Compositional Scalar-on-Function Regression with Application to Sediment Particle Size Distributions

Talská, Renáta; Hron, Karel; Grygar, Tomáš Matys

doi:10.1007/s11004-021-09941-1

Cited by 12 publications

(8 citation statements)

References 42 publications

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Section: Methodsmentioning

confidence: 99%

“…Hence, CFISA can be described in terms of the basic operations in Bayes spaces as a perturbation of f false~ by a weighting PDF g, which represents a shift of f false~ in the compositional sense. Due to the centreing of the sample f 1 , … , f n in SFPCA, it results from the formulation of the functional regression model (15) that β 0 = β ~ 0 − ∫ I β 1 ( t ) ⋅ f false¯ ( t ) d t , t ∈ I, 25 where β ~ 0 is the intercept from the regression model with the centred functional covariate. After this re-computation, the CFISA model can be expressed as where β ^ 0 and β ^ 1 are the estimates of the regression parameters from the compositional scalar-on-function regression model (17).…”

Section: Compositional Functional Isotemporal Substitution Analysis (...mentioning

confidence: 99%

“…6 This is commonly achieved using regression models. In this section, we introduce a compositional scalar-on-function regression model, 25 which provides an appropriate means of including a time-use distribution as an explanatory or predictive variable in a regression model through its characterisation as a PDF and using a ZB-spline representation as described above. Let us consider a set of n pairs (y 1 , f 1 ), … , (y n , f n ), where y i denote observations of a response variable and f i are functional predictors in L 2 (I), i = 1, … , n. The functional linear regression model is then formulated as…”

Section: Compositional Scalar-on-function Regressionmentioning

confidence: 99%

“…where 𝛽 0 ∈ ℝ and 𝛽 1 (t) ∈  2 (I) are unknown regression parameters and 𝜖 is a vector of independent and identically distributed random errors with mean zero. 25 As mentioned above, the clr transformation can be applied on PDFs so that the regression model is equivalently formulated in clr space as…”

Section: Compositional Scalar-on-function Regressionmentioning

confidence: 99%

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Compositional functional regression and isotemporal substitution analysis: Methods and application in time-use epidemiology

Jašková,

Palarea-Albaladejo,

Gába

et al. 2023

Stat Methods Med Res

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The distribution of time that people spend in physical activity of various intensities has important health implications. Physical activity (commonly categorised by the intensity into light, moderate and vigorous physical activity), sedentary behaviour and sleep, should not be analysed separately, because they are parts of a time-use composition with a natural constraint of [Formula: see text] h/day. To find out how are relative reallocations of time between physical activity of various intensities associated with health, herewith we describe compositional scalar-on-function regression and a newly developed compositional functional isotemporal substitution analysis. Physical activity intensity data can be considered as probability density functions, which better reflects the continuous character of their measurement using accelerometers. These probability density functions are characterised by specific properties, such as scale invariance and relative scale, and they are geometrically represented using Bayes spaces with the Hilbert space structure. This makes possible to process them using standard methods of functional data analysis in the [Formula: see text] space, via centred logratio (clr) transformation. The scalar-on-function regression with clr transformation of the explanatory probability density functions and compositional functional isotemporal substitution analysis were applied to a dataset from a cross-sectional study on adiposity conducted among school-aged children in the Czech Republic. Theoretical reallocations of time to physical activity of higher intensities were found to be associated with larger and more progressive expected decreases in adiposity. We obtained a detailed insight into the dose–response relationship between physical activity intensity and adiposity, which was enabled by using the compositional functional approach.

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Section: Methodsmentioning

confidence: 99%

Section: Compositional Functional Isotemporal Substitution Analysis (...mentioning

confidence: 99%

Section: Compositional Scalar-on-function Regressionmentioning

confidence: 99%

Section: Compositional Scalar-on-function Regressionmentioning

confidence: 99%

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Compositional functional regression and isotemporal substitution analysis: Methods and application in time-use epidemiology

Jašková,

Palarea-Albaladejo,

Gába

et al. 2023

Stat Methods Med Res

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“…Although this approach provides a promising framework for density-valued response regression, extensions which (additionally) allow for densityvalued explanatory variables remain extremely limited. A first linear Bayes Hilbert space regression model for scalar responses and density-valued covariates was proposed by Talská et al (2021) using a constrained spline representation (Machalová et al, 2021) and extended further by Scimone et al (2021), allowing for both density-valued responses and covariates. While this model allows for linear effects of the functional composition on the response, extensions to generalised (functional) additive models where parts of the predictor are finite or infinite compositions still remains an open topic.…”

Section: Introductionmentioning

confidence: 99%

Generalised functional additive mixed models with compositional covariates for areal Covid-19 incidence curves

Eckardt¹,

Mateu²,

Greven³

2022

Preprint

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We extend the generalised functional additive mixed model to include (functional) compositional covariates carrying relative information of a whole. Relying on the isometric isomorphism of the Bayes Hilbert space of probability densities with a subspace of the L 2 , we include functional compositions as transformed functional covariates with constrained effect function. The extended model allows for the estimation of linear, nonlinear and time-varying effects of scalar and functional covariates, as well as (correlated) functional random effects, in addition to the compositional effects. We use the model to estimate the effect of the age, sex and smoking (functional) composition of the population on regional Covid-19 incidence data for Spain, while accounting for climatological and socio-demographic covariate effects and spatial correlation.

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Multivariate Scalar on Multidimensional Distribution Regression With Application to Modeling the Association Between Physical Activity and Cognitive Functions

Ghosal,

Matabuena

2024

Biometrical J

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We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as predictors. However, these approaches are suboptimal because (i) they fail to utilize the dependence between the distributional predictors and (ii) neglect the correlation structure of the response. To overcome these limitations, we propose a multivariate distributional analysis framework that harnesses the power of multivariate density functions and multitask learning. We develop a computationally efficient semiparametric estimation method for modeling the effect of the latent joint density on the multivariate response of interest. Additionally, we introduce a new conformal prediction algorithm for quantifying the uncertainty of our multivariate predictions based on subject characteristics and individualized distributional predictors, providing valuable insights into the conditional distribution of the response. We validate the effectiveness of our proposed method through comprehensive numerical simulations, clearly demonstrating its superior performance compared to traditional methods. The application of the proposed method is demonstrated on triaxial accelerometer data from the National Health and Nutrition Examination Survey 2011–2014 for modeling the association between cognitive scores across various domains and distributional representation of physical activity among the older adult population. Our results highlight the advantages of the proposed approach, emphasizing the significance of incorporating multidimensional distributional information in the triaxial accelerometer data.

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Compositional Scalar-on-Function Regression with Application to Sediment Particle Size Distributions

Cited by 12 publications

References 42 publications

Compositional functional regression and isotemporal substitution analysis: Methods and application in time-use epidemiology

Compositional functional regression and isotemporal substitution analysis: Methods and application in time-use epidemiology

Generalised functional additive mixed models with compositional covariates for areal Covid-19 incidence curves

Multivariate Scalar on Multidimensional Distribution Regression With Application to Modeling the Association Between Physical Activity and Cognitive Functions

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