prob_multinomial: Calculate Probabilities from Multinomial Regression

In jmleach-bst/ssnet: Fit Spike-and-Slab Elastic Net GLM With Spatial Priors on Parameters

Calculate Probabilities from Multinomial Regression

Description

Uses design matrix and parameter estimates to calculate probabilities for each class for each subject.

Usage

prob_multinomial(x, b, a0, classify = TRUE)

Arguments

x	Design, or input, matrix, of dimension nobs x nvars; each row is an observation vector. It is recommended that x have user-defined column names for ease of identifying variables. If missing, then colnames are internally assigned x1, x2, ... and so forth.
b	A list whose elements are vectors of parameter estimates and whose names correspond to the values of y. If fitted.model is obtained from ssnet, then these estimates are stored in fitted.model$coefficients.
a0	A matrix of with nrow equal the number of class and a single column containing the intercept estimates for each class. If fitted.model is obtained from ssnet, then these estimates are stored in fitted.model$a0. Note that the row names should correspond to the class labels from y.
classify	Logical. When TRUE (default), appends a column containing the class with the largest predicted probability.

Details

The parameterization employed here is as in Friedman (2010), i.e., over-parameterized, which under the elastic net penalty allows for unique parameter estimates. Thus, there is not a reference class, but each class has an associated set of parameter estimates. Probabilities are then obtained by Pr(Y_i = k | X_i) = \exp(X_i^T B_k) / \sum_{v=1}^V \exp(X_i^T B_v) where X_i is a the design matrix for subject i, V is the number of classes, and B_v is the vector of parameters associated with class v.

Value

A data frame where each column contains predicted class probabilities for each subject.

References

\insertRef

Friedman:2010ssnet

Examples

x <- matrix(rnorm(10*5), nrow = 10, ncol = 5)
colnames(x) <- paste0("x", seq_len(ncol(x)))
x0 <- cbind(x0 = 1, x)
b <- list(a = runif(5), b = runif(5), c = runif(5))
for (i in seq_len(length(b))) {
    names(b[[i]]) <- colnames(x)
}
a0 <- matrix(runif(3), nrow = 3, ncol= 1)
prob_multinomial(x = x, b = b, a0 = a0)

jmleach-bst/ssnet documentation built on March 4, 2024, 5:04 p.m.