Quasi-Least Squares Regression by Justine Shults

By Justine Shults

Drawing at the authors' titanic services in modeling longitudinal and clustered facts, Quasi-Least Squares Regression presents an intensive remedy of quasi-least squares (QLS) regression-a computational procedure for the estimation of correlation parameters in the framework of generalized estimating equations (GEEs). The authors current a close overview of QLS method, demonstrating the advantages Read more...

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Extra resources for Quasi-Least Squares Regression

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Rather than specify a particular form for the distribution of the yi , he only assumed that the variance can be expressed as a particular function of the mean and perhaps a scalar parameter. 2, quasi-likelihood estimation retains the assumption of the systematic component but discards the assumption of an exponential family distribution in the random component of the GLM. The motivation for quasi-likelihood stems from the observation that it is often more difficult in practice to determine the distribution than it is to identify the relationship between the mean and variance of the yi .

0 0 0 ... 1 n i ×n i However, incorrect application of the working independence structure can result in a serious loss in efficiency in estimation of β , as shown by Wang and Carey (2003), Shults et al. (2006a), Sutradhar and Das (1999), Sutradhar and Das (2000), and many others. In practice, if the number of measurements per subject is fairly small and if the measurement times are reasonably constant between subjects, a reasonable first step in the analysis might be to fit an unstructured correlation matrix with GEE.

In Chapter 4 we will relate the birth-weight of subjects with variables that include their mother’s birth-weight and whether or not the subject is male, or was first-born. In this analysis it will be important to estimate the correlation in birth-weight between father and infant (father–infant correlation), mother and infant (mother– infant correlation), and mother and father (mother–father). For example, Magnus et al. (2001) reported that because the mother–father correlations were extremely low, this implied that the non-negligible father–child correlations were explained by genetic effects.

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