Edsel Peña
Department of Statistics
University of South Carolina
Global Validation of Linear Model Assumptions
One of the most-used statistical models in many scientific areas is
the general linear model which relates a vector of responses Y to a matrix
of fixed covariates X according to the equation Y = Xb + se, where e is a
vector of unobserved errors. The model parameters are the regression
coefficient vector b and the error standard deviation s. The validity of
this model relies on four assumptions: (i) linearity of the relationship;
(2) homoscedastic (equal) variances at each x; (3) normal error
distribution; and (4) uncorrelated errors. The breakdown of any of these
assumptions invalidates many inferential methods pertaining to this model
such as point estimation, construction of confidence intervals, and tests of
hypotheses pertaining to the model parameters. Many existing methods for
validating these model assumptions, especially those taught at our
undergraduate and graduate-level statistics courses, are ad hoc, graphical,
and usually does not take into account the synergy of effects inherent in
simultaneous violations. In this talk I will describe a global procedure for
validating simultaneously these model assumptions, and indicate how specific
model assumption violations could be pinpointed. The procedure will be
demonstrated using real data sets. It is hoped that the procedure will help
in partially eliminating the subjectivity inherent in existing graphical
procedures.
This is joint research work with Prof. Elizabeth Slate of the
Medical University of South Carolina.
Back to Colloquium Series