Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

E. Andres Houseman, Louise Ryan and Brent Coull
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E. Andres Houseman: Harvard School of Public Health
Louise Ryan: Harvard School of Public Health and Dana-Farber Cancer Institute
Brent Coull: Harvard School of Public Health

No 1019, Harvard University Biostatistics Working Paper Series from Berkeley Electronic Press

Abstract: 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 paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional 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 (1989), Pierce (1982), and Randles (1982). 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 satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

Keywords: Cumulative distribution function; Goodness-of-fit; Linear mixed model; Random effects; Residual diagnostics (search for similar items in EconPapers)
Date: 2004-10-18
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (6)

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