69 research outputs found
Restricted Likelihood Ratio Testing in Linear Mixed Models with General Error Covariance Structure
We consider the problem of testing for zero variance components in linear mixed models with correlated or heteroscedastic errors. In the case of independent and identically distributed errors, a valid test exists, which is based on the exact finite sample distribution of the restricted likelihood ratio test statistic under the null hypothesis. We propose to make use of a transformation to derive the (approximate) test distribution for the restricted likelihood ratio test statistic in the case of a general error covariance structure. The proposed test proves its value in simulations and is finally applied to an interesting question in the field of well-being economics
Generalized Functional Additive Mixed Models
We propose a comprehensive framework for additive regression models for
non-Gaussian functional responses, allowing for multiple (partially) nested or
crossed functional random effects with flexible correlation structures for,
e.g., spatial, temporal, or longitudinal functional data as well as linear and
nonlinear effects of functional and scalar covariates that may vary smoothly
over the index of the functional response. Our implementation handles
functional responses from any exponential family distribution as well as many
others like Beta- or scaled non-central -distributions. Development is
motivated by and evaluated on an application to large-scale longitudinal
feeding records of pigs. Results in extensive simulation studies as well as
replications of two previously published simulation studies for generalized
functional mixed models demonstrate the good performance of our proposal. The
approach is implemented in well-documented open source software in the "pffr()"
function in R-package "refund"
Nonlinear association structures in flexible Bayesian additive joint models
Joint models of longitudinal and survival data have become an important tool
for modeling associations between longitudinal biomarkers and event processes.
The association between marker and log-hazard is assumed to be linear in
existing shared random effects models, with this assumption usually remaining
unchecked. We present an extended framework of flexible additive joint models
that allows the estimation of nonlinear, covariate specific associations by
making use of Bayesian P-splines. Our joint models are estimated in a Bayesian
framework using structured additive predictors for all model components,
allowing for great flexibility in the specification of smooth nonlinear,
time-varying and random effects terms for longitudinal submodel, survival
submodel and their association. The ability to capture truly linear and
nonlinear associations is assessed in simulations and illustrated on the widely
studied biomedical data on the rare fatal liver disease primary biliary
cirrhosis. All methods are implemented in the R package bamlss to facilitate
the application of this flexible joint model in practice.Comment: Changes to initial commit: minor language editing, additional
information in Section 4, formatting in Supplementary Informatio
Functional Linear Mixed Models for Irregularly or Sparsely Sampled Data
We propose an estimation approach to analyse correlated functional data which
are observed on unequal grids or even sparsely. The model we use is a
functional linear mixed model, a functional analogue of the linear mixed model.
Estimation is based on dimension reduction via functional principal component
analysis and on mixed model methodology. Our procedure allows the decomposition
of the variability in the data as well as the estimation of mean effects of
interest and borrows strength across curves. Confidence bands for mean effects
can be constructed conditional on estimated principal components. We provide
R-code implementing our approach. The method is motivated by and applied to
data from speech production research
Longitudinal Scalar-on-Function Regression with Application to Tractography Data
We propose a class of estimation techniques for scalar-on-function regression in longitudinal studies where both outcomes, such as test results on motor functions, and functional predictors, such as brain images, may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging (DTI) tractography study. One of the primary goals of the study is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and functional predictors measurements per patient; (3) Gaussian or non-Gaussian outcomes; and, (4) missing values within functional predictors. We review existing approaches designed to handle such types of data and discuss their limitations. We propose two versions of a new method, longitudinal functional principal components regression. These methods extend the well-known functional principal component regression and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The different methods are compared in simulation studies, and the most promising approaches are used for analyzing the tractography data
On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models
In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia
Principal component analysis in Bayes spaces for sparsely sampled density functions
This paper presents a novel approach to functional principal component
analysis (FPCA) in Bayes spaces in the setting where densities are the object
of analysis, but only few individual samples from each density are observed. We
use the observed data directly to account for all sources of uncertainty,
instead of relying on prior estimation of the underlying densities in a
two-step approach, which can be inaccurate if small or heterogeneous numbers of
samples per density are available. To account for the constrained nature of
densities, we base our approach on Bayes spaces, which extend the Aitchison
geometry for compositional data to density functions. For modeling, we exploit
the isometric isomorphism between the Bayes space and the
subspace with integration-to-zero constraint through the
centered log-ratio transformation. As only discrete draws from each density are
observed, we treat the underlying functional densities as latent variables
within a maximum likelihood framework and employ a Monte Carlo Expectation
Maximization (MCEM) algorithm for model estimation. Resulting estimates are
useful for exploratory analyses of density data, for dimension reduction in
subsequent analyses, as well as for improved preprocessing of sparsely sampled
density data compared to existing methods. The proposed method is applied to
analyze the distribution of maximum daily temperatures in Berlin during the
summer months for the last 70 years, as well as the distribution of rental
prices in the districts of Munich
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