qmix (version 0.1.2.0)

qmix: Fitting finite quantile mixture models

Description

The main function for running the finite quantile mixture model. The function returns a qmix object that can be further investigated using standard functions such as plot, print, and coef. The model can be passed using a formula as in lm(). Convergence diagnotics can be performed using either print(object, "mcmc") or plot(object, "mcmc").

Usage

qmix(formula, data, nmix = 3, design = "fixed", q = NULL,
  nsim = 1000, burnin = NULL, thin = 1, CIsize = 0.95,
  nchain = 1, seeds = 12345, offset = 1e-20, inverse_distr = FALSE)

Arguments

formula

An object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

A data frame containing the variables in the model.

nmix

The number of mixture components.

design

Quantile specification. Options include "fixed" and "random". The default choice is "fixed" which requires quantile inputs from the user.

q

The quantile value.

nsim

The number of iterations.

burnin

The number of burnin iterations.

thin

Thinning parameter.

CIsize

The size of posterior confidence interval.

nchain

The number of parallel chains.

seeds

Random seeds to replicate the results.

offset

Offset values to enhance sampling stability. The default value is 1e-20.

inverse_distr

If FALSE, the ALD will not be reversed. The default is FALSE.

Value

A qmix object. An object of class qmix contains the following elements

Call

The matched call.

formula

Symbolic representation of the model.

nmix

Number of mixture components. If unspecified in the fixed-quantile specification, the value equals the number of quantiles specified. Otherwise, an error will be generated for the missing value.

design

Options include "fixed" and "random" for fixed- and random-quantile specification.

q

Quantiles in the fixed-quantile specification.

nsim

Number of iterations.

Burnin

Number of burnin iterations.

thin

Thinning.

seeds

Random seeds for reproducibility. The default is 12345.

CIsize

Size of the posterior confidence interval.

inverse_distr

Indicating whether ALD should be inversed.

offset

Offset to enhance stability in estimation. The default value is 1e-20.

data

Data used.

x

Independent variables.

y

Dependent variables.

xnames

Names of the independent variables.

stanfit

Output from stan.

sampledf

Posterior samples.

summaryout

Summary of the posterior samples.

npars

Number of covariates.

ulbs

Upper and lower bounds based on the specified confidence interval.

means

Mean estimates.

thetas

Estimated proportions of each mixture component.

binarylogic

Indicating whether the data contain a binary dependent variable.

References

Lu, Xiao (2019). Beyond the Average: Conditional Hypothesis Testing with Quantile Mixture. Working Paper.

Examples

# NOT RUN {
# simulate a mixture of 2 ALDs
k <- 2
N <- 50
# true effects: -10 and 10 respectively for two mixture components
beta1 <- -10
beta2 <- 10
set.seed(34324)
x1 <- rnorm(N,0,1)
x2 <- rnorm(N,0,1)
xb1 <- x1*beta1
xb2 <- x2*beta2
y1 <- y2 <- NA
# quantiles at 0.1 and 0.9
p1 <- 0.1
p2 <- 0.9
for (i in 1:N){
    y1[i] <- rald(1,mu = xb1[i],p = p1,sigma = 1)
    y2[i] <- rald(1,mu = xb2[i],p = p2,sigma = 1)
}
y <- c(y1,y2)
x <- c(x1,x2)
dat <- as.data.frame(cbind(y,x))
# Estimate the model using both the fixed- and random-quantile specification
model <- qmix(y ~ x, data = dat, nmix = 2, design = "fixed", q = c(0.1, 0.9))
# Summary the results
coef(model)
print(model)
# check traceplots
plot(model)

# }