Functional Regression Models with Highly Irregular Designs
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In this work we present a new approach, which we call MISFIT, to fitting functional data models with sparsely and irregularly sampled data. The limitations of current methods have created major challenges in the fitting of more complex nonlinear models. Indeed, currently many models cannot be consistently estimated unless one assumes that the number of observed points per curve grows sufficiently quickly with the sample size. In contrast, we demonstrate that MISFIT, which is based on a multiple imputation framework, has the potential to produce consistent estimates without such an assumption. Just as importantly, it propagates the uncertainty of not having completely observed curves, allowing for a more accurate assessment of the uncertainty of parameter estimates, something that most methods currently cannot accomplish. This work is motivated by a longitudinal study on macrocephaly, or atypically large head size, in which electronic medical records allow for the collection of a great deal of data. However, the sampling is highly variable from child to child. Using the MISFIT approach we are able to clearly demonstrate that the development of pathologic conditions related to macrocephaly is associated with both the overall head circumference of the children as well as the velocity of their head growth.
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