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#' Multinomial Prediction Function (Observed Value Approach)
#'
#' This function predicts probabilities for all choices of a multinomial logit
#' model over a specified span of values.
#'
#' @param model the multinomial model, from a \code{\link{multinom}}()-function call (see the \code{\link{nnet}} package)
#' @param data the data with which the model was estimated
#' @param x the name of the variable that should be varied (the x-axis variable in prediction plots)
#' @param z if you want to hold a specific variable stable over all scenarios, you can name it here (optional).
#' @param z_value determine at which value you want to fix the \code{z}.
#' @param xvari former argument for \code{x} (deprecated).
#' @param scenname former argument for \code{z} (deprecated).
#' @param scenvalue former argument for \code{z_value} (deprecated).
#' @param by define the steps of \code{x}.
#' @param nsim numbers of simulations
#' @param seed set a seed for replication purposes.
#' @param probs a vector with two numbers, defining the significance levels. Default to 5\% significance level: \code{c(0.025, 0.975)}
#'
#' @return The function returns a list with several elements. Most importantly the list includes the simulated draws `S`, the simulated predictions `P`, and a data set for plotting `plotdata`.
#' @export
#'
#' @examples
#' library(nnet)
#' library(MASS)
#'
#' dataset <- data.frame(y = c(rep("a", 10), rep("b", 10), rep("c", 10)),
#' x1 = rnorm(30),
#' x2 = rnorm(30, mean = 1),
#' x3 = sample(1:10, 30, replace = TRUE))
#'
#' mod <- multinom(y ~ x1 + x2 + x3, data = dataset, Hess = TRUE)
#'
#' pred <- mnl_pred_ova(model = mod, data = dataset,
#' x = "x1",
#' nsim = 10)
#'
#'
#' @importFrom stats coef na.omit quantile
#' @importFrom utils setTxtProgressBar txtProgressBar
#' @importFrom MASS mvrnorm
mnl_pred_ova <- function(model,
data,
x,
by = NULL,
z = NULL,
z_value = NULL,
xvari,
scenname,
scenvalue,
nsim = 1000,
seed = "random",
probs = c(0.025, 0.975)){
# Create list that is returned in the end.
output <- list()
# Warnings for deprecated arguments
if (!missing(xvari)) {
warning("The argument 'xvari' is deprecated; please use 'x' instead.\n\n",
call. = FALSE)
x <- xvari
}
if (!missing(scenname)) {
warning("The argument 'scenname' is deprecated; please use 'z' instead.\n\n",
call. = FALSE)
z <- scenname
}
if (!missing(scenvalue)) {
warning("The argument 'scenvalue' is deprecated; please use 'z_value' instead.\n\n",
call. = FALSE)
z_value <- scenvalue
}
# Errors:
if (is.null(model) == TRUE) {
stop("Please supply a model")
}
if (sum(grepl("multinom", model$call)) == 0) {
stop("Please supply a multinom()-model")
}
if (is.null(data) == TRUE) {
stop("Please supply a data set")
}
if (is.null(x) == TRUE | is.character(x) == FALSE) {
stop("Please supply a character string of your x-variable of interest")
}
if (is.null(model$Hessian) == TRUE) {
stop("There is no Hessian matrix. Please specify Hess = TRUE in your multinom() call.")
}
# Names of variables in model (without the "list" character in the vector)
variables <- as.character(attr(model$terms, "variables"))[-1]
if(!(x %in% variables) == TRUE){
stop("x-variable is not an independent variable in the model. There might be a typo.")
}
# Check if scenario is supplied correctly
if (is.null(z) == FALSE & is.character(z) == FALSE) {
stop("Please supply a character string of your scenario of interest")
}
if(is.null(z) == FALSE){
if (!(z %in% variables) == TRUE) {
stop("The scenario variable is not an independent variable in the model. There might be a typo.")
}
}
# > Handeling the IVs --------------------------------------------------------
# Name of independent variables
iv <- variables[2:length(variables)]
output[["IV"]] <- iv
# Variables have to be numeric
if (length(iv) > 1) {
if (sum(apply(data[, iv], 2, class) %in% c("numeric", "integer")) < ncol(data[, iv])) {
stop("Please supply data that consists of numeric values. The package can not handle factor or character variables, yet. For workarounds, please take a look at the github issues (https://github.com/ManuelNeumann/MNLpred/issues/1). The problem will hopefully be fixed with the 0.1.0 release.")
}
} else {
if (class(eval(parse(text = paste0("data$", iv)))) %in% c("numeric", "integer") == FALSE) {
stop("Please supply data that consists of numeric values. The package can not handle factor or character variables, yet. For workarounds, please take a look at the github issues (https://github.com/ManuelNeumann/MNLpred/issues/1). The problem will hopefully be fixed with the 0.1.0 release.")
}
}
# > Handeling the DVs --------------------------------------------------------
# Name of dependent variable
dv <- variables[1]
output[["DV"]] <- dv
# > Full observations (listwise deletion) ------------------------------------
data_redux <- na.omit(data[, c(dv, iv)])
# Number of full observations
obs <- nrow(data_redux)
output[["Observations"]] <- obs
# > Working with the model ---------------------------------------------------
# Get matrix of coefficients out of the model
coefmatrix <- coef(model)
# Number of coefficients
ncoef <- ncol(coefmatrix)
# Model coefficients as a vector
mu <- as.vector(t(coef(model)))
# Variance-covariance matrix of estimates
varcov <- solve(model$Hessian)
# Set seed if needed:
if (seed != "random") {
set.seed(seed = seed)
}
# Simulate a sampling distribution
S <- mvrnorm(nsim, mu, varcov)
output[["S"]] <- S
# Artificial variation of independent variable of interest (x)
if (is.null(by) == TRUE) {
by <- abs(min(eval(parse(text = paste0("data$", x))), na.rm = TRUE) -
max(eval(parse(text = paste0("data$", x))), na.rm = TRUE))
}
variation <- seq(from = min(eval(parse(text = paste0("data$", x))),
na.rm = TRUE),
to = max(eval(parse(text = paste0("data$", x))),
na.rm = TRUE),
by = by)
output[["Variation"]] <- variation
# Length of sequence
nseq <- length(variation)
if (nseq == 1) {
stop("Please supply a dataset or a x-variable with variation")
}
output[["nVariation"]] <- nseq
# Choice categories of the dependent variable
categories <- sort(unique(eval(parse(text = paste0("data$", dv)))))
J <- length(categories)
if (J < 3) {
stop("Please supply a dataset with a dependent variable that has a sufficient number of outcomes (> 2)")
}
output[["ChoiceCategories"]] <- categories
output[["nChoices"]] <- J
# Numbers of interactions
ninteraction <- sum(grepl(":", model$coefnames))
# Matrix of observations
X <- matrix(NA, ncol = ncoef, nrow = obs)
colnames(X) <- model$coefnames
# 1 for the Intercept
X[, 1] <- 1
# Values of the independent variables
X[, 2:(length(iv)+1)] <- as.matrix(data_redux[, iv])
# Prepare array to fill in the matrix with the observed values
ovacases <- array(NA, c(dim(X), nseq))
# Fill in the matrices:
ovacases[,,] <- X
# Select the position of the variable which should vary:
varidim <- which(colnames(X) == x)
# Artificially alter the variable in each dimension according to
# the preferred sequence:
for (i in 1:nseq) {
ovacases[, varidim, i] <- variation[i]
}
# Hold a second variable steady (if need be)
if(is.null(z) == FALSE) {
scendim <- which(colnames(X) == z)
for (i in 1:nseq) {
ovacases[, scendim, i] <- z_value
}
}
# Compute interactions:
if (ninteraction != 0) {
# Get position of interaction terms
interactionterms <- which(grepl(":", model$coefnames) == TRUE)
# Compute the terms:
for (i in c(interactionterms)) {
# First variable name of the interaction:
firstint <- gsub(":.*", "", model$coefnames[i])
# Second variable name of the interaction:
secondint <- gsub(".*:", "", model$coefnames[i])
# Get position in matrix:
intdim1 <- which(colnames(X) == firstint)
intdim2 <- which(colnames(X) == secondint)
# Compute interaction term:
for(j in 1:nseq) {
ovacases[, i, j] <- ovacases[, intdim1, j]*ovacases[, intdim2, j]
}
}
}
# Prepare array of observed values:
ovaV <- array(NA, c(obs, nsim, nseq, J))
# Add progress bar
pb_multiplication <- txtProgressBar(min = 0, max = nseq, initial = 0)
# Loop over all scenarios
cat("Multiplying values with simulated estimates:\n")
# Loop over all scenarios
for(i in 1:nseq){
ovaV[, , i, 1] <- apply(matrix(0,
nrow = nsim,
ncol = ncol(X)),
1,
function(s) ovacases[, , i] %*% s)
# ^ This will be zero because of the baseline category ^
# For each choice, the cases will now be multiplied with the simulated estimates
for (k in 2:J) {
coefstart <- (k-2)*ncoef+1
coefend <- (k-1)*ncoef
element <- parse(text = paste0("ovaV[,, i,", k, "] <- apply(S[, ",
coefstart,
":",
coefend,
"], 1, function(s) ovacases[,, i] %*% s)"))
eval(element)
}
# Progress bar:
setTxtProgressBar(pb_multiplication, i)
}
# Multinomial link function:
# 1. Part: Sum over cases
Sexp <- rowSums(exp(ovaV), dims = 3L)
# Create P (array with predictions)
P <- array(NA, c(nsim, J, nseq))
# 2. Part: take the exponent and divide through the sum of all (Sexp)
# Add progress bar
pb_link <- txtProgressBar(min = 0, max = nseq, initial = 0)
# Loop over all scenarios
cat("\nApplying link function:\n")
for (l in 1:nseq) {
for (m in 1:J) {
P[, m, l] <- colMeans(exp(ovaV[, , l, m]) / Sexp[, , l])
if (sum(is.na(P[, m, l])) != 0) {
stop("Stop")
}
}
# Progress bar:
setTxtProgressBar(pb_link, l)
}
output[["P"]] <- P
# Aggregate the simulations
# Create tibble for plot
# if (is.null(z_value) == TRUE) {
# plotdat <- tibble::tibble(iv = rep(variation, J),
# categories = rep(categories, each = length(variation)),
# mean = NA,
# lower = NA,
# upper = NA)
# } else {
# plotdat <- tibble::tibble(iv = rep(variation, J),
# categories = rep(categories, each = length(variation)),
# scen = rep(z_value, each = length(categories)),
# mean = NA,
# lower = NA,
# upper = NA)
# }
if (is.null(z_value) == TRUE) {
plotdat <- data.frame(iv = rep(variation, J),
categories = rep(categories, each = length(variation)),
mean = NA,
lower = NA,
upper = NA)
} else {
plotdat <- data.frame(iv = rep(variation, J),
categories = rep(categories, each = length(variation)),
scen = rep(z_value, each = length(variation)),
mean = NA,
lower = NA,
upper = NA)
}
# Aggregate
start <- 1
for (i in 1:J) {
end <- i*length(variation)
plotdat[c(start:end), "mean"] <- colMeans(P[, i,])
plotdat[c(start:end), "lower"] <- apply(P[, i,], 2, quantile, probs = probs[1])
plotdat[c(start:end), "upper"] <- apply(P[, i,], 2, quantile, probs = probs[2])
start <- end+1
}
# Rename the variables in the plot data
if (is.null(z) == TRUE) {
colnames(plotdat)[1:2] <- c(x, dv)
} else {
colnames(plotdat)[1:3] <- c(x, dv, z)
}
# Put the data in the output
output[["plotdata"]] <- plotdat
cat("\nDone!\n\n")
return(output)
}
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