arXiv subjects

Luisa Barbanti

Publications and source records attributed to Luisa Barbanti.

3 recordsLinked to original sources

arXiv2026

Joint Count Transformation Models with Covariate-dependent Correlations

Joint Species Distribution Models are essential for understanding how ecological covariates shape species communities. However, most existing approaches are limited by rigid parametric distributions for count data and the inability to model how interspecific associations change with those covariates. We introduce joint count transformation models, a novel framework designed to overcome these limitations. Our approach combines distribution-free marginal count transformation models for multiple species with a covariate-dependent latent Gaussian copula to model interspecific correlations, interpretable as Spearman's rank correlation on the observed count scale. All model parameters are estimated efficiently via joint maximum likelihood estimation, implemented in the R package tram. We apply this framework to model the joint abundance of three fish-eating bird species, using seasonality as the primary covariate. Our model successfully captured the complex, species-specific seasonal abundance patterns, including periods of high zero-counts and seasonal shifts in variance. Furthermore, the model revealed strong, seasonally-varying correlations between the species. These findings are consistent with an empirical approach and similar to those from the computationally expensive parametric Bayesian Hierarchical Modelling of Species Communities (HMSC) framework. Consistency, accuracy and feasibility of our approach are demonstrated in a simulation study for up to 10 species.

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arXiv2022

A Transformation Perspective on Marginal and Conditional Models

Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multi-centre trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal distributions are described by a linear transformation model and the correlations by a joint multivariate normal distribution. The joint model provides an analytic formula for the marginal distribution. Owing to the richness of transformation models, the techniques are applicable to any type of response variable, including bounded, skewed, binary, ordinal, or survival responses. We demonstrate how the common normal assumption for reaction times can be relaxed in the sleep deprivation benchmark dataset and report marginal odds ratios for the notoriously difficult toe nail data. We furthermore discuss the analysis of two clinical trials aiming at the estimation of marginal treatment effects. In the first trial, pain was repeatedly assessed on a bounded visual analog scale and marginal proportional-odds models are presented. The second trial reported disease-free survival in rectal cancer patients, where the marginal hazard ratio from Weibull and Cox models is of special interest. An empirical evaluation compares the performance of the novel approach to general estimation equations for binary responses and to conditional mixed-effects models for continuous responses. An implementation is available in the "tram" add-on package to the R system and was benchmarked against established models in the literature.

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arXiv2020

Multivariate Conditional Transformation Models

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that they often rely on rather simplistic assumptions, e.g. a constant dependency structure that is not allowed to vary with the covariates or the restriction to linear dependence between the responses only. We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way conditional on nonlinear effects of covariates. The framework can be embedded into likelihood-based inference, including results on asymptotic normality, and allows the dependence structure to vary with covariates. In addition, the framework scales well beyond bivariate response situations, which were the main focus of most earlier investigations. We illustrate the application of multivariate conditional transformation models in a trivariate analysis of childhood undernutrition and demonstrate empirically that our approach can be beneficial compared to existing benchmarks such that complex truly multivariate data-generating processes can be inferred from observations.

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