Correlation Goodness‐of‐fit Test for the Logarithmically‐Decreasing Survival Distribution

In this paper, we use the correlation‐type goodness‐of‐fit test for the logarithmically‐decreasing survival distribution. This model was intoduced by Sultan , Balakrishnan and Childs (2001) as a special case of Type‐I truncated logistic distribution. The power of the test based on normal, Weibull and gamma distributions is also calculated. We also give application to real example.     

Open population maximum likelihood spatial capture‐recapture

Open population capture‐recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modeling with spatial capture‐recapture (SCR), allowing for estimation of the effective area sampled and population density. Here, open population SCR is formulated as a hidden Markov model (HMM), allowing inference by maximum likelihood for both Cormack‐Jolly‐Seber and Jolly‐Seber models, with and without activity center movement. The method is applied to a 12‐year survey of male jaguars (Panthera onca) in the Cockscomb Basin Wildlife Sanctuary, Belize, to estimate survival probability and population abundance over time. For this application, inference is shown to be biased when assuming activity centers are fixed over time, while including a model for activity center movement provides negligible bias and nominal confidence interval coverage, as demonstrated by a simulation study. The HMM approach is compared with Bayesian data augmentation and closed population models for this application. The method is substantially more computationally efficient than the Bayesian approach and provides a lower root‐mean‐square error in predicting population density compared to closed population models.     

A goodness‐of‐fit test for occupancy models with correlated within‐season revisits

Occupancy modeling is important for exploring species distribution patterns and for conservation monitoring. Within this framework, explicit attention is given to species detection probabilities estimated from replicate surveys to sample units. A central assumption is that replicate surveys are independent Bernoulli trials, but this assumption becomes untenable when ecologists serially deploy remote cameras and acoustic recording devices over days and weeks to survey rare and elusive animals. Proposed solutions involve modifying the detection‐level component of the model (e.g., first‐order Markov covariate). Evaluating whether a model sufficiently accounts for correlation is imperative, but clear guidance for practitioners is lacking. Currently, an omnibus goodness‐of‐fit test using a chi‐square discrepancy measure on unique detection histories is available for occupancy models (MacKenzie and Bailey, Journal of Agricultural, Biological, and Environmental Statistics, 9, 2004, 300; hereafter, MacKenzie–Bailey test). We propose a join count summary measure adapted from spatial statistics to directly assess correlation after fitting a model. We motivate our work with a dataset of multinight bat call recordings from a pilot study for the North American Bat Monitoring Program. We found in simulations that our join count test was more reliable than the MacKenzie–Bailey test for detecting inadequacy of a model that assumed independence, particularly when serial correlation was low to moderate. A model that included a Markov‐structured detection‐level covariate produced unbiased occupancy estimates except in the presence of strong serial correlation and a revisit design consisting only of temporal replicates. When applied to two common bat species, our approach illustrates that sophisticated models do not guarantee adequate fit to real data, underscoring the importance of model assessment. Our join count test provides a widely applicable goodness‐of‐fit test and specifically evaluates occupancy model lack of fit related to correlation among detections within a sample unit. Our diagnostic tool is available for practitioners that serially deploy survey equipment as a way to achieve cost savings.     

Spatio‐temporal Modelling of Weeds by Shot‐noise G Cox processes

Tractable space‐time point processes models are needed in various fields. For example in weed science for gaining biological knowledge, for prediction of weed development in order to optimize local treatments with herbicides or in epidemiology for prediction of the risk of a disease. Motivated by the spatio‐temporal point patterns for two weed species, we propose a spatio‐temporal Cox model with intensity based on gamma random fields. The model is an extension of Neyman–Scott and shot‐noise Cox processes to the space‐time domain and it allows spatial and temporal inhomogeneity. We use the weed example to give a first intuitive interpretation of the model and then show how the model is constructed more rigorously and how to estimate the parameters. The weed data are analysed using the proposed model, and both spatially and temporally the model shows a good fit to the data using classical goodness‐of‐fit tests.     

Effect of detection heterogeneity in occupancy‐detection models: an experimental test of time‐to‐first‐detection methods

Imperfect detection can bias estimates of site occupancy in ecological surveys but can be corrected by estimating detection probability. Time‐to‐first‐detection (TTD) occupancy models have been proposed as a cost–effective survey method that allows detection probability to be estimated from single site visits. Nevertheless, few studies have validated the performance of occupancy‐detection models by creating a situation where occupancy is known, and model outputs can be compared with the truth. We tested the performance of TTD occupancy models in the face of detection heterogeneity using an experiment based on standard survey methods to monitor koala Phascolarctos cinereus populations in Australia. Known numbers of koala faecal pellets were placed under trees, and observers, uninformed as to which trees had pellets under them, carried out a TTD survey. We fitted five TTD occupancy models to the survey data, each making different assumptions about detectability, to evaluate how well each estimated the true occupancy status. Relative to the truth, all five models produced strongly biased estimates, overestimating detection probability and underestimating the number of occupied trees. Despite this, goodness‐of‐fit tests indicated that some models fitted the data well, with no evidence of model misfit. Hence, TTD occupancy models that appear to perform well with respect to the available data may be performing poorly. The reason for poor model performance was unaccounted for heterogeneity in detection probability, which is known to bias occupancy‐detection models. This poses a problem because unaccounted for heterogeneity could not be detected using goodness‐of‐fit tests and was only revealed because we knew the experimentally determined outcome. A challenge for occupancy‐detection models is to find ways to identify and mitigate the impacts of unobserved heterogeneity, which could unknowingly bias many models.     

Goodness‐of‐fit tests for disorder detection in NGS experiments

Next‐generation sequencing (NGS) experiments are often performed in biomedical research nowadays, leading to methodological challenges related to the high‐dimensional and complex nature of the recorded data. In this work we review some of the issues that arise in disorder detection from NGS experiments, that is, when the focus is the detection of deletion and duplication disorders for homozygosity and heterozygosity in DNA sequencing. A statistical model to cope with guanine/cytosine bias and phasing and prephasing phenomena at base level is proposed, and a goodness‐of‐fit procedure for disorder detection is derived. The method combines the proper evaluation of local p‐values (one for each DNA base) with suitable corrections for multiple comparisons and the discrete nature of the p‐values. A global test for the detection of disorders in the whole DNA region is proposed too. The performance of the introduced procedures is investigated through simulations. A real data illustration is provided.     

Survival and abundance of short‐finned pilot whales in the archipelago of Madeira,NE Atlantic

Estimates of population parameters for the short‐finned pilot whale, Globicephala macrorhynchus, are scarce in literature, contributing to an International Union for Conservation of Nature (IUCN) status of Data Deficient. In this study, photo‐identification data collected over 7 yr from Madeira were used to estimate for the first time survivorship, capture probability, and abundance in this species using mark‐recapture methodology. The Cormack‐Jolly‐Seber model estimated that the adult island‐associated (i.e., resident and regular visitor) whales had a constant survival rate of 0.960 (95% CI: 0.853–0.990) and an annual capture probability varying between 0.372 (CI: 0.178–0.619) and 0.843 (CI: 0.619–0.947). A parameterization of the Jolly‐Seber model estimated that 140 island‐associated whales (CI: 131–151) used the area throughout the course of the study. Based on a closed population model, the most precise (lower CV) annual estimate of the total number of pilot whales using the southern and eastern waters of Madeira (~900 km²) in a 3 mo period covering summer/autumn was 334 animals (CI: 260–437). No trend was observed. Despite including biases, the approach used in this study provided plausible estimates of population parameters, which can contribute to the regional conservation strategies.     

State–space mark–recapture estimates reveal a recent decline in abundance of North Atlantic right whales

North Atlantic right whales (Eubalaena glacialis Müller 1776) present an interesting problem for abundance and trend estimation in marine wildlife conservation. They are long lived, individually identifiable, highly mobile, and one of the rarest of cetaceans. Individuals are annually resighted at different rates, primarily due to varying stay durations among several principal habitats within a large geographic range. To date, characterizations of abundance have been produced that use simple accounting procedures with differing assumptions about mortality. To better characterize changing abundance of North Atlantic right whales between 1990 and 2015, we adapted a state–space formulation with Jolly‐Seber assumptions about population entry (birth and immigration) to individual resighting histories and fit it using empirical Bayes methodology. This hierarchical model included accommodation for the effect of the substantial individual capture heterogeneity. Estimates from this approach were only slightly higher than published accounting procedures, except for the most recent years (when recapture rates had declined substantially). North Atlantic right whales' abundance increased at about 2.8% per annum from median point estimates of 270 individuals in 1990 to 483 in 2010, and then declined to 2015, when the final estimate was 458 individuals (95% credible intervals 444–471). The probability that the population's trajectory post‐2010 was a decline was estimated at 99.99%. Of special concern was the finding that reduced survival rates of adult females relative to adult males have produced diverging abundance trends between sexes. Despite constraints in recent years, both biological (whales' distribution changing) and logistical (fewer resources available to collect individual photo‐identifications), it is still possible to detect this relatively recent, small change in the population's trajectory. This is thanks to the massive dataset of individual North Atlantic right whale identifications accrued over the past three decades. Photo‐identification data provide biological information that allows more informed inference on the status of this species.     

Testing goodness of fit for stochastic models of carcinogenesis.

This paper considers the utility of statistical goodness of fit testing in the context of mechanistic models of carcinogenesis. Two stochastic models of carcinogenesis were tested with several sets of experimental and epidemiological data using a formal goodness of fit test specially designed to accommodate censored observations: these were the two-stage model allowing for clonal expansion of initiated cells and its simpler version with gamma distributed promotion time. The results of this application, supplemented by visual examination of local likelihood kernel estimates of the hazard function and the corresponding model-based estimates, show that mechanistic models of carcinogenesis provide a good fit to the data in the majority of cases under study.     

Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

In capture–recapture models, survival and capture probabilities can be modelled as functions of time‐varying covariates, such as temperature or rainfall. The Cormack–Jolly–Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi‐parametrically modelling capture and survival probabilities using a frequentist approach via P‐splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi‐parametric Bayesian approaches on simulated and real data sets.     

Protein instability during HIC: Evidence of unfolding reversibility,and apparent adsorption strength of disulfide bond‐reduced α‐lactalbumin variants

A two‐conformation, four‐state model has been proposed to describe protein adsorption and unfolding behavior on hydrophobic interaction chromatography (HIC) resins. In this work, we build upon previous study and application of a four‐state model to the effect of salt concentration on the adsorption and unfolding of the model protein α‐lactalbumin in HIC. Contributions to the apparent adsorption strength of the wild‐type protein from native and unfolded conformations, obtained using a deuterium labeling technique, reveal the free energy change and kinetics of unfolding on the resin, and demonstrate that surface unfolding is reversible. Additionally, variants of α‐lactalbumin in which one of the disulfide bonds is reduced were synthesized to examine the effects of conformational stability on apparent retention. Below the melting temperatures of the wild‐type protein and variants, reduction of a single disulfide bond significantly increases the apparent adsorption strength (～6–8 kJ/mol) due to increased instability of the protein. Finally, the four‐state model is used to accurately predict the apparent adsorption strength of a disulfide bond‐reduced variant. Biotechnol. Bioeng. 2009;102: 1416–1427. © 2008 Wiley Periodicals, Inc.     

Goodness of Fit Tests with Misclassified Data Based on φ‐Divergences

The well known χ² goodness of fit test for a multinomial distribution is generally biased when observations are subject to misclassification. In this paper, based on a double sampling scheme, the family of φ‐divergence test statistics is introduced for testing goodness of fit under misclassification of the data. The case of binomial data is discussed and an illustrative example is also given.     

A comparison of abundance estimates from extended batch‐marking and Jolly–Seber‐type experiments

Little attention has been paid to the use of multi‐sample batch‐marking studies, as it is generally assumed that an individual's capture history is necessary for fully efficient estimates. However, recently, Huggins et al. ( 2010 ) present a pseudo‐likelihood for a multi‐sample batch‐marking study where they used estimating equations to solve for survival and capture probabilities and then derived abundance estimates using a Horvitz–Thompson‐type estimator. We have developed and maximized the likelihood for batch‐marking studies. We use data simulated from a Jolly–Seber‐type study and convert this to what would have been obtained from an extended batch‐marking study. We compare our abundance estimates obtained from the Crosbie–Manly–Arnason–Schwarz (CMAS) model with those of the extended batch‐marking model to determine the efficiency of collecting and analyzing batch‐marking data. We found that estimates of abundance were similar for all three estimators: CMAS, Huggins, and our likelihood. Gains are made when using unique identifiers and employing the CMAS model in terms of precision; however, the likelihood typically had lower mean square error than the pseudo‐likelihood method of Huggins et al. ( 2010 ). When faced with designing a batch‐marking study, researchers can be confident in obtaining unbiased abundance estimators. Furthermore, they can design studies in order to reduce mean square error by manipulating capture probabilities and sample size.     

On a Model for Hazard Rates

This note proposes a new model for summarising data on survival distribution. A simple graphical method (or equivalently a linear-regression-based method) for estimation of parameters is given. The model is shown to describe adequately data on Survivorship of Starling Birds reported by LACK (1943) and data on power generators reported by DHILLON (1981). A comment is added to illustrate how one can obtain a goodness of fit statistic which has a chi-squared distributions.     

Generalized Student's t‐distribution mixtures for autoradiographic image spread modelling

In this paper, a new class of models for autoradiographic hot‐line data is proposed. The models, for which there is theoretical justification, are a linear combination of generalized Student's t‐distributions and have as special cases all currently accepted line‐spread models. The new models are used to analyse experimental hot‐line data and compared with the fit of current models. The data are from a line source labelled with iodine‐125 in a resin section of 0.6 m in thickness. It will be shown that a significant improvement in goodness of fit, over that of previous models, can be achieved by choosing from this new class of models. A single model from this class will be proposed that has a simple form made up of only two components, but which fits experimental data significantly better than previous models. A short sensitivity analysis indicates that estimation is reliable. The modelling approach, although motivated by and applied to autoradiography, is appropriate for any mixture modelling situation.     

Parameter estimation and goodness-of-fit in log binomial regression

An estimate of the risk, adjusted for confounders, can be obtained from a fitted logistic regression model, but it substantially over-estimates when the outcome is not rare. The log binomial model, binomial errors and log link, is increasingly being used for this purpose. However this model's performance, goodness of fit tests and case-wise diagnostics have not been studied. Extensive simulations are used to compare the performance of the log binomial, a logistic regression based method proposed by Schouten et al. (1993) and a Poisson regression approach proposed by Zou (2004) and Carter, Lipsitz, and Tilley (2005). Log binomial regression resulted in "failure" rates (non-convergence, out-of-bounds predicted probabilities) as high as 59%. Estimates by the method of Schouten et al. (1993) produced fitted log binomial probabilities greater than unity in up to 19% of samples to which a log binomial model had been successfully fit and in up to 78% of samples when the log binomial model fit failed. Similar percentages were observed for the Poisson regression approach. Coefficient and standard error estimates from the three models were similar. Rejection rates for goodness of fit tests for log binomial fit were around 5%. Power of goodness of fit tests was modest when an incorrect logistic regression model was fit. Examples demonstrate the use of the methods. Uncritical use of the log binomial regression model is not recommended.     

Do U.S. county data disprove linear no‐threshold predictions of lung cancer risk for residential radon?‐A preliminary assessment of biological plausibility

Lung‐cancer mortality (LCM) is elevated in underground miners who chronically inhaled the mutagenic, cytotoxic α‐decay products of radon gas. Epidemiologie studies of LCM rates vs. residential‐radon concentration levels are generally considered inconclusive. However, Cohen (Health Physics 68, 157–174, 1995) has hypothesized that data on LCM vs. residential radon concentrations at the U.S. county level are clearly inconsistent with a linear no‐threshold (LN) dose‐response model, and rather are consistent with threshold or hormesis model. Cohen's hypothesis has been criticized as “ecological fallacy,”; particularly because LN (but not threshold or hormesis) models are generally considered biologically plausible for agents like α radiation that damage DNA in linear proportion to dose. To assess the biological plausibility of Cohen's hypothesis, a preliminary study was made of whether a biologically realistic, cytodynamic 2‐stage (CD2) cancer model can provide a good, joint fit to Cohen's set of U.S. county data as well as to underground‐miner data. The CD2 model used adapts a widely applied, mechanistic, 2‐stage stochastic model of carcinogenesis to realistically account for interrelated cell killing and mutation (both assumed to have a LN dose‐response), cell turnover, and incomplete exposure of stem cells. A CD2 fit was obtained to combined summary data on LCM vs. radon‐exposure in white males in 1, 601 U.S. counties (from Cohen) and in white male Colorado Plateau (CP) uranium miners (from the National Research Council's “BEIRIV”; report). The CD2 fit is shown to: (i) be consistent with the combined data; (ii) have parameter values all consistent with biological data; and (iii) predict inverse dose‐rate‐effects data for CP and other radon‐exposed miners, despite the fact that optimization had not involved any of these dose‐rate data. The latter data were not predicted by a simplified CD2 model in which all stem cells were presumed to be exposed. It is concluded that this study provides preliminary evidence that Cohen's hypothesis is biologically plausible.     

An evaluation of behavior inferences from Bayesian state‐space models: A case study with the Pacific walrus

State‐space models offer researchers an objective approach to modeling complex animal location data sets, and state‐space model behavior classifications are often assumed to have a link to animal behavior. In this study, we evaluated the behavioral classification accuracy of a Bayesian state‐space model in Pacific walruses using Argos satellite tags with sensors to detect animal behavior in real time. We fit a two‐state discrete‐time continuous‐space Bayesian state‐space model to data from 306 Pacific walruses tagged in the Chukchi Sea. We matched predicted locations and behaviors from the state‐space model (resident, transient behavior) to true animal behavior (foraging, swimming, hauled out) and evaluated classification accuracy with kappa statistics (κ) and root mean square error (RMSE). In addition, we compared biased random bridge utilization distributions generated with resident behavior locations to true foraging behavior locations to evaluate differences in space use patterns. Results indicated that the two‐state model fairly classified true animal behavior (0.06 ≤ κ ≤ 0.26, 0.49 ≤ RMSE ≤ 0.59). Kernel overlap metrics indicated utilization distributions generated with resident behavior locations were generally smaller than utilization distributions generated with true foraging behavior locations. Consequently, we encourage researchers to carefully examine parameters and priors associated with behaviors in state‐space models, and reconcile these parameters with the study species and its expected behaviors.     

An Improved Goodness of Fit Statistic for Probability Prediction Models

We consider the general case of probability prediction models having two or more outcomes and propose an adjusted χ² statistic which can be used to assess the goodness of fit of these models. We present a simulation study to show that our proposed statistic has an approximate χ² distribution under the null hypothesis. Two applications are provided to illustrate the use of the new statistic. The first application examines the fit of a logistic regression model using both the proposed statistic and the popular Hosmer-Lemeshow statistic and we compare and contrast these two methods. The second application evaluates the goodness of fit of a polychotomous regression model.