Association models for a multivariate binary response

Models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders. The w-order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterization supports likelihood-based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood-based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.     

Prediction error variance and expected response to selection,when selection is based on the best predictor – for Gaussian and threshold characters,traits following a Poisson mixed model and survival traits

In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found – otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits – and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.     

On the role of feedback in promoting conflicting goals of the adaptive immune system.

We explored here the implications of two premises. 1) In their response over days or weeks to pathogen invasion, cells of the immune system combine several overlapping and perhaps contradictory goals. 2) The immune system has ways to monitor progress toward these goals via receptors that bind chemicals whose concentrations are related to such progress. We illustrate with simple mathematical models how such monitoring can lead to feedbacks that improve the efficiency of a given effector type in accomplishing its specialized task, and also how feedbacks can shift the balance among a variety of effectors toward a preponderance of the more effective. Specific suggestions are given for feedback molecules.     

Alarm Calls of Marmosets (Callithrix geoffroyi) to Snakes and Perched Raptors

Communication about the presence of predators is an important benefit of group living. Critical information about the nature of danger can be conveyed through referential alarm calls. Raptors pose a significant predatory threat to callitrichid species. Unlike a raptor in flight, a perched raptor cannot attack suddenly at great speed, and it can be monitored from a safe distance. In this sense a perched bird may pose a threat more similar to that of a terrestrial predator such as a snake. Here we compare predatory contexts by addressing these two questions: 1) Do marmosets produce acoustically distinct alarm calls to snake models and perched raptor models? 2) Do the visual responses of the marmosets to the playbacks of perched raptor–elicited calls differ from those given to the playbacks of calls given in response to snakes? We recorded alarm calls from two groups of outdoor-housed Geoffroy’s marmosets (Callithrix geoffroyi) in response to predator models. Later, we played back stimuli created from these recordings to the marmosets and scored their gaze direction. Results show that calls given to models of perched raptors are acoustically distinct from those given to models of snakes. Further, the relative number of upward to downward looks while listening to the playbacks of perched raptor–elicited calls was significantly greater than it was for snake-elicited calls. Reactions to airborne raptors are known to elicit freezing or rapid flight, neither of which occurred in response to our playbacks. Our data suggest a greater complexity in the alarm call repertoire of marmosets than previously demonstrated.     

Bayesian isotonic density regression

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered.     

可交换条件下多维结构回归模型总体平均处理效应的估计

在可交换条件下，当响应变量为多维时，利用结构回归模型研究总体平均处理效应的估计。     

A nonparametric Bayesian modeling approach for cytogenetic dosimetry

In cytogenetic dosimetry, samples of cell cultures are exposed to a range of doses of a given agent. In each sample at each dose level, some measure of cell disability is recorded. The objective is to develop models that explain cell response to dose. Such models can be used to predict response at unobserved doses. More important, such models can provide inference for unknown exposure doses given the observed responses. Typically, cell disability is viewed as a Poisson count, but in the present work, a more appropriate response is a categorical classification. In the literature, modeling in this case is very limited. What exists is purely parametric. We propose a fully Bayesian nonparametric approach to this problem. We offer comparison with a parametric model through a simulation study and the analysis of a real dataset modeling blood cultures exposed to radiation where classification is with regard to number of micronuclei per cell.     

Household epidemic models with varying infection response

This paper is concerned with SIR (susceptible → infected → removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback–Leibler divergence for the two fitted models to these data.     

Effects of spatial grouping on the functional response of predators.

A unified mechanistic approach is given for the derivation of various forms of functional response in predator-prey models. The derivation is based on the principle of mass action but with the crucial refinement that the nature of the spatial distribution of predators and/or opportunities for predation are taken into account in an implicit way. If the predators are assumed to have a homogeneous spatial distribution, then the derived functional response is prey-dependent. If the predators are assumed to form a dense colony or school in a single (possibly moving) location, or if the region where predators can encounter prey is assumed to be of limited size, then the functional response depends on both predator and prey densities in a manner that reflects feeding interference between predators. Depending on the specific assumptions, the resulting functional response may be of Beddington-DeAngelis type, of Hassell-Varley type, or ratio-dependent.     

Binary Responses and the Three-period Cross-over

Problems with carry-over effects in the simple two-period cross-over have lead to interest in more complex cross-over designs. A method for analysing the optimum two-treatment three-period design with binary response variables is given by making a simple extension to Gart's logistic model. The method gives independent tests for, and estimates of the difference in treatment and first-order carry-over effects. An example of the analysis is given, using the loglinear models facility in GLIM.     

Semiparametric models for missing covariate and response data in regression models

We consider a class of semiparametric models for the covariate distribution and missing data mechanism for missing covariate and/or response data for general classes of regression models including generalized linear models and generalized linear mixed models. Ignorable and nonignorable missing covariate and/or response data are considered. The proposed semiparametric model can be viewed as a sensitivity analysis for model misspecification of the missing covariate distribution and/or missing data mechanism. The semiparametric model consists of a generalized additive model (GAM) for the covariate distribution and/or missing data mechanism. Penalized regression splines are used to express the GAMs as a generalized linear mixed effects model, in which the variance of the corresponding random effects provides an intuitive index for choosing between the semiparametric and parametric model. Maximum likelihood estimates are then obtained via the EM algorithm. Simulations are given to demonstrate the methodology, and a real data set from a melanoma cancer clinical trial is analyzed using the proposed methods.     

Detection of Interactive Effects in Carcinogenesis

The multistage theory for cancer is used to derive models for independent effects and for interactive effects of two carcinogenic agents. The derivation assumes that a tumor is of single cell origin and that a normal cell is transformed to a cancer cell by undergoing a finite number of irreversible, heritable, mutation-like transitions. The interactions enter the proposed models at the level of single cell transition rates rather than, as is conventional, at the level of animal response proportions. Suggestions are given for the design and analysis of fixed time, binary response, two factor, cancer bioassay experiments.     

Generalized linear models with unspecified reference distribution

We propose a new class of semiparametric generalized linear models. As with existing models, these models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. Here, however, the "baseline" distribution of Y at a given reference mean mu(0) is left unspecified and is estimated from the data. The response distribution when the mean differs from mu(0) is then generated via exponential tilting of the baseline distribution, yielding a response model that is a natural exponential family, with corresponding canonical link and variance functions. The resulting model has a level of flexibility similar to the popular proportional odds model. Maximum likelihood estimation is developed for response distributions with finite support, and the new model is studied and illustrated through simulations and example analyses from aging research.     

Sex ratio manipulation by the parasitoid waspSpalangia cameroni in response to host age: A test of the host-size model

Summary A sex ratio response to host resources as measured by external host dimensions has been demonstrated in many parasitoid wasps, includingSpalangia cameroni. The responses generally are in the direction predicted by sex ratio theory, specifically the host-size models. Here I show that femaleS. cameroni also respond to differences in resource availability not associated with changes in external host dimensions, and this response is in the direction predicted by host-size models. When given old and young hosts simultaneously, femaleS. cameroni oviposit a greater proportion of sons in old than in young host pupae, at least for 0-day old versus 3-day old hosts. Old hosts weigh less than young hosts but are not significantly different in external width. Thus it appears that the offspring sex ratio response may result from mothers detecting physical or chemical changes within the host which are associated with host age. No evidence is found that the manipulation in response to host age has been selected for via an effect of host age on wasp size; there was no significant effect of host age on either male of female wasp size. A second prediction of the host-size models is also supported by this study: when each female is presented with only a single host age, rather than two host ages simultaneously, host age has no effect on offspring sex ratio.     

Functional responses in the habitat selection of a generalist mega‐herbivore,the African savannah elephant

Resource selection function (RSF) models are commonly used to quantify species/habitat associations and predict species occurrence on the landscape. However, these models are sensitive to changes in resource availability and can result in a functional response to resource abundance, where preferences change as a function of availability. For generalist species, which utilize a wide range of habitats and resources, quantifying habitat selection is particularly challenging. Spatial and temporal changes in resource abundance can result in changes in selection preference affecting the robustness of habitat selection models. We examined selection preference across a wide range of ecological conditions for a generalist mega‐herbivore, the African savanna elephant Loxodonta africana, to quantify general patterns in selection and to illustrate the importance of functional responses in elephant habitat selection. We found a functional response in habitat selection across both space and time for tree cover, with tree cover being unimportant to habitat selection in the mesic, eastern populations during the wet season. A temporal functional response for water was also evident, with greater variability in selection during the wet season. Selection for low slopes, high tree cover, and far distance from people was consistent across populations; however, variability in selection coefficients changed as a function of the abundance of a given resource within the home range. This variability of selection coefficients could be used to improve confidence estimations for inferences drawn from habitat selection models. Quantifying functional responses in habitat selection is one way to better predict how wildlife will respond to an ever‐changing environment, and they provide promising insights into the habitat selection of generalist species.     

Temperature dependence of the functional response

The Arrhenius equation has emerged as the favoured model for describing the temperature dependence of consumption in predator-prey models. To examine the relevance of this equation, we undertook a meta-analysis of published relationships between functional response parameters and temperature. We show that, when plotted in lin-log space, temperature dependence of both attack rate and maximal ingestion rate exhibits a hump-shaped relationship and not a linear one as predicted by the Arrhenius equation. The relationship remains significantly downward concave even when data from temperatures above the peak of the hump are discarded. Temperature dependence is stronger for attack rate than for maximal ingestion rate, but the thermal optima are not different. We conclude that the use of the Arrhenius equation to describe consumption in predator-prey models requires the assumption that temperatures above thermal optima are unimportant for population and community dynamics, an assumption that is untenable given the available data.     

NONPARAMETRIC MODELS FOR DISCRIMINATION METHODS AND SENSITIVITY ANALYSIS FOR TRIADS

Nonparametric models for sensory discrimination methods are developed. In these models, the relationship between the probability of a correct response, P_c, and the measures for sensory discriminability or sensory difference, p₁ and p₂ are given. On the basis of the models, different sensitivities for triadic tests were compared including 3-AFC and triangle methods with the strong stimulus as the odd sample and with the weak stimulus as the odd sample. Predictions were made which can be tested experimentally.     

On boundary solutions and identifiability in categorical regression with non‐ignorable non‐response

This paper considers the regression analysis of categorical variables when the response variable is incompletely observed and the non‐response mechanism is assumed to be non‐ignorable. Maximum likelihood estimation of the model parameters can lead to substantively implausible boundary solutions where the estimated proportion of non‐respondents taking certain values of the response variable is zero. A geometric explanation of why boundary solutions occur was given in a previous paper for a simple model. By extending this explanation, it is possible to define the sub‐class of non‐ignorable models whose parameters are identified, and to show all models not in this sub‐class are non‐identified. The conditions under which a model is a member of this class are easily established.