In this article I develop a wild bootstrap procedure for cluster-robust inference in linear quantile regression models. I show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small, heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process. The proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much smaller than the sample size. An application to Project STAR data is provided. Supplementary materials for this article are available online.

/pdf/cluster-robust-bootstrap-inference-in-quantile-regression-4t4buyi8ay.pdf

Cluster-Robust Bootstrap Inference in Quantile Regression Models

Quantile regression for longitudinal data with a working correlation model

This paper estimates the impact of pension-related policies on household spending. The identification strategy exploits the deviation in pensioner income and expenditure caused by the introduction of a new pension system during the 1980s and 1990s in Spain and constructs a new narrative series of legislated pension changes. I present a variety of estimates, some of them imply that increases in the average pension have a roughly one-for-one effect on pensioner spending. The strongest effects are on the pensioners with the highest levels of expenditure, income, and wealth. Estimates for different categories of expenditure indicate that benefit increases trigger these pensioners to spend more on durables. At the same time, pension-related policies targeted to pensioners with low income levels seem to affect the spending on non-durables and necessities such as food positively.

The effects of pension-related policies on household spending

We provide an overview of linear quantile regression models for continuous responses repeatedly measured over time. We distinguish between marginal approaches, that explicitly model the data association structure, and conditional approaches, that consider individual-specific parameters to describe dependence among data and overdispersion. General estimation schemes are discussed and available software options are listed. We also mention methods to deal with non-ignorable missing values, with spatially dependent observations and nonparametric and semiparametric models. The paper is concluded by an overview of open issues in longitudinal quantile regression.

/pdf/linear-quantile-regression-models-for-longitudinal-5430g3s4zq.pdf

Linear quantile regression models for longitudinal experiments: an overview

Despite the widespread popularity of linear models for correlated outcomes (e.g., linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this article we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. The resulting “rotated” residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan, Pierce, and Randles. Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce...

https://www.jstor.org/stable/pdfplus/27590394.pdf

Cholesky residuals for assessing normal errors in a linear model with correlated outcomes

We consider the problem of regression analysis for data which consist of a large number of independent small groups or clusters of correlated observations. Instead of using the standard mean regression, we regress various percentiles of each marginal response variable over its covariates to obtain a more accurate assessment of the covariate effect. Our inference procedures are derived using the generalized estimating equations approach. The new proposal is robust and can be easily implemented. Graphical and numerical methods for checking the adequacy of the fitted quantile regression model are also proposed. The new methods are illustrated with an animal study in toxicology.

Quantile Regression for Correlated Observations

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Quantile Regression for Correlated Observations