qmix: Fitting finite quantile mixture models
In qmix: Finite Quantile Mixture Models

Description Usage Arguments Value References Examples

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").

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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)

`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.

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.

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

# 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)