lqmix-package {lqmix}

Overview of the package lqmix

Description

The lqmix package allows for the estimation of finite mixtures of linear quantile regression models based on Time-Constant (TC) and/or Time-Varying (TV), discrete, random coefficients for the analysis of longitudinal data

Details

lqmix is an R package devoted to the estimation of a class of linear quantile regression models for longitudinal data, in the presence of Time-Constant (TC) and/or Time-Varying (TV), unit-specific, random coefficients, having unspecific distribution. The parameters of this distribution, together with all the others characterizing the model, are estimated in a maximum likelihood framework, via an extended Expectation-Maximization algorithm. This approach leads to the estimation of discrete distributions for the random coefficients, which give rise to a likelihood function similar to that of standard finite mixture models (in the case of TC random coefficients only), hidden Markov models (in the case of TV random coefficients only), or mixed hidden Markov models with discrete effects (in the case of both TC and TV random coefficients).

Parameters' standard errors are estimated via a block-bootstrap procedure, while model selection is performed by either maximizing the log-likelihood function, or minimizing the Akaike Information Criterion or the Bayesian Information Criterion.

Missing data are allowed and treated under a Missing at Random assumption.

Author(s)

Maria Francesca Marino [aut,cre], Marco Alfo' [aut], Nicola Salvati [aut], and Maria Giovanna Ranalli [aut]

Maintainer: Maria Francesca Marino <[e-mail]>

References

Alfo' M, Salvati N, Ranalli MG (2017). “Finite Mixtures of Quantiles and M-quantile models.” Statistics and Computing, 27, 547-570.

Aitkin M (1996). “A general maximum likelihood analysis of overdispersion in generalized linear models.” Statistics and Computing, 6, 251-262.

Aitkin M (1999). “A general maximum likelihood analysis of variance components in generalized linear models.” Biometrics, 55, 117–128.

Farcomeni A (2012). “Quantile regression for longitudinal data based on latent Markov subject-specific parameters.” Statistics and Computing, 22.

Bartolucci F, Farcomeni A, Pennoni F (2012). Latent Markov models for longitudinal data. Taylor & Francis.

Zucchini W, MacDonald IL, Langrock R (2017). Hidden Markov models for time series, Monographs on Statistics and Applied Probability. Chapman and Hall/CRC.

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.