136,416 research outputs found
Regression Trees for Longitudinal Data
While studying response trajectory, often the population of interest may be
diverse enough to exist distinct subgroups within it and the longitudinal
change in response may not be uniform in these subgroups. That is, the
timeslope and/or influence of covariates in longitudinal profile may vary among
these different subgroups. For example, Raudenbush (2001) used depression as an
example to argue that it is incorrect to assume that all the people in a given
population would be experiencing either increasing or decreasing levels of
depression. In such cases, traditional linear mixed effects model (assuming
common parametric form for covariates and time) is not directly applicable for
the entire population as a group-averaged trajectory can mask important
subgroup differences. Our aim is to identify and characterize longitudinally
homogeneous subgroups based on the combination of baseline covariates in the
most parsimonious way. This goal can be achieved via constructing regression
tree for longitudinal data using baseline covariates as partitioning variables.
We have proposed LongCART algorithm to construct regression tree for the
longitudinal data. In each node, the proposed LongCART algorithm determines the
need for further splitting (i.e. whether parameter(s) of longitudinal profile
is influenced by any baseline attributes) via parameter instability tests and
thus the decision of further splitting is type-I error controlled. We have
obtained the asymptotic results for the proposed instability test and examined
finite sample behavior of the whole algorithm through simulation studies.
Finally, we have applied the LongCART algorithm to study the longitudinal
changes in choline level among HIV patients
Inverse regression for longitudinal data
Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li
[J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension
reduction method for regression models with multivariate covariates. It has
been extended by Ferr\'{e} and Yao [Statistics 37 (2003) 475-488, Statist.
Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755]
to functional covariates where the whole trajectories of random functional
covariates are completely observed. The focus of this paper is to develop
sliced inverse regression for intermittently and sparsely measured longitudinal
covariates. We develop asymptotic theory for the new procedure and show, under
some regularity conditions, that the estimated directions attain the optimal
rate of convergence. Simulation studies and data analysis are also provided to
demonstrate the performance of our method.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1193 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org). With Correction
Functional linear regression analysis for longitudinal data
We propose nonparametric methods for functional linear regression which are
designed for sparse longitudinal data, where both the predictor and response
are functions of a covariate such as time. Predictor and response processes
have smooth random trajectories, and the data consist of a small number of
noisy repeated measurements made at irregular times for a sample of subjects.
In longitudinal studies, the number of repeated measurements per subject is
often small and may be modeled as a discrete random number and, accordingly,
only a finite and asymptotically nonincreasing number of measurements are
available for each subject or experimental unit. We propose a functional
regression approach for this situation, using functional principal component
analysis, where we estimate the functional principal component scores through
conditional expectations. This allows the prediction of an unobserved response
trajectory from sparse measurements of a predictor trajectory. The resulting
technique is flexible and allows for different patterns regarding the timing of
the measurements obtained for predictor and response trajectories. Asymptotic
properties for a sample of subjects are investigated under mild conditions,
as , and we obtain consistent estimation for the regression
function. Besides convergence results for the components of functional linear
regression, such as the regression parameter function, we construct asymptotic
pointwise confidence bands for the predicted trajectories. A functional
coefficient of determination as a measure of the variance explained by the
functional regression model is introduced, extending the standard to the
functional case. The proposed methods are illustrated with a simulation study,
longitudinal primary biliary liver cirrhosis data and an analysis of the
longitudinal relationship between blood pressure and body mass index.Comment: Published at http://dx.doi.org/10.1214/009053605000000660 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Functional single index models for longitudinal data
A new single-index model that reflects the time-dynamic effects of the single
index is proposed for longitudinal and functional response data, possibly
measured with errors, for both longitudinal and time-invariant covariates. With
appropriate initial estimates of the parametric index, the proposed estimator
is shown to be -consistent and asymptotically normally distributed.
We also address the nonparametric estimation of regression functions and
provide estimates with optimal convergence rates. One advantage of the new
approach is that the same bandwidth is used to estimate both the nonparametric
mean function and the parameter in the index. The finite-sample performance for
the proposed procedure is studied numerically.Comment: Published in at http://dx.doi.org/10.1214/10-AOS845 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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