Bimodality of Plasma Glucose Distributions in Whites: A Bootstrap Approach to Testing Mixture Models
Volume 8, Issue 3 (2010), pp. 483–493
Pub. online: 10 July 2021
Type: Research Article
Open Access
Open Access
Published
10 July 2021
10 July 2021
Abstract
Abstract: The null distribution of the likelihood ratio test (LRT) of a onecomponent normal model versus two-component normal mixture model is
unknown. In this paper, we take a bootstrap approach to the likelihood ratio
test for testing bimodality of plasma glucose concentrations from Rancho
Bernardo Diabetes Study. The small p-values from this approach support the
hypothesis that a bimodal normal mixture model fits the data significantly
better than a unimodal normal model. The size and power of the bootstrap
based LRT are evaluated through simulations. The results suggest that a
sample size of close to 500 would be necessary in order to attain a power of
90% for detecting the unbalanced mixtures with means and variances similar
to those in the Rancho Bernardo data. Besides sample size, the power also
depends on the two means and variances of the two components in the data.