Computing regression statistics from grouped data

Abstract

This paper considers regression techniques for grouped data. In particular, it is shown how regression statistics obtained from individual level data can be replicated by means of grouped data. Three common regression approaches are considered: ordinary least squares, instrumental variables and nonlinear least squares regression. Also provided is code to implement the grouped-data techniques in the econometric software package Stata. An empirical example illustrates that the grouped-data formulas indeed replicate the statistics obtained from the individual level data. It is also argued why grouped data are important for empirical research.

Analysis of published and clinical sample data to develop new ranges of liver and blood concentrations of vitamin A for diagnosis of vitamin A deficiency in cattle

“…This discussion focuses on correlations between tissues from unpaired samples, which we term "herd-based" (or composite-sample) correlation. Size-weighted regression on grouped data replicates the coefficients obtained from paired values, 37,38 but the standard errors are underestimated.…”