lqmix: Linear Quantile Mixture with TC and/or TV, discrete, random...

In lqmix: Linear Quantile Mixture Models

Linear Quantile Mixture with TC and/or TV, discrete, random coefficients

Description

Estimate a finite mixture of linear quantile regression models with TC and/or TV discrete random coefficients, for a given number of components and/or states.

Usage

lqmix(formula, randomTC = NULL, randomTV = NULL, group, time, G = NULL,
  m = NULL, data, qtl = 0.5, eps = 10^-5, maxit = 1000, se = TRUE,
  R = 200, start = 0, parInit = list(betaf = NULL, betarTC = NULL,
  betarTV = NULL, pg = NULL, delta = NULL, Gamma = NULL, scale = NULL),
  verbose = TRUE, seed = NULL, parallel = FALSE, ncores = 2)

Arguments

formula	an object of class formula: a symbolic description of the model to be fitted
randomTC	a one-sided formula of the form ~z1+z2+...+zd, where z1,..., zd denote the variables associated to TC random coefficients (1 for the intercept)
randomTV	a one-sided formula of the form ~w1+w2+...+wl, where w1,..., wl denote the variables associated to TV random coefficients (1 for the intercept). Note that only TC variables are allowed
group	a string indicating the grouping variable, i.e., the factor identifying the unit longitudinal measurements refer to
time	a string indicating the time variable
G	number of mixture components associated to TC random coefficients
m	number of states associated to TV random coefficients
data	a data frame containing the variables named in formula, randomTC, randomTV, group, and time
qtl	quantile to be estimated
eps	tolerance level for convergence of the EM algorithm
maxit	maximum number of iterations for the EM algorithm
se	if set to TRUE, standard error are computed
R	number of bootstrap samples for computing standard errors
start	type of starting values (0 = deterministic, 1 = random, 2 = initial values in input)
parInit	list of initial model parameters when start=2
verbose	if set to FALSE, no printed output is given during the function execution
seed	an integer value for random numbers generation, used for random parameter initialization and bootstrap standard errors
parallel	if set to TRUE, a parallelized code is use for standard error computation (if se = TRUE)
ncores	number of cores used for computing bootstrap standard errors (if required)

Details

The function computes ML estimates for a linear quantile mixture model with TC and/or TV random coefficients. Estimates are derived by maximizing the (log-)likelihood of an Asymmetric Laplace regression, where the location parameter is modeled as a function of fixed coefficients, together with TC, TV, or TC and TV discrete random coefficients, as proposed by Alfo' et. al (2017), Farcomeni (2012), and Marino et. al (2018), respectively.

The function requires data in long-format and two additional columns indicating the group identifier and the time occasion. The model is specified by means of the arguments formula, formulaTC, and formulaTV: formula is associated to fixed coefficients; formulaTC is associated to TC random coefficients; formulaTV is associated to TV random coefficients. In this latter, only TC variables (predictors) are allowed.

The function allows for missing data, including dropouts (monotone missing data) and intermittent missingness, under a missing-at-random assumption. Note that, when TV random coefficients are considered, intermittent missingness may cause biased inference.

If se=TRUE, standard errors based on a block bootstrap procedure are computed.

Value

Return an object of class lqmix. This is a list containing the following elements:

betaf	a vector of fixed regression coefficients
betarTC	a matrix of TC random coefficients, if present in the model
betarTV	a matrix of TV random coefficients, if present in the model
pg	the prior probabilities of the finite mixture associated to TC random coefficients, if present in the model
delta	the initial probability vector of the hidden Markov chain associated to TV random coefficients, if present in the model
Gamma	the transition probability matrix of the hidden Markov chain associated to TV random coefficients, if present in the model
scale	the scale parameter
sigma.e	the standard deviation of error terms
lk	the log-likelihood at convergence of the EM algorithm
npar	the total number of model parameters
aic	the AIC value
bic	the BIC value
qtl	the estimated quantile
G	the number of mixture components associated to TC random coefficients (if present)
m	the number of hidden states associated to TV random coefficients (if present)
nsbjs	the number of subjects (units)
nobs	the total number of observations
se.betaf	the standard errors for fixed regression coefficients
se.betarTC	the standard errors for TC random coefficients, if present in the model
se.betarTV	the standard errors for TV random coefficients, if present in the model
se.Mprob	the standard errors for the prior probabilities of the finite mixture associated to TC random coefficients, if present in the model
se.Init	the standard errors for the initial probabilities of the hidden Markov chain associated to TV random coefficients, if present in the model
se.Trans	the standard errors for the transition probabilities of the hidden Markov chain associated to TV random coefficients, if present in the model
se.scale	the standard error for the scale parameter
vcov	the bootstrap variance-covariance matrices of the regression coefficients
postTC	a matrix of size nsbjs x G with the estimated posterior probabilities for the finite mixture components associated to TC random coefficients, if present in the model
postTV	a matrix of size nObs x m with the estimated posterior probabilities for the hidden states associated to TV random coefficients, if present in the model
miss	the missingness type
model	the estimated model
call	the matched call
mmf	the model matrix associated with fixed regression coefficients
mmrTC	the model matrix associated with TC random coefficients, if present in the model
mmrTV	the model matrix associated with TV random coefficients, if present in the model
y	the model response
formula	the fixed model formula
randomTC	the model formula for the TC random coefficients, if present in the model
randomTV	the model formula for the TV random coefficients, if present in the model
group	the grouping variable
time	the time variable

References

\insertRef

ref:lqmixTClqmix

\insertRef

ref:lqmixTVlqmix

\insertRef

ref:lqmixTCTVlqmix

Examples

outTC = lqmix(formula=meas~trt+time+trt:time,randomTC=~1,
              group="id",time="time",G=2,data=pain,se=TRUE,R=10)


outTV = lqmix(formula=meas~trt+time+trt:time,randomTV=~1,
              group="id",time="time",m=2,data=pain,R=10)

outTCTV = lqmix(formula=meas~trt+time+trt:time,randomTC=~time,
                    randomTV=~1,group="id",time="time",m=2,G=2,data=pain,R=10)

lqmix documentation built on Nov. 5, 2025, 7:15 p.m.