ABSTRACT
QLS models are evaluated as to fit based on the same basis as GEE models. In gen-
eral, assessing fit is challenging for semi-parametric methods such as QLS and GEE,
as these approaches are not based on maximizing an objective function. In contrast,
maximum likelihood-based approaches estimate the regression parameter by maxi-
mizing the log-likelihood, whose estimated value can then be used to compare the fit
of different models. For example, the Akaike information criterion (AIC) is widely
used for assessing the relative fit of models based on maximum likelihood (Akaike,
AIC = 2p− 2ln(L βˆML
), (8.1)
where p is the dimension of the regression parameter β , βˆ ML is the maximum likeli-
hood estimate of β , and ln(L βˆ ) is the natural-log of the likelihood evaluated at βˆ ML.
The AIC criterion can be used to compare several candidate models, assuming the
proposed model includes the true model, by designating the model with the smallest
AIC as the model with the best relative fit. The AIC values will tend to be smaller if
the number of parameters in the model is smaller, and if the estimated log-likelihood
is larger. The AIC is therefore favorably influenced by models that are more parsi-
monious, and that have greater estimated log-likelihoods.
