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Abstract:
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We present a statistical approach for testing the smooth coefficient in a generalized scalar-on-function linear model. Specifically, we test for functional linearity, necessity of functional form, and inclusion of the predictor, focusing on binary responses. Using functional principal components analysis and spline smoothing, we reformulate and standardize the generalized functional linear model to an equivalent working linear mixed effects model. This allows us to frame our hypothesis tests in terms of zero-value variance components and build off existing testing methods and software. Performance and versatility of the approach is presented through a simulation study and application to diffusion tensor imaging of intracranial white matter tracts from multiple sclerosis patients.
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