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Title: lqmix: An R package to model longitudinal data via mixtures of linear quantile regressions Authors:  Maria Francesca Marino - University of Florence (Italy) [presenting]
Marco Alfo - University La Sapienza, Rome (Italy)
Maria Giovanna Ranalli - University of Perugia (Italy)
Nicola Salvati - University of Pisa (Italy)
Abstract: Quantile regression represents a well-established technique for the modeling of data when researchers are interested in the effect of predictors on the conditional quantiles of the response. When responses are repeatedly collected over time, dependence needs to be properly considered to avoid misleading inference. A standard way of proceeding is that of including unit-specific random coefficients in the model. The distribution of such parameters may be either specified parametrically or left unspecified. Following this latter approach, the lqmix R package for estimating the parameters of a linear quantile regression model for longitudinal data is introduced. Discrete, time-constant and/or time-varying, random coefficients are considered and estimated directly from the data, in a finite mixture perspective. Based on the nature of the random coefficients included in the model, a static, dynamic, or mixed-type mixture of linear quantile regression equations is obtained. An EM algorithm is used to derive estimates and a block-bootstrap procedure is employed for deriving model parameters' standard errors. Standard penalized likelihood criteria are used to identify the optimal number of mixture components. A potential missing at random mechanism in the responses is also taken into account.