R Programming/Multinomial Models

Multinomial Logit mlogit package. mnlogit package Bayesm package multinom() nnet multinomial(), which is used by vglm() VGAM Conditional Logit clogit() in the survival package mclogit package. Multinomial Probit mprobit package Harry Joe, Laing Wei Chou and Hongbin Zhang (2006). mprobit: Multivariate probit model for binary/ordinal response. R package version 0.9-2. MNP package to fit a multinomial probit. Multinomial ordered logit model We consider a multinomial ordered logit model with unknown thresholds. First, we simulate fake data. We draw the residuals in a logistic distribution. Then we draw some explanatory variable x and we define ys the latent variable as a linear function of x. Note that we set the constant to 0 because the constant and the thresholds cannot be identified simultaneously in this model. So we need to fix one of the parameters. Then, we define thresholds (-1,0,1) and we define our observed variable y using the cut() function. So y is an ordered multinomial variable. N <- 10000 u <- rlogis(N) x <- rnorm(N) ys <- x + u mu <- c(-Inf,-1,0,1, Inf) y <- cut(ys, mu) plot(y,ys) df <- data.frame(y,x) Maximum likelihood estimation This model can be estimated by maximum likelihood using the polr() function in the MASS package. Since it is not possible to achieve identification of the constant and the thresholds, R assumes by default that the constant is equal to 0. library(MASS) fit <- polr(y ~ x, method = "logistic", data = df) summary(fit) Bayesian estimation bayespolr() (arm) performs a bayesian estimation of the multinomial ordered logit library("arm") fit <- bayespolr(y ~ x, method = "logistic", data = df) summary(fit) Multinomial ordered probit model We generate fake data by drawing an error term in normal distribution and cutting the latent variables in 4 categories. N <- 1000 u <- rnorm(N) x <- rnorm(N) ys <- x + u mu <- c(-Inf,-1,0,1, Inf) y <- cut(ys, mu) plot(y,ys) df <- data.frame(x,y) Maximum likelihood estimation The model can be fitted using maximum likelihood method. This can be done using the polr() function in the MASS package with the probit method. library(MASS) fit <- polr(y ~ x, method = "probit", data = df) summary(fit) Bayesian estimation bayespolr() (arm) performs a bayesian estimation of the multinomial ordered probit Rank Ordered Logit Model This model was introduced in econometrics by Beggs, Cardell and Hausman in 1981.10.1016/0304-4076(81)90056-7 Assessing the potential demand for electric cars Journal of Econometrics 17 1–19 1981 Beggs S Cardell S Hausman J One application is the Combes et alii paper explaining the ranking of candidates to become professor.10.1016/j.labeco.2007.04.003 Publish or peer-rich? The role of skills and networks in hiring economics professors Labour Economics 15 3 423–41 2008 Combes Pierre-Philippe Linnemer Laurent Visser Michael Is is also known as Plackett–Luce model in biomedical literature or as exploded logit model in marketing. Conditionally Ordered Hierarchical Probit The Conditionally Ordered Hierarchical Probit can be estimated using the anchors package developed by Gary King and his coauthors Jonathan Wand, Gary King, Olivia Lau (2009). anchors: Software for Anchoring Vignette Data. Journal of Statistical Software, Forthcoming. URL http://www.jstatsoft.org/.. References 2