A Bayesian latent variable approach to functional principal components analysis with binary and count data

Linde, Angelika van der

doi:10.1007/s10182-009-0113-6

Cited by 21 publications

(7 citation statements)

References 16 publications

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“…However, methods for curve‐level estimation and inference are not presented, and incorporating covariate effects in the mean is not considered. van der Linde () develops a variational Bayesian algorithm for generalized FPCA that uses low‐dimensional spline representations for the mean and basis functions.…”

Section: Introductionmentioning

confidence: 99%

Generalized Multilevel Function-on-Scalar Regression and Principal Component Analysis

2015

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Summary This manuscript considers regression models for generalized, multilevel functional responses: functions are generalized in that they follow an exponential family distribution and multilevel in that they are clustered within groups or subjects. This data structure is increasingly common across scientific domains and is exemplified by our motivating example, in which binary curves indicating physical activity or inactivity are observed for nearly six hundred subjects over five days. We use a generalized linear model to incorporate scalar covariates into the mean structure, and decompose subject-specific and subject-day-specific deviations using multilevel functional principal components analysis. Thus, functional fixed effects are estimated while accounting for within-function and within-subject correlations, and major directions of variability within and between subjects are identified. Fixed effect coefficient functions and principal component basis functions are estimated using penalized splines; model parameters are estimated in a Bayesian framework using , a programming language that implements a Hamiltonian Monte Carlo sampler. Simulations designed to mimic the application have good estimation and inferential properties with reasonable computation times for moderate datasets, in both cross-sectional and multilevel scenarios; code is publicly available. In the application we identify effects of age and BMI on the time-specific change in probability of being active over a twenty-four hour period; in addition, the principal components analysis identifies the patterns of activity that distinguish subjects and days within subjects.

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Section: Introductionmentioning

confidence: 99%

Generalized Multilevel Function-on-Scalar Regression and Principal Component Analysis

2015

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“…The smoothing step can be adapted to the smoothness of the data and could in principle also be done using other bases than splines. For at most two nested functional random intercepts and scalar covariates, alternatives exist-some of these for generalized functional responses-that directly estimate the FPCs under orthonormality constraints within one overall model (e.g., James et al, 2000;Van der Linde, 2009;Peng and Paul, 2012;Goldsmith et al, 2015).…”

Section: Choice Of Basesmentioning

confidence: 99%

A general framework for functional regression modelling

Greven

Scheipl

2017

Statistical Modelling

103

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Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for 'generalized' functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases-particularly splines and functional principal components-and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost, respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.

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“…This kind of situations can be handled via the family of generalized functional regression models. Bayesian methods are popular approaches for analyzing such data, see Goldsmith et al [3], Meyer et al [12] and van der Linde [18] among others. However, Bayesian methods show some limitations, including heavy computations and lengthy fitting procedures.…”

Section: Introductionmentioning

confidence: 99%

Latent function-on-scalar regression models for observed sequences of binary data: a restricted likelihood approach

Asgari¹,

Alamatsaz²,

Vitelli³

et al. 2020

Preprint

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In this paper, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational framework for maximum likelihood analysis via the parameter expansion technique. Compared to existing methods, our proposal relies on the use of a complete data likelihood, with the advantage of being able to handle non-equally spaced and missing observations effectively. The proposed method is used in the Function-on-Scalar regression setting, with the latent response variable being a Gaussian random element taking values in a separable Hilbert space. Smooth estimations of functional regression coefficients and principal components are provided by introducing an adaptive MCEM algorithm that circumvents selecting the smoothing parameters. Finally, the performance of our novel method is demonstrated by various simulation studies and on a real case study. The proposed method is implemented in the R package dfrr.

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A Bayesian latent variable approach to functional principal components analysis with binary and count data

Abstract: Probabilistic PCA, Logistic PCA, Factor analysis, Exponential family, Variational algorithm, Working observations, Splines,

Cited by 21 publications

References 16 publications

Generalized Multilevel Function-on-Scalar Regression and Principal Component Analysis

Generalized Multilevel Function-on-Scalar Regression and Principal Component Analysis

A general framework for functional regression modelling

Latent function-on-scalar regression models for observed sequences of binary data: a restricted likelihood approach

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