Nothing

```
mlm.spike <- function(subject.formula,
choice.formula = NULL,
niter,
data,
choice.name.separator = ".",
contrasts = NULL,
subset,
prior = NULL,
ping = niter / 10,
proposal.df = 3,
rwm.scale.factor = 1,
nthreads = 1,
mh.chunk.size = 10,
proposal.weights = c("DA" = .5, "RWM" = .25, "TIM" = .25),
seed = NULL,
...) {
## Spike and slab regression for multinomial logit models.
## Extensive details about the model and MCMC algorithm are
## supplied below.
##
## Args:
## subject.formula: A model formula for the portion of the model
## relating the response to the subject level predictors. The
## response variable in this formula must be coercible to a
## factor. If only subject level intercepts are desired the
## formula should look like 'y ~ 1`. If subject level
## intercepts are not desired then `y ~ 0`.
## choice.formula: An optional formula relating the response
## variable to choice level characteristics. The response
## variable should be the same as in subject.formula (though
## technically it can be omitted). The variable names used in
## the formula should omit the choice levels (which are a
## required part of the variable names in the 'data'
## argument). Thus the formula should be 'y ~ MPG + HP', not
## 'y ~ MPG.Honda + HP.Honda'.
## niter: The desired number of MCMC iterations.
## data: A data frame containing the data referenced in the
## 'subject.formula' and 'choice.formula' arguments. If
## 'choice.formula' is NULL then this argument is optional,
## and variables will be pulled from the parent environment if
## it is omitted. If 'choice.formula' is non-NULL, then
## 'data' must be supplied. A variable measuring a choice
## characteristic must be present for each choice level in the
## response variable. The stem for the variable names
## measuring the same concept must be identical, and choice
## level must be appended as a suffix, separated by a "."
## character. Thus, if 'HP' is a variable to be considered,
## and the response levels are 'Toyota', 'Honda', 'Chevy',
## then the data must contain variables named 'HP.Toyota',
## 'HP.Honda', and 'HP.Chevy', measuring HP for the different
## choices, whether they were chosen or not.
## choice.name.separator: The character used to separate the
## predictor names from the choice values for the choice-level
## predictor variables in 'data'.
## contrasts: An optional list indicating how contrasts and
## dummy variables are to be coded in the design matrix. See
## the contrasts.arg argument of 'model.matrix.default'.
## subset: an optional vector specifying a subset of
## observations to be used in the fitting process.
## prior: An object of class IndependentSpikeSlabPrior
## specifying the prior distribution of coefficient vector.
## See 'details' for more explanation about how the model
## is parameterized.
## ping: The frequency with which status updates are printed to
## the console. Measured in MCMC iterations.
## proposal.df: The tail thickness ("degress of freedom")
## parameter for the T distribution used to make
## Metropolis-Hastings proposals.
## rwm.scale.factor: A positive scalar. The scale factor
## applied to the asymptotic variance estimate for random walk
## Metropolis proposals. Larger values produce proposals with
## larger variances, which will be accepted less often, but
## which will produce larger jumps. Values between 0 and 1
## produce smaller jumps that will be accepted more often.
## nthreads: The number of threads to use during data
## augmentation. If the data size is very large then multiple
## threads can make data augmentation much faster, though they
## can actually slow things down in small problems.
## mh.chunk.size: The Metropolis-Hastings portions of the
## algorithm will operate on the model parameters a chunk at a
## time.
## proposal.weights: A vector of 3 probabilities (summing to 1)
## indicating the probability of each type of MH proposal
## during each iteration.
## seed: An integer to use as a seed for the C++ random number
## generator. If left NULL, the RNG will be seeded using the
## system clock.
## ...: Extra arguments passed to MultinomialLogitSpikeSlabPrior.
## These are ignored if 'prior' is non-NULL.
##
## Model details:
## A multinomial logit model has two sets of predictors: one measuring
## characterisitcs of the subject making the choice, and the other
## measuring characteristics of the items being chosen. The model
## can be written
##
## Pr(y[i] = m) \propto exp(beta.subject[, m] * x.subject[i, ]
## + beta.choice * x.choice[i, , m])
##
## The coefficients in this model are beta.subject and beta.choice.
## beta.choice is a subject.xdim by ('nchoices' - 1) matrix. Each row
## multiplies the design matrix produced by subject.formula for a
## particular choice level, where the first choice level is omitted
## (logically set to zero) for identifiability. beta.choice is a
## vector multiplying the design matrix produced by choice.formula,
## and thre are 'nchoices' of such matrices.
##
## The coefficient vector 'beta' is the concatenation
## c(beta.subject, beta.choice), where beta.subject is vectorized
## by stacking its columns (in the usual R fashion). This means
## that the first contiguous region of beta contains the
## subject-level coefficients for choice level 2.
##
## MCMC details:
## The MCMC algorithm randomly moves between three tyes of updates:
## data augmentation (DA), random walk Metropolis (RWM), and
## tailored independence Metropolis (TIM).
##
## * DA: Each observation in the model is associated with a set of
## latent variables that renders the complete data posterior
## distribution conditionally Gaussian. The augmentation scheme
## is described in Tuchler (2008). The data augmentation
## algorithm conditions on the latent data, and integrates out
## the coefficients, to sample the inclusion vector (i.e. the
## vector of indicators showing which coefficients are nonzero)
## using Gibbs sampling. Then the coefficients are sampled given
## complete data conditional on inclusion. This is the only move
## that attemps a dimension change.
##
## * RWM: A chunk of the coefficient vector (up to mh.chunk.size)
## is selected. The proposal distribution is either
## multivariate normal or multivariate T (depending on
## 'proposal.df') centered on current values of this chunk.
## The precision parameter of the normal (or T) is the negative
## Hessian of the un-normalized log posterior, evaluated at the
## current value. The precision is divided by
## rwm.scale.factor. Only coefficients currently included in
## the model at the time of the proposal will be modified.
##
## * TIM: A chunk of the coefficient vector (up to mh.chunk.size)
## is selected. The proposal distribution is constructed by
## locating the posterior mode (using the current value as a
## starting point). The proposal is a Gaussian (or
## multivariate T) centered on the posterior mode, with
## precision equal to the negative Hessian evaluated at the
## mode. This is an expensive, but effective step. If the
## posterior mode finding fails (for numerical reasons) then a
## RWM proposal will be attempted instead.
##
## Value:
## Returns an object of class mlm.spike, which is a list containing
## beta: A matrix containing the MCMC draws of the model
## coefficients. Rows in the matrix correspond to MCMC draws.
## Columns correspond to different coefficients.
## prior: The prior distribution used to fit the model.
## MH.accounting: A summary of the amount of time spent, successes
## and failures for each move type.
## Create the model matrix for the subject predictors.
function.call <- match.call(expand.dots = FALSE)
important.arguments <- match(c("subject.formula", "data", "subset"),
names(function.call),
0L)
subject.frame.call <- function.call[c(1L, important.arguments)]
subject.frame.call[[1L]] <- quote(stats::model.frame)
names(subject.frame.call)[2] <- "formula"
subject.frame.call[["drop.unused.levels"]] <- TRUE
subject.frame <- eval(subject.frame.call, parent.frame())
subject.terms <- attr(subject.frame, "terms")
subject.predictor.matrix <- model.matrix(subject.terms,
subject.frame,
contrasts)
response <- as.factor(model.response(subject.frame))
if (!is.factor(response)) {
stop("'", deparse(subject.formula[[2]]), "' is not a factor")
}
## Create the model matrix for the choice predictors.
choice.predictor.matrix <- NULL
choice.predictor.subject.id <- NULL
choice.predictor.choice.id <- NULL
response.levels <- levels(response)
if (!is.null(choice.formula)) {
if (missing(data)) {
stop("Choice predictors must be contained in a data frame ",
"passed by the 'data' argument.")
## TODO(figure out a way to support data in the parent.frame)
}
pattern <- paste0(choice.name.separator, response.levels, collapse = "|")
choice.predictor.names <- names(data)[grep(choice.name.separator, names(data), fixed = TRUE)]
long.data <- reshape(data,
varying = choice.predictor.names,
times = response.levels,
direction = "long",
sep = choice.name.separator)
names(long.data)[names(long.data) == "time"] <- "potential.choice"
important.arguments <- match(c("choice.formula", "data", "subset"),
names(function.call),
0L)
choice.frame.call <- function.call[c(1L, important.arguments)]
choice.frame.call[[1L]] <- quote(stats::model.frame)
names(choice.frame.call)[2] <- "formula"
choice.frame.call[["formula"]] <-
update(as.formula(choice.frame.call[["formula"]]), ~ . -1)
choice.frame.call[["data"]] <- quote(long.data)
subject.frame.call[["drop.unused.levels"]] <- TRUE
choice.frame <- eval(choice.frame.call)
choice.terms <- attr(choice.frame, "terms")
choice.predictor.matrix <- model.matrix(choice.terms, choice.frame, contrasts)
}
## Setup the prior.
if (is.null(prior)) {
prior <- MultinomialLogitSpikeSlabPrior(
response = response,
subject.x = subject.predictor.matrix,
choice.x = choice.predictor.matrix,
...)
}
stopifnot(inherits(prior, "IndependentSpikeSlabPrior"))
## Check the proposal weights.
stopifnot(is.numeric(proposal.weights))
stopifnot(length(proposal.weights) == 3)
if (any(proposal.weights < 0)) {
stop("You can't have a negative proposal weight.")
}
proposal.weights.sum <- sum(proposal.weights)
if (proposal.weights.sum <= 0) {
stop("At least one entry in proposal.weights must be positive.")
}
proposal.weights <- proposal.weights / proposal.weights.sum
proposal.weight.names <- names(proposal.weights)
if (!is.null(proposal.weight.names)) {
## If the proposal weights were given, be sure they are in the
## right order.
if (!all(c("DA", "RWM", "TIM") %in% proposal.weight.names)) {
stop("Proposal weight names should include 'DA', 'RWM', and 'TIM'.")
}
proposal.weights <- c("DA" = proposal.weights["DA"],
"RMW" = proposal.weights["RWM"],
"TIM" = proposal.weights["TIM"])
}
## Run the sampler.
ans<- .Call(analysis_common_r_multinomial_logit_spike_slab,
response,
subject.predictor.matrix,
choice.predictor.matrix,
choice.predictor.subject.id,
choice.predictor.choice.id,
prior,
niter,
ping,
proposal.df,
rwm.scale.factor,
nthreads,
mh.chunk.size,
proposal.weights,
seed)
ans$prior <- prior
subject.beta.names <- NULL
if (length(subject.predictor.matrix) > 0) {
subject.predictor.names <- colnames(subject.predictor.matrix)
subject.beta.names <- outer(subject.predictor.names,
response.levels[-1],
FUN = paste,
sep = ":")
}
choice.beta.names <- NULL
if (length(choice.predictor.matrix) > 0) {
choice.beta.names <- colnames(choice.predictor.matrix)
}
colnames(ans$beta) <- c(subject.beta.names, choice.beta.names)
class(ans) <- c("mlm.spike", "logit.spike", "lm.spike")
return(ans)
}
##======================================================================
MultinomialLogitSpikeSlabPrior <- function(
response,
subject.x,
expected.subject.model.size = 1,
choice.x = NULL,
expected.choice.model.size = 1,
max.flips = -1,
nchoices = length(levels(response)),
subject.dim = ifelse(is.null(subject.x), 0, ncol(subject.x)),
choice.dim = ifelse(is.null(choice.x), 0, ncol(choice.x))) {
## Build a prior distribution to be used with mlm.spike.
##
## Args:
## response: The response variable in the multinomial logistic
## regression. The response variable is optional if nchoices
## is supplied. If 'response' is provided then the prior
## means for the subject level intercpets will be chosen to
## match the empirical values of the response.
## subject.x: The design matrix for subject-level predictors.
## This can be NULL or of length 0 if no subject-level
## predictors are present.
## expected.subject.model.size: The expected number of non-zero
## coefficients -- per choice level -- in the subject specific
## portion of the model. All coefficients can be forced into
## the model by setting this to a negative number, or by setting
## it to be larger than the dimension of the subject-level
## predictors.
## choice.x: The design matrix for choice-level predictors. Each
## row of this matrix represents the characteristics of a choice
## in a choice occasion, so it takes 'nchoices' rows to encode
## one observation. This can be NULL or of length 0 if no
## choice-level predictors are present.
## expected.choice.model.size: The expected number of non-zero
## coefficients in the choice-specific portion of the model.
## All choice coefficients can be forced into the model by
## setting this to a negative number, or by setting it to be
## larger than the dimension of the choice-level predictors (for
## a single response level).
## max.flips: The maximum number of variable inclusion indicators
## the sampler will attempt to sample each iteration. If negative
## then all indicators will be sampled.
## nchoices: Tne number of potential response levels.
## subject.dim: The number of potential predictors in the
## subject-specific portion of the model.
## choice.dim: The number of potential predictors in the
## choice-specific portion of the model.
##
## Returns:
## An object of class IndependentSpikeSlabPrior, with elements
## arranged as expected by mlm.spike.
subject.beta.dim <- (nchoices - 1) * subject.dim
##-------- Build prior.inclusion.probabilities ---------
if (expected.subject.model.size > subject.dim
|| expected.subject.model.size < 0) {
subject.prior.inclusion.probabilities <- rep(1, subject.beta.dim)
expected.subject.model.size <- (nchoices - 1) * subject.dim
} else {
subject.prior.inclusion.probabilities <-
rep(expected.subject.model.size / subject.dim, subject.beta.dim)
}
choice.prior.inclusion.probabilities <- numeric(0)
if (choice.dim > 0) {
if (expected.choice.model.size >= choice.dim
|| expected.choice.model.size < 0) {
choice.prior.inclusion.probabilities <- rep(1, choice.dim)
expected.choice.model.size <- choice.dim
} else {
choice.prior.inclusion.probabilities <-
rep(expected.choice.model.size / choice.dim, choice.dim)
}
}
prior.inclusion.probabilities <- c(subject.prior.inclusion.probabilities,
choice.prior.inclusion.probabilities)
##------ Build prior.mean --------
subject.prior.mean <- matrix(0, nrow = subject.dim, ncol = nchoices - 1)
choice.prior.mean <- rep(0, choice.dim)
subject.intercept <- FALSE
if (!missing(response) &&
!is.null(subject.x) &&
all.equal(subject.x[, 1],
rep(1, nrow(subject.x)),
check.attributes = FALSE) == TRUE) {
## If the response was supplied and the model has subject level
## intercepts, set the intercept prior means to correspond to
## the MAP estimate under a Jeffreys prior. That is, add 1
## prior observation, evenly split among all levels.
subject.intercept <- TRUE
response.table <- table(response)
response.table <- response.table + 1.0 / length(response.table)
intercept.map.estimate <- response.table / length(response)
logits <- log(intercept.map.estimate / intercept.map.estimate[1])
subject.prior.mean[1, ] <- logits[-1]
}
prior.mean <- c(subject.prior.mean, choice.prior.mean)
##------- Build prior.variance
subject.prior.beta.sd <- numeric(0)
choice.prior.beta.sd <- numeric(0)
if (!is.null(subject.x)) {
subject.x.sd <- sqrt(apply(subject.x, 2, var))
if (subject.intercept) {
subject.x.sd[1] <- 1
}
## The prior is that the total variation in X * beta is something
## like -6..6, so the variance of X * beta is 4, and the variance of
## each x[i] * beta[i] will be 4 / (expected.model.size)
subject.prior.beta.sd <- 2 / (subject.x.sd * expected.subject.model.size)
subject.prior.beta.sd <- rep(subject.prior.beta.sd, nchoices - 1)
}
if (!is.null(choice.x)) {
choice.x.sd <- sqrt(apply(choice.x, 2, var))
choice.prior.beta.sd <- 2 / (choice.x.sd * expected.choice.model.size)
}
prior.beta.sd <- c(subject.prior.beta.sd, choice.prior.beta.sd)
ans <- IndependentSpikeSlabPrior(
prior.inclusion.probabilities = prior.inclusion.probabilities,
optional.coefficient.estimate = prior.mean,
prior.beta.sd = prior.beta.sd,
sdy = 1,
mean.y = 1,
expected.r2 = .5,
prior.df = 1,
number.of.observations = 0,
number.of.variables = length(prior.mean),
sdx = 1)
ans$max.flips <- max.flips
## TODO(stevescott): should we give this object its own class, and
## keep the choice/subject information separate?
return(ans)
}
```

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