Mathematics - Colloquium
Tuesday, February 23, 2010
11:00 AM-12:00 PM
ABSTRACT: Generalized additive models (GAMs) have distinct advantages over generalized linear models as they allow investigators to make inferences about associations between outcomes and predictors without placing parametric restrictions on associations. The predictor of interest is often smoothed using a locally weighted regression (LOESS) and the optimal span (degree of smoothing) can be determined by minimizing the Akaike Information Criterion. Such models can be applied in spatial statistics using a bivariate smoother to determine whether there is an association between geographic location and disease status. A natural hypothesis when using GAMs is to test whether the smoothing term is necessary or if a simpler model would suffice. An approximate chi-square test is available from commonly used software such as R and S-Plus but is known to be biased. Permutation tests are a reasonable alternative. The type I error rates and power of the GAM hypothesis testing methods have yet to be evaluated, even under simple scenarios. This research uses simulated data generated under null and simple alternative hypotheses to evaluate the properties of the approximate chi-square and three permutation testing methods. GAM hypothesis tests are then compared to the popular spatial scan statistic, known to have high power in a variety of settings, through application to synthetic data generated under three alternative hypotheses. The methods are compared in their type I error rates, powers, theoretical appropriateness, and computational efficiency.
Suggested Audiences: Adult, College
E-mail:
ma-chair@wpi.edu
Last Modified: February 12, 2010 at 11:46 AM
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