3,800 research outputs found
Finite mixtures of quantile and M-quantile regression models
In this paper we define a finite mixture of quan- tile and M-quantile regression models for heterogeneous and /or for dependent/clustered data. Components of the finite mixture represent clusters of individuals with homogeneous values of model parameters. For its flexibility and ease of estimation, the proposed approaches can be extended to ran- dom coefficients with a higher dimension than the simple random intercept case. Estimation of model parameters is obtained through maximum likelihood, by implementing an EM-type algorithm. The standard error estimates for model parameters are obtained using the inverse of the observed information matrix, derived through the Oakes (J R Stat Soc Ser B 61:479–482, 1999) formula in the M-quantile setting, and through nonparametric bootstrap in the quantile case. We present a large scale simulation study to analyse the practical behaviour of the proposed model and to evaluate the empiri- cal performance of the proposed standard error estimates for model parameters. We considered a variety of empirical set- tings in both the random intercept and the random coefficient case. The proposed modelling approaches are also applied to two well-known datasets which give further insights on their empirical behaviour
An Extension of Generalized Linear Models to Finite Mixture Outcome Distributions
Finite mixture distributions arise in sampling a heterogeneous population.
Data drawn from such a population will exhibit extra variability relative to
any single subpopulation. Statistical models based on finite mixtures can
assist in the analysis of categorical and count outcomes when standard
generalized linear models (GLMs) cannot adequately account for variability
observed in the data. We propose an extension of GLM where the response is
assumed to follow a finite mixture distribution, while the regression of
interest is linked to the mixture's mean. This approach may be preferred over a
finite mixture of regressions when the population mean is the quantity of
interest; here, only a single regression function must be specified and
interpreted in the analysis. A technical challenge is that the mean of a finite
mixture is a composite parameter which does not appear explicitly in the
density. The proposed model is completely likelihood-based and maintains the
link to the regression through a certain random effects structure. We consider
typical GLM cases where means are either real-valued, constrained to be
positive, or constrained to be on the unit interval. The resulting model is
applied to two example datasets through a Bayesian analysis: one with
success/failure outcomes and one with count outcomes. Supporting the extra
variation is seen to improve residual plots and to appropriately widen
prediction intervals
Nonlinear quantile mixed models
In regression applications, the presence of nonlinearity and correlation
among observations offer computational challenges not only in traditional
settings such as least squares regression, but also (and especially) when the
objective function is non-smooth as in the case of quantile regression. In this
paper, we develop methods for the modeling and estimation of nonlinear
conditional quantile functions when data are clustered within two-level nested
designs. This work represents an extension of the linear quantile mixed models
of Geraci and Bottai (2014, Statistics and Computing). We develop a novel
algorithm which is a blend of a smoothing algorithm for quantile regression and
a second order Laplacian approximation for nonlinear mixed models. To assess
the proposed methods, we present a simulation study and two applications, one
in pharmacokinetics and one related to growth curve modeling in agriculture.Comment: 26 pages, 8 figures, 8 table
lqmix: an R package for longitudinal data analysis via linear quantile mixtures
The analysis of longitudinal data gives the chance to observe how unit
behaviors change over time, but it also poses series of issues. These have been
the focus of a huge literature in the context of linear and generalized linear
regression moving also, in the last ten years or so, to the context of linear
quantile regression for continuous responses. In this paper, we present lqmix,
a novel R package that helps estimate a class of linear quantile regression
models for longitudinal data, in the presence of time-constant and/or
time-varying, unit-specific, random coefficients, with unspecified
distribution. Model parameters are estimated in a maximum likelihood framework,
via an extended EM algorithm, and parameters' standard errors are estimated via
a block-bootstrap procedure. The analysis of a benchmark dataset is used to
give details on the package functions.Comment: 25 pages, 2 figure
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