' In prep.

Examples

Run this code

#   Fit NPMR to simulated data

K = 5
n = 1000
m = 10000
p = 10
r = 2

# Simulated training data
set.seed(8369)
A = matrix(rnorm(p*r), p, r)
C = matrix(rnorm(K*r), K, r)
B = tcrossprod(A, C)            # low-rank coefficient matrix
X = matrix(rnorm(n*p), n, p)    # covariate matrix with iid Gaussian entries
eta = X 
P = exp(eta)/rowSums(exp(eta))
Y = t(apply(P, 1, rmultinom, n = 1, size = 1))

# Simulate test data
Xtest = matrix(rnorm(m*p), m, p)
etatest = Xtest 
Ptest = exp(etatest)/rowSums(exp(etatest))
Ytest = t(apply(Ptest, 1, rmultinom, n = 1, size = 1))

# Fit NPMR for a sequence of lambda values without CV:
fit2 = npmr(X, Y, lambda = exp(seq(7, -2)))

# Produce a biplot:
plot(fit2, lambda = 20)