hensm: Friendly interface to softmax regression under Henery model.

Description

A user friendly interface to the softmax regression under the Henery model.

Usage

hensm(formula, data, group = NULL, weights = NULL, ngamma = 4,
  na.action = na.omit)
# S3 method for hensm
vcov(object, ...)
# S3 method for hensm
print(x, ...)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

group

the string name of the group variable in the data, or a bare character with the group name. The group indices need not be integers, but that is more efficient. They need not be sorted.

weights

an optional vector of weights, or the string or bare name of the weights in the data for use in the fitting process. The weights are attached to the outcomes, not the participant. Set to NULL for none.

ngamma

The number of gammas to fit. Should be at least 2.

na.action

How to deal with missing values in y, g, X, wt, eta0.

object

an object of class hensm.

...

additional arguments to be passed to the low level regression fitting functions (see below).

logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response, the QR decomposition) are returned.

Value

An object of class hensm, but also of maxLik with the fit.

Details

Performs a softmax regression by groups, via Maximum Likelihood Estimation. It is assumed that successive sub-races maintain the proportional probability of the softmax, up to some gamma coefficients, \(\gamma_2, \gamma_3, ..., \gamma_n\), which we fit. This model nests the Harville model fit by harsm, by fixing all the gammas equal to 1.

Examples

Run this code

# NOT RUN {
nfeat <- 5
set.seed(1234)
g <- ceiling(seq(0.1,1000,by=0.1))
X <- matrix(rnorm(length(g) * nfeat),ncol=nfeat)
beta <- rnorm(nfeat)
eta <- X %*% beta
# 2FIX: do rhenery
y <- rsm(eta,g)
# now the pretty frontend
data <- cbind(data.frame(outcome=y,race=g),as.data.frame(X))

fmla <- outcome ~ V1 + V2 + V3 + V4 + V5
fitm <- hensm(fmla,data,group=race)

# with offset
eta0 <- rowMeans(X)
data <- cbind(data.frame(outcome=y,race=g,eta0=eta0),as.data.frame(X))
fmla <- outcome ~ offset(eta0) + V1 + V2 + V3 + V4 + V5
fitm <- hensm(fmla,data,group=race)

# on horse race data
library(dplyr)
data(race_data)
df <- race_data %>%
	group_by(EventId) %>%
		mutate(eta0=log(WN_pool / sum(WN_pool))) %>%
	ungroup() %>%
	mutate(weights=ifelse(!is.na(Finish),1,0)) %>%
	mutate(fac_age=cut(Age,c(0,3,5,7,Inf),include.lowest=TRUE)) 

# Henery Model with market efficiency
hensm(Finish ~ eta0,data=df,group=EventId,weights=weights,ngamma=3)

# look for age effect not captured by consensus odds.
hensm(Finish ~ offset(eta0) + fac_age,data=df,group=EventId,weights=weights,ngamma=2)


# }