Grace S. Chiu

Bent-Cable Regression Theory and Applications

We use the so-called “bent-cable” model to describe natural phenomena that exhibit a potentially sharp change in slope. The model comprises two linear segments, joined smoothly by a quadratic bend. The class of bent cables includes, as a limiting case, the popular piecewise-linear model (with a sharp kink), otherwise known as the broken stick. Associated with bent-cable regression is the estimation of the bend-width parameter, through which the abruptness of the underlying transition may be assessed. We present worked examples and simulations to demonstrate the regularity and irregularity of bent-cable regression encountered in finite-sample settings. We also extend existing bent-cable asymptotics that previously were limited to the basic model with known linear slopes of 0 and 1. Practical conditions on the design are given to ensure regularity of the full bent-cable estimation problem if the underlying bend segment has nonzero width. Under such conditions, the least-squares estimators are shown to be consistent and to asymptotically follow a multivariate normal distribution. Furthermore, the deviance statistic (or the likelihood ratio statistic, if the random errors are normally distributed) is shown to have an asymptotic chi-squared distribution.

A unifying approach for food webs, phylogeny, social networks, and statistics

A food web consists of nodes, each consisting of one or more species. The role of each node as predator or prey determines the trophic relations that weave the web. Much effort in trophic food web research is given to understand the connectivity structure, or the nature and degree of dependence among nodes. Social network analysis (SNA) techniques—quantitative methods commonly used in the social sciences to understand network relational structure—have been used for this purpose, although postanalysis effort or biological theory is still required to determine what natural factors contribute to the feeding behavior. Thus, a conventional SNA alone provides limited insight into trophic structure. Here we show that by using novel statistical modeling methodologies to express network links as the random response of within- and internode characteristics (predictors), we gain a much deeper understanding of food web structure and its contributing factors through a unified statistical SNA. We do so for eight empirical food webs: Phylogeny is shown to have nontrivial influence on trophic relations in many webs, and for each web trophic clustering based on feeding activity and on feeding preference can differ substantially. These and other conclusions about network features are purely empirical, based entirely on observed network attributes while accounting for biological information built directly into the model. Thus, statistical SNA techniques, through statistical inference for feeding activity and preference, provide an alternative perspective of trophic clustering to yield comprehensive insight into food web structure.

A statistical social network model for consumption data in trophic food webs

Abstract We adapt existing statistical modeling techniques for social networks to study consumption data observed in trophic food webs. These data describe the feeding volume (non-negative) among organisms grouped into nodes, called trophic species, that form the food web. Model complexity arises due to the extensive amount of zeros in the data, as each node in the web is predator/prey to only a small number of other trophic species. Many of the zeros are regarded as structural (non-random) in the context of feeding behavior. The presence of basal prey and top predator nodes (those who never consume and those who are never consumed, with probability 1) creates additional complexity to the statistical modeling. We develop a special statistical social network model to account for such network features. The model is applied to two empirical food webs; focus is on the web for which the population size of seals is of concern to various commercial fisheries.

Bent-cable asymptotics when the bend is missing

A linear-quadratic-linear model is fitted to two-phase linear regression data. Only the width of the quadratic phase is estimated. The MLE is shown to converge at rate n-1/3 to an impractically complex limiting distribution, or more slowly.

Therapeutic Hypothermia: Quantification of the Transition of Core Body Temperature Using the Flexible Mixture Bent‐Cable Model for Longitudinal Data

Summary Hypothermia which is induced by reducing core body temperature is a therapeutic tool used to prevent brain damage resulting from physical trauma. However, all physiological systems begin to slow down due to hypothermia and this can result in increased risk of mortality. Therefore quantification of the transition of core body temperature to early hypothermia is of great clinical interest. Conceptually core body temperature may exhibit an either gradual or abrupt transition. Bent-cable regression is an appealing statistical tool to model such data due to the models flexibility and readily interpretable regression coefficients. It handles more flexibly models that traditionally have been handled by low-order polynomial models (for gradual transition) or piecewise linear changepoint models (for abrupt change). We consider a rat model to quantify the temporal trend of core body temperature primarily to address the question: What is the critical time point associated with a breakdown in the compensatory mechanisms following the start of hypothermia therapy? To this end, we develop a Bayesian modelling framework for bent-cable regression of longitudinal data to simultaneously account for gradual and abrupt transitions. Our analysis reveals that: (i) about 39% of rats exhibit a gradual transition in core body temperature; (ii) the critical time point is approximately the same regardless of transition type; and (iii) both transition types show a significant increase of core body temperature followed by a significant decrease.

Model-Based Assessment of Estuary Ecosystem Health Using the Latent Health Factor Index, with Application to the Richibucto Estuary

The ability to quantitatively assess ecological health is of great interest to those tasked with monitoring and conserving ecosystems. For decades, biomonitoring research and policies have relied on multimetric health indices of various forms. Although indices are numbers, many are constructed based on qualitative procedures, thus limiting the quantitative rigor of the practical interpretations of such indices. The statistical modeling approach to construct the latent health factor index (LHFI) was recently developed. With ecological data that otherwise are used to construct conventional multimetric indices, the LHFI framework expresses such data in a rigorous quantitative model, integrating qualitative features of ecosystem health and preconceived ecological relationships among such features. This hierarchical modeling approach allows unified statistical inference of health for observed sites (along with prediction of health for partially observed sites, if desired) and of the relevance of ecological drivers, all accompanied by formal uncertainty statements from a single, integrated analysis. Thus far, the LHFI approach has been demonstrated and validated in a freshwater context. We adapt this approach to modeling estuarine health, and illustrate it on the previously unassessed system in Richibucto in New Brunswick, Canada, where active oyster farming is a potential stressor through its effects on sediment properties. Field data correspond to health metrics that constitute the popular AZTI marine biotic index and the infaunal trophic index, as well as abiotic predictors preconceived to influence biota. Our paper is the first to construct a scientifically sensible model that rigorously identifies the collective explanatory capacity of salinity, distance downstream, channel depth, and silt–clay content–all regarded a priori as qualitatively important abiotic drivers–towards site health in the Richibucto ecosystem. This suggests the potential effectiveness of the LHFI approach for assessing not only freshwater systems but aquatic ecosystems in general.