Categorical data analysis using discretization of continuous variables to investigate associations in marine ecosystems

H. Solvang; S. Imori; M. Biuw; U. Lindstrøm; T. Haug

Home/Archive/arXiv

arXiv · 2308.14505

Categorical data analysis using discretization of continuous variables to investigate associations in marine ecosystems

H. Solvang·S. Imori·M. Biuw·U. Lindstrøm·T. Haug

View original source ↗Read source document ↗Export metadata ↓

Abstract

Understanding and predicting interactions between predators and prey and their environment are fundamental for understanding food web structure, dynamics, and ecosystem function in both terrestrial and marine ecosystems.Thus, estimating the conditional associations between species and their environments is important for exploring connections or cooperative links in the ecosystem, which in turn can help to clarify such causal relationships. For this purpose, a relevant and practical statistical method is required to link presence/absence observations with biomass, abundance, and physical quantities obtained as continuous real values.These data are sometimes sparse in oceanic space and too short as time series data. To meet this challenge, we provide an approach based on applying categorical data analysis to present/absent observations and real-number data.This approach consists of a two-step procedure for categorical data analysis:1) finding the appropriate threshold to discretize the real-number data for applying an independent test;and 2) identifying the best conditional probability model to investigate the possible associations among the data based on a statistical information criterion.We conduct a simulation study to validate our proposed approach. Furthermore, the approach is applied to two datasets: 1) one collected during an international synoptic krill survey in the Scotia Sea west of the Antarctic Peninsula to investigate associations among krill, fin whale (Balaenoptera physalus),surface temperature, depth, slope in depth, and temperature gradient; 2) the other collected by ecosystem surveys conducted during August-September in 2014 - 2017 to investigate associations among common minke whales, the predatory fish Atlantic cod, and their main prey groups in Arctic Ocean waters to the west and north of Svalbard, Norway.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

H. Solvang, S. Imori, M. Biuw, U. Lindstrøm, T. Haug. 2023-08-28. Categorical data analysis using discretization of continuous variables to investigate associations in marine ecosystems. https://arxiv.org/abs/2308.14505

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bias-Correction for Privacy-Protected Spatial Autoregressive Models with Application to Restaurant Network Analysis

Spatial autoregressive (SAR) models and their extensions are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement protection measures that render standard SAR models inapplicable. In this study, we introduce a privacy-protected SAR model that incorporates noise into both the response and covariates to meet privacy requirements. With noise present in both components, the traditional quasi-maximum likelihood estimator becomes difficult to compute because the likelihood function cannot be directly formulated. To bypass this hurdle, we begin with a pseudo-likelihood approach, initially omitting the noise in the covariates. A Newton-Raphson algorithm is then applied to compute the estimator; however, the estimator is biased. To address this, we propose a bias-corrected Newton-Raphson-type algorithm that simultaneously accounts for noise in both the response and covariates. We further show, under appropriate regularity conditions, that the resulting estimator is consistent and asymptotically normal. To further enhance computational efficiency, we also develop a bias-corrected least squares estimator. Several extensions are discussed, and the finite-sample performance of the proposed methods is evaluated through extensive simulations. We apply the proposed methodology to restaurant transaction data from a third-party payment platform. Our method identifies a statistically significant competitive network effect among restaurants and further reveals meaningful restaurant-customer interaction patterns.

stat.ME↗

arXiv2026

A variational framework for modal estimation

Multivariate mode estimation arises in many statistical problems such as inverse problems, multimodal sampling, and density-based clustering, but becomes challenging in moderate to high dimensions, especially when the underlying density is not directly evaluable. We introduce GERVE (Gibbs-measure Entropy-Regularized Variational Estimation), a sample-based method for estimating multivariate modes by approximating Gibbs distributions directly from samples, without estimating or evaluating the density. GERVE uses Gaussian-mixture variational annealing and natural-gradient optimization, producing a mixture concentrated in high-density regions whose component responsibilities also provide a clustering of the observations. We prove theoretical guarantees in two regimes: as the Gibbs temperature goes to zero, the optimal variational mixture concentrates around the global modes of the population density; at fixed positive temperature, we prove existence, consistency, and asymptotic normality of empirical maximizers and propose a bootstrap procedure for uncertainty quantification. Simulations and a real-data experiment show that GERVE accurately recovers modes and produces meaningful clusters.

stat.ME↗

arXiv2026

Objective Model Prior Probabilities in Variable Selection

For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the increasingly huge model spaces being considered in genomics and other fields. A popular replacement was to adopt a suggestion of Harold Jeffreys for the variable selection problem in which a total of $k$ possible variables are being considered for inclusion in the model: give the collection of all models containing $d$ variables ($d = 0, . . . , k$) prior probability $1/(k + 1)$ and then divide this prior probability equally among the models in the collection. Many other choices of model prior probabilities that impose severe parsimony have also been introduced. We begin by reviewing the problems with using equal model prior probabilities and then discuss some serious problems with the Jeffreys choice. Finally, we introduce and study a number of objective alternative choices of model prior probabilities, from both numerical and theoretical perspectives.

stat.ME↗