ohenery (version 0.1.3)

harsmfit: Experts only softmax regression under Harville model.

Description

An “experts only” softmax fitting function for the Harville model.

Usage

harsmfit(
  y,
  g,
  X,
  wt = NULL,
  eta0 = NULL,
  beta0 = NULL,
  normalize_wt = FALSE,
  method = c("BFGS", "NR", "CG", "NM")
)

Value

An object of class harsm, maxLik, and linodds.

Arguments

y

a vector of the ranked outcomes within each group. Only the order within a group matters.

g

a vector giving the group indices. Need not be integers, but that is more efficient. Need not be sorted. Must be the same length as y.

X

a matrix of the independent variables. Must have as many rows as the length of y.

wt

an optional vector of the observation level weights. These must be non-negative, otherwise an error is thrown. Note that the weight of the last ranked outcome within a group is essentially ignored. Must be the same length as y.

eta0

an optional vector of the consensus odds. These are added to the fit odds in odds space before the likelihood caclulation. If given, then when the model is used to predict, similar consensus odds must be given. Must be the same length as y.

beta0

an optional vector of the initial estimate of beta for ‘warm start’ of the estimation procedure. Must be the same length as number of columns in X. Should only affect the speed of the computation, not the results. Defaults to all zeroes.

normalize_wt

if TRUE, we renormalize wt, if given, to have mean value 1. Note that the default value has changed since version 0.1.0 of this package. Moreover, non-normalized weights can lead to incorrect inference. Use with caution.

method

maximisation method, currently either "NR" (for Newton-Raphson), "BFGS" (for Broyden-Fletcher-Goldfarb-Shanno), "BFGSR" (for the BFGS algorithm implemented in R), "BHHH" (for Berndt-Hall-Hall-Hausman), "SANN" (for Simulated ANNealing), "CG" (for Conjugate Gradients), or "NM" (for Nelder-Mead). Lower-case letters (such as "nr" for Newton-Raphson) are allowed. The default method is "NR" for unconstrained problems, and "NM" or "BFGS" for constrained problems, depending on if the grad argument was provided. "BHHH" is a good alternative given the likelihood is returned observation-wise (see maxBHHH).

Note that stochastic gradient ascent (SGA) is currently not supported as this method seems to be rarely used for maximum likelihood estimation.

Author

Steven E. Pav

Details

Given a number of events, indexed by group, and a vector \(y\) of the ranks of each entry within that group, perform maximum likelihood estimation under the softmax and proportional probability model.

The user can optionally supply a vector of \(\eta_0\), which are taken as the fixed, or ‘consensus’ odds. The estimation is then conditional on these fixed odds.

Weighted estimation is supported.

The code relies on the likelihood function of harsmlik, and MLE code from maxLik.

References

Harville, D. A. "Assigning probabilities to the outcomes of multi-entry competitions." Journal of the American Statistical Association 68, no. 342 (1973): 312-316. tools:::Rd_expr_doi("10.1080/01621459.1973.10482425")

See Also

the likelihood function, harsmlik, and the expected rank function (the inverse link), erank.

Examples

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
y <- rsm(eta,g)
     
mod0 <- harsmfit(y=y,g=g,X=X)
summary(mod0)
# now upweight finishers 1-5
modw <- harsmfit(y=y,g=g,X=X,wt=1 + as.numeric(y < 6))
summary(modw)