Daniel,
Here are few references you might find useful:
Lane, P.W., 2002, "Generalized linear models in soil science,"
European Journal of Soil Science 53, 241-251.
Abstract: Classical linear models are easy to understand and fit.
However, when assumptions are not met, violence should not be used on
the data to force them into the linear mould. Transformation of
variables may allow successful linear modeling, but it affects several
aspects of the model simultaneously. In particular, it can interfere
with the scientific interpretation of the model. Generalized linear
models are a wider class, and they retain the concept of additive
explanatory effects. They provide generalizations of the
distributional assumptions of the response variable, while at the same
time allowing a transformed scale on which the explanatory effects
combine. These models can be fitted reliably with standard software,
and the analysis is readily interpreted in an analogous way to that of
linear models. Many further generalizations to the generalized linear
model have been proposed, extending them to deal with smooth effects,
non-linear parameters, and extra compone
nts of variation. Though the extra complexity of generalized linear
models gives rise to some additional difficulties in analysis, these
difficulties are outweighed by the flexibility of the models and ease
of interpretation. The generalizations allow the intuitively more
appealing approach to analysis of adjusting the model rather than
adjusting the data.
Manning, Willard G., 1998. "The logged dependent variable,
heteroscedasticity, and the retransformation problem," Journal of
Health Economics, vol. 17(3), pages 283-295, June.
Willard G. Manning & John Mullahy, 1999. "Estimating Log Models: To
Transform or Not to Transform?" NBER Technical Working Papers 0246,
National Bureau of Economic Research, Inc.
Abstract: Data on health care expenditures, length of stay,
utilization of health services, consumption of unhealthy commodities,
etc. are typically characterized by: (a) nonnegative outcomes; (b)
nontrivial fractions of zero outcomes in the population (and sample);
and (c) positively-skewed distributions of the nonzero realizations.
Similar data structures are encountered in labor economics as well.
This paper provides simulation-based evidence on the finite-sample
behavior of two sets of estimators designed to look at the effect of a
set of covariates x on the expected outcome, E(y|x), under a range of
data problems encountered in every day practice: generalized linear
models (GLM), a subset of which can simply be viewed as differentially
weighted nonlinear least-squares estimators, and those derived from
least-squares estimators for the ln(y). We consider the first- and
second- order behavior of these candidate estimators under alternative
assumptions on the data generat
ing processes. Our results indicate that the choice of estimator for
models of ln(E(x|y)) can have major implications for empirical results
if the estimator is not designed to deal with the specific data
generating mechanism. Garden-variety statistical problems - skewness,
kurtosis, and heteroscedasticity - can lead to an appreciable bias for
some estimators or appreciable losses in precision for others.
Scott
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