search_lqmix: Search the Global Maximum of a Linear Quantile Mixture

In lqmix: Linear Quantile Mixture Models

Search the Global Maximum of a Linear Quantile Mixture

Description

Search the global maximum of the log-likelihood function for a finite mixture of linear quantile regression models with TC and/or TV, discrete, random coefficients, for varying number of components and/or states.

Usage

search_lqmix(formula, randomTC = NULL, randomTV = NULL, group, time,
  Gv = NULL, mv = NULL, data, method = "bic", nran = 0, qtl = 0.5,
  eps = 10^-5, maxit = 1000, se = TRUE, R = 200, 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
Gv	vector of possible number of mixture components associated to TC random coefficients, if present in the model
mv	vector of possible number of states associated to the TV random coefficients, if present in the model
data	a data frame containing the variables named in formula, randomTC, randomTV, group, and time
method	method to use for selecting the optimal model. Possible values are "lk", "aic", or "bic"
nran	number of repetitions of each random initialization
qtl	quantile to be estimated
eps	tolerance level for convergence of the EM algorithm
maxit	maximum number of iterations for the EM algorithm
se	standard error computation for the optimal model
R	number of bootstrap samples for computing standard errors
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 allows to identify the optimal model specification in terms of number of mixture components and/or hidden states associated to TC and/or TV random coefficients, respectively. This is done by considering a multi-start strategy based on both deterministic and random starting points. The number or random starts is proportional to the number of mixture components and/or hidden states associated to the random coefficients in the model. For models based on TC random coefficients, nran x (G-1) random starts are considered; for models based on TV or TC and TV random coefficients, the number of random start is set to nran x (m-1) and nran x (G-1) x (m-1), respectively.

If method = "lk", the optimal model selected by the function is that providing the highest log-likelihood value; if method = "AIC", (method = "BIC", respectively), the optimal model selected by the function is that providing the lowest AIC (BIC, respectively) value.

If se=TRUE, standard errors based on a block bootstrap procedure are computed for the identified optimal model.

Value

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

optimal	the identified optimal model
allmodels	the output of each estimated model in the form of a list of lists; the former and the latter list are associated with TC and TV random coefficients, respectively
lkv	the vector of likelihood values for each fitted model
aicv	the vector of AIC values for each fitted model
bicv	the vector of BIC values for each fitted model
qtl	the estimated quantile
mv	the vector of possible number of states associated to TV random coefficients (if present)
Gv	the vector of possible number of mixture components associated to TC random coefficients (if present)
method	the method used to select the optimal model
call	the matched call

Examples

sTC = search_lqmix(formula=meas~trt+time+trt:time,
                   randomTC=~1,group="id",time="time",Gv=1:3,method="bic",data=pain,se=FALSE)

sTV = search_lqmix(formula=meas~trt+time+trt:time,
randomTV=~1,group="id",time="time",mv=1:3,method="bic",data=pain,se=FALSE)

sTCTV = search_lqmix(formula=meas~trt+time+trt:time,
randomTC=~time,randomTV=~1,group="id",time="time",mv=1:3,Gv=1:3,method="bic",data=pain,se=FALSE)

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