| lqmix {lqmix} | R Documentation |
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 = 50, start = 0, parInit = list(betaf = NULL, betarTC = NULL, betarTV
= NULL, pg = NULL, delta = NULL, Gamma = NULL, scale = NULL),
verbose = TRUE, seed = NULL, parallel = FALSE)
Arguments
formula |
an object of class |
randomTC |
a one-sided formula of the form |
randomTV |
a one-sided formula of the form |
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 the TV random coefficients |
data |
a data frame containing the variables named in |
qtl |
quantile to be estimated |
eps |
tolerance level for (relative) 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 |
start |
type of starting values (0 = deterministic, 1 = random, 2 = initial values in input) |
parInit |
list of initial model parameters when |
verbose |
if set to FALSE, no printed output is given during the function execution |
seed |
an integer value for random numbers generation |
parallel |
if set to TRUE, a parallelized code is use for standard error computation (if se=TRUE) |
Details
The function computes ML estimates for the parameters of a linear quantile mixture model, based on TC and/or TV random coefficients. Estimates are derived by maximizing the (log-)likelihood of a Laplace regression where the location parameter is modeled as a function of fixed coefficients, together with TC and/or 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 admits the presence of missing data, both in terms of drop-outs (monotone missing data) and intermittent missing, 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 containing fixed regression coefficients |
betarTC |
a matrix containing the TC random coefficients, if present in the model |
betarTV |
a matrix containing the 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 |
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) |
se.betarTV |
the standard errors for TV random coefficients (if present) |
se.Mprob |
the standard errors for the prior probabilities of the finite mixture associated to TC random coefficients (if present) |
se.Init |
the standard errors for the initial probabilities of the hidden Markov chain associated to TV random coefficients(if present) |
se.Trans |
the standard errors for the transition probabilities of the hidden Markov chain associated to TV random coefficients (if present) |
se.scale |
the standard error for the scale parameter |
miss |
the missingness type |
model |
the estimated model |
call |
the matched call |
References
Marino MF, Tzavidis N, Alfo' M (2018). “Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences.” Statistical Methods in Medical Research, 27, 2231-2246.
Altman RJ (2007). “Mixed hidden Markov models: an extension of the hidden Markov model to the longitudinal data setting.” Journal of the American Statistical Association, 102, 201–210.
Maruotti A (2011). “Mixed Hidden Markov Models for Longitudinal Data: An Overview.” International Statistical Review, 79. ISSN 1751-5823.
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)