Abstract
Inference in quantile analysis has received considerable attention in the recent years. Linear quantile mixed models (Geraci and Bottai 2014) represent a flexible statistical tool to analyze data from sampling designs such as multilevel, spatial, panel or longitudinal, which induce some form of clustering. In this paper, I will show how to estimate conditional quantile functions with random effects using the R package lqmm. Modeling, estimation and inference are discussed in detail using a real data example. A thorough description of the optimization algorithms is also provided.
Highlights
In classical statistics, a common assumption is that sample observations are drawn independently from the same population
2 Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression individuals who rank differently according to some outcome variable might be affected by risk factors to a different extent or even in opposite ways
A typical formulation of a linear mixed model (LMM) for clustered data is given by yij = xij β + zij ui + ij, j = 1, . . . , ni, i = 1, . . . , M, where β and ui, i = 1, . . . , M, are, respectively, fixed and random effects associated with p and q model covariates and the response vector yi is assumed to follow a multivariate normal distribution characterized by some parameter θ
Summary
A common assumption is that sample observations are drawn independently from the same population. Mixed models are based on the assumption that predictors affect the conditional distribution of the outcome only through its location parameter (i.e., the mean). The negative effects of maternal smoking during pregnancy or lack of prenatal care have been amply documented. These factors have been shown to decrease the average weight of infants at birth. Infants who rank lower in the distribution (i.e., low birthweight infants) are affected by smoking and lack of prenatal care at a greater extent than average-weighting infants, and the latter at a greater extent than those who rank higher in the distribution (Abrevaya 2001; Koenker and Hallock 2001; Geraci 2013).
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