We propose classification models for binary and multicategory data where the
predictor is a random function. The functional predictor could be irregularly and
sparsely sampled or characterized by high dimension and sharp localized changes. In
the former case, we employ Bayesian modeling utilizing flexible spline basis which is
widely used for functional regression. In the latter case, we use Bayesian modeling
with wavelet basis functions which have nice approximation properties over a large
class of functional spaces and can accommodate varieties of functional forms observed
in real life applications. We develop an unified hierarchical model which accommodates
both the adaptive spline or wavelet based function estimation model as well as
the logistic classification model. These two models are coupled together to borrow
strengths from each other in this unified hierarchical framework. The use of Gibbs
sampling with conjugate priors for posterior inference makes the method computationally
feasible. We compare the performance of the proposed models with the naive
models as well as existing alternatives by analyzing simulated as well as real data. We
also propose a Bayesian unified hierarchical model based on a proportional hazards model and generalized linear model for survival analysis with irregular longitudinal
covariates. This relatively simple joint model has two advantages. One is that using
spline basis simplifies the parameterizations while a flexible non-linear pattern of
the function is captured. The other is that joint modeling framework allows sharing
of the information between the regression of functional predictors and proportional
hazards modeling of survival data to improve the efficiency of estimation. The novel
method can be used not only for one functional predictor case, but also for multiple
functional predictors case. Our methods are applied to analyze real data sets and
compared with a parameterized regression method.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1205 |
| Date | 15 May 2009 |
| Creators | Wang, Xiaohui |
| Contributors | Mallick, Bani K. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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