ZDPMix: Function for posterior sampling of DP mixture of...

In stablemarkets/ChiRP: Chinese Restaurant Process Mixtures of Regressions

Description

This function takes in a training data.frame and optional testing data.frame and performs posterior sampling. It returns posterior predictions and posterior clustering for training and test sets. The function is built for zero-inflated, but otherwise continuous, outcomes.

Usage

ZDPMix(
  d_train,
  formula,
  d_test = NULL,
  burnin = 100,
  iter = 1000,
  phi_y = c(shape = 5, rate = 1000),
  beta_prior_mean = NULL,
  beta_prior_var = NULL,
  gamma_prior_mean = NULL,
  gamma_prior_var = NULL,
  init_k = 10,
  beta_var_scale = 1000,
  mu_scale = 1,
  tau_scale = 1,
  prop_sigma_z = diag(rep(0.025, nparams))
)

Arguments

d_train	A data.frame object with outcomes and model covariates/features. All features must be as.numeric - either continuous or binary with binary variables coded using 1 and 0. Categorical features are not supported. We recommend standardizing all continuous features. NA values are not allowed and each row should represent a single subject, longitudinal data is not supported.
formula	Specified in the usual way, e.g. for p=2 covariates, y ~ x1 + x2. All covariates - continuous and binary - must be as.numeric , with binary variables coded as 1 or 0. We recommend standardizing all continuous features. NA values are not allowed and each row should represent a single subject, longitudinal data is not supported.
d_test	Optional data.frame object containing a test set of subjects containing all variables specifed in formula. All the same rules for d_train apply to d_test.
burnin	integer specifying number of burn-in MCMC draws.
iter	integer greater than burnin specifying how many total MCMC draws to take.
phi_y	Optional. Length two as.numeric vector specifying the shape and rate, respectively, of the Inverse Gamma hyper-prior placed on the outcome variance.
beta_prior_mean	Optional. If there are p covariates, it is a length p+1 as.numeric vector specifying mean of the Gaussian prior on the outcome model's conditional mean parameter vector. Default is regression coefficients from running OLS on positive outcomes.
beta_prior_var	Optional. If there are p covariates, a length p+1 as.numeric vector specifying variance of the Gaussian prior on the outcome model's conditional mean parameter vector. The full covarince of the prior is set to be diagonal. This vector specifies the diagonal enteries of this prior covariance. Default is estimated variances from running OLS on positive outcomes.
gamma_prior_mean	Optional. If there are p covariates, a length p+1 as.numeric vector specifying mean of the Gaussian prior on the zero probability logistic model's conditional mean parameter vector. Default is a vector of 0s - i.e., null-centered prior mean.
gamma_prior_var	Optional. If there are p covariates, a length p+1 as.numeric vector specifying variance of the Gaussian prior on the zero probability logistic model's conditional mean parameter vector. Default is vector of 2s - moderately flat on the odds ratio scale.
init_k	Optional. integer specifying the initial number of clusters to kick off the MCMC sampler.
beta_var_scale	Optional. A multiplicative constant that scales beta_prior_var. If you leave beta_prior_mean and beta_prior_var at their defaults, This constant toggles how wide new cluster parameters are dispersed around the observed data parameters, larger values implies wider distribution.
mu_scale	Optional. An numeric, scalar constant that controls how widely distributed new cluster continuous covariate means are distributed around the empirical covariate mean. Specifically, all continuous covariates are assumed to have Gaussian likelihood with Gaussian prior on their means. mu_scale=2 specifies that the variance of the Gaussian prior is twice as large as the empirical variance.
tau_scale	Optional. An numeric, scalar constant that controls how widely distributed new cluster continuous covariate variances are distributed around the empirical variance. Specifically, all continuous covariates are assumed to have Gaussian likelihood with Inverse Gamma prior on their variance. tau_scale=2 specifies that the rate of the InvGamma prior is twice as large as the empirical variance.
prop_sigma_z	Optional. If you specified p covariates in formula, p+1 regression parameters are sampled for the probability of the outcome being zero using a Metropolis step. prop_sigma_z is a p+1 by p+1 covariance matrix for the Metropolis proposal distribution.

Details

Please see https://stablemarkets.github.io/ChiRPsite/index.htmlfor examples and detailed model and parameter descriptions.

Please see https://arxiv.org/abs/1810.09494 for a methodological reference.

Value

Returns predictions$train and cluster_inds$train. predictions$train returns an nrow(d_train) by iter - burnin matrix of posterior predictions. cluster_inds$train returns an nrow(d_train) by iter - burnin matrix of cluster assignment indicators, which can be input into the function cluster_assign_mode() to compute posterior mode assignment. predictions$test and cluster_inds$test are returned if d_test is specified.

Examples

set.seed(1)
n<-200 ## generate from clustered, skewed, data distribution
X11 <- rnorm(n = n, mean = 10, sd = 3)
X12 <- rnorm(n = n, mean = 0, sd = 2)
X13 <- rnorm(n = n, mean = -10, sd = 4)

Y1 <- rnorm(n = n, mean = 100 + .5*X11, 20)*(1-rbinom(n, 1, prob = pnorm( -10 + 1*X11 ) ))
Y2 <- rnorm(n = n, mean = 200 + 1*X12, 30)*(1-rbinom(n, 1, prob = pnorm( 1 + .05*X12 ) ))
Y3 <- rnorm(n = n, mean = 300 + 2*X13, 40)*(1-rbinom(n, 1, prob = pnorm( -3 -.2*X13 ) ))

d <- data.frame(X1=c(X11, X12, X13), Y = c(Y1, Y2, Y3))

d$X1 <- scale(d$X1)

ids <- sample(1:600, size = 500, replace = FALSE )
d_train <- d[ids,]
d_test <- d[-ids, ]

res <- ChiRP::ZDPMix(d_train = d_train, d_test = d_test, formula = Y ~ X1,
                     burnin=100, iter=200, init_k = 5, phi_y = c(10, 10000))

stablemarkets/ChiRP documentation built on July 26, 2021, 2:25 a.m.