Hierarchical Generalized Linear Model

This study takes up inference in linear models with generalized error and generalized t distributions. For the generalized error distribution, two computational algorithms are proposed. The first is based on indirect Bayesian inference using an approximating finite scale mixture of normal distributions. The second is based on Gibbs sampling. The Gibbs sampler involves only drawing random numbers from standard distributions. This is important because previously the impression has been that an exact analysis of the generalized error regression model using Gibbs sampling is not possible. Next, we describe computational Bayesian inference for linear models with generalized t disturbances based on Gibbs sampling, and exploiting the fact that the model is a mixture of generalized error distributions with inverse generalized gamma distributions for the scale parameter. The linear model with this specification has also been thought not to be amenable to exact Bayesian analysis. All computational methods are applied to actual data involving the exchange rates of the British pound, the French franc, and the German mark relative to the U.S. dollar.

The use of graphical methods for comparing the quality of prediction throughout the design space of an experiment has been explored extensively for responses modeled with standard linear models. In this paper, fraction of design space (FDS) plots are adapted to evaluate designs for generalized linear models (GLMs). Since the quality of designs for GLMs depends on the model parameters, initial parameter estimates need to be provided by the experimenter. Consequently, an important question to consider is the design's robustness to user misspecification of the initial parameter estimates. FDS plots provide a graphical way of assessing the relative merits of different designs under a variety of types of parameter misspecification. Examples using logistic and Poisson regression models with their canonical links are used to demonstrate the benefits of the FDS plots.

Aim Conservation managers are increasingly looking for modelled projections of species distributions to inform management strategies; however, the coarse resolution of available data usually compromises their helpfulness. The aim of this paper is to delineate and test different approaches for converting coarse-grain occurrence data into high-resolution predictions, and to clarify the conceptual circumstances affecting the accuracy of downscaled models.

Relationships between albacore tuna (Thunnus alalunga) longline catch per unit effort (CPUE) and environmental variables from model outputs in New Caledonia's Exclusive Economic Zone (EEZ) were examined through generalized linear models at a 1°s patial resolution and 10-day temporal resolution. At a regional (EEZ) scale, the study demonstrated that a large part of albacore CPUE variability can be explained by seasonal, interannual and spatial variation of the habitat. Results of the generalized linear models indicated that catch rates are higher than average in the northwestern part of the EEZ at the beginning of the year (January) and during the second half of the year (July-December). In the northwestern region of the EEZ, high CPUEs are associated with waters <20.5°in the intermediate layer and with moderate values of primary production. Longline CPUE also appeared to be dependent on prey densities, as predicted from a micronekton model. Albacore CPUE was highest at moderate densities of prey in the epipelagic layer during the night and for relatively low prey densities in the mesopelagic layer during the day. We also demonstrated that the highest CPUEs were recorded from 1986 to 1998, which corresponds to a period with frequent El Niño events.

Variable selection is fundamenta l to high-dimensiona l statistical modeling, including nonparametri c regression. Many approaches in use are stepwise selection procedures , which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized likelihood approache s are proposed to handle these kinds of problems. The proposed methods select variables and estimate coef cients simultaneously. Hence they enable us to construct con dence intervals for estimated parameters. The proposed approaches are distinguished from others in that the penalty functions are symmetric, nonconcav e on 401ˆ5, and have singularities at the origin to produce sparse solutions. Furthermore, the penalty functions should be bounded by a constant to reduce bias and satisfy certain conditions to yield continuous solutions. A new algorithm is proposed for optimizing penalized likelihood functions. The proposed ideas are widely applicable. They are readily applied to a variety of parametric models such as generalized linear models and robust regression models. They can also be applied easily to nonparametri c modeling by using wavelets and splines. Rates of convergenc e of the proposed penalized likelihood estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well as if the correct submodel were known. Our simulation shows that the newly proposed methods compare favorably with other variable selection techniques. Furthermore, the standard error formulas are tested to be accurate enough for practical applications.

Latent class models (LCMs) can be used to assess diagnostic test performance when no reference test (a gold standard) is available, considering two latent classes representing disease or non-disease status. One of the basic assumptions in such models is that of local or conditional independence: all indicator variables (tests) are statistically independent within each latent class. However, in practice this assumption is often violated; hence, the two-LCM fits the data poorly. In this paper, we propose the use of Biplot methods to identify the conditional dependence between pairs of manifest variables within each latent class. Additionally, we propose incorporating such dependence in the corresponding latent class using the log-linear formulation of the model. The LCM is also used to evaluate the reasons for agreement/disagreement between clinical diagnoses or opinions provided by different raters/observers . The model, constructed under the assumption of conditional independence, assumes that within each latent class the evaluation provided by each of the specialists is statistically independent from the evaluations provided by the others.

Stock-recruitment (S-R) models are commonly fitted to S-R data with a least-squares method. Errors in modeling are usually assumed to be normal or lognormal, regardless of whether such an assumption is realistic. A Monte Carlo simulation approach was used to evaluate the impact of the assumption of error structure on S-R modeling. The generalized linear model, which can readily deal with different error structures, was used in estimating parameters. This study suggests that the quality of S-R parameter estimation, measured by estimation errors, can be influenced by the realism of error structure assumed in an estimation, the number of S-R data points, and the number of outliers in modeling. A small number of S-R data points and the presence of outliers in S-R data could increase the difficulty in identifying an appropriate error structure in modeling, which might lead to large biases in the S-R parameter estimation. This study shows that generalized linear model methods can help identify an appropriate error distribution in S-R modeling, leading to an improved estimation of parameters even when there are outliers and the number of S-R data points is small. We recommend the generalized linear model be used for quantifying stock-recruitment relationships.

Considering the time-series ARIMA(p, d, q) model and fuzzy regression model, this paper develops a fuzzy ARIMA (FARIMA) model and applies it to forecasting the exchange rate of NT dollars to US dollars. This model includes interval models with interval parameters and the possibility distribution of future values is provided by FARIMA. This model makes it possible for decision makers to forecast the best-and worst-possible situations based on fewer observations than the ARIMA model.

We used aerial counts to monitor the trend in numbers of harbor seals, Pboca vitulina ricbardsi, in Prince William Sound, Alaska, following the 1989 Exxon Valdez oil spill. Repetitive counts were made at 25 haul-out sites during the annual molt period each year from 1990 through 1997. A generalized linear model indicated that time of day, date, and time relative to low tide significantly affected seal counts. When Poisson regression was used to adjust counts to a standardized set of survey conditions, results showed a highly significant decline of 4.6% per year. Unadjusted counts indicated a slight, but not statistically significant, decline in the number of seals. The number of harbor seals on the trend-count route in eastern and central PWS has been declining since at least 1984, with an overall population reduction of 63% through 1997.

In fitting production models and age-structured models to an index of the relative abundance of a fish population, errors are usually assumed to follow a log-normal or normal distribution, without any diagnostic analyses. A generalized linear model can readily deal with many types of error structures. In this paper, a generalized linear model is coupled with a production model and a sequential population model to assess the stock of the Atlantic cod (Gadus morhua) 2J3KL. This study suggests that the parameter estimates in these models can be greatly influenced by the assumption about the error structures in the estimation and that log-normal and gamma distributions are appropriate for the production model in assessing the Atlantic cod 2J3KL stock, whereas gamma distribution is appropriate for the sequential population model. We recommend that generalized linear models should be used to identify the appropriate error structure in modeling fish population dynamics.

This study aims primarily to assess the response of two invertebrate groups to the effects of pastoralism and military training, at one site in the tropical savanna of north-eastern Queensland. The richness and species composition of ants and terrestrial spiders were examined at two contrasting times of year across three land use treatments (pastoralism, military training and undisturbed) and four landscape positions (upper slope to riparian). Ant species richness was least in the grazed sites, and a high proportion of the ant species recorded varied significantly in frequency between the grazed and the two ungrazed land uses. This variation was generally greater than that associated with landscape position. Although variation in the richness of spiders was significantly related to land-use type, this effect was less pronounced than for ants, was less marked than variation associated with landscape position and was confounded by a strong interaction between land use and landscape position. Quadratscale variation in the composition of spider assemblages was influenced most by season of sampling. For both spiders and ants, there were few differences in richness or species composition between undisturbed land and that managed for military use.

Extreme value data with a high clump-at-zero occur in many domains. Moreover, it might happen that the observed data are either truncated below a given threshold and/or might not be reliable enough below that threshold because of the recording devices. These situations occur, in particular, with radio audience data measured using personal meters that record environmental noise every minute, that is then matched to one of the several radio programs. There are therefore genuine zeros for respondents not listening to the radio, but also zeros corresponding to real listeners for whom the match between the recorded noise and the radio program could not be achieved. Since radio audiences are important for radio broadcasters in order, for example, to determine advertisement price policies, possibly according to the type of audience at different time points, it is essential to be able to explain not only the probability of listening to a radio but also the average time spent listening to the radio by means of the characteristics of the listeners. In this paper we propose a generalized linear model for zero-inflated truncated Pareto distribution (ZITPo) that we use to fit audience radio data. Because it is based on the generalized Pareto distribution, the ZITPo model has nice properties such as model invariance to the choice of the threshold and from which a natural residual measure can be derived to assess the model fit to the data. From a general formulation of the most popular models for zero-inflated data, we derive our model by considering successively the truncated case, the generalized Pareto distribution and then the inclusion of covariates to explain the nonzero proportion of listeners and their average listening time. By means of simulations, we study the performance of the maximum likelihood estimator (and derived inference) and use the model to fully analyze the audience data of a radio station in a certain area of Switzerland.

Generalized linear models (GLM) allow for a wide range of statistical models for regression data. In particular, the logistic model is usually applied for binomial observations. Canonical links for GLM's such as the logit link in the binomial case, are often used because in this case su cient statistics for the regression parameter exist which a l l o w for simple interpretation of the results. However, in some applications, the overall t as measured by the p-values of goodness of t statistics (as the residual deviance) can be improved signi cantly by the use of a noncanonical link. In this case, the interpretation of the in uence of the covariables is more complicated compared to GLM's with canonical link functions. It will be illustrated through simulation that the p-value associated with the common goodness of link tests is not appropriate to quantify the changes to mean response estimates and other quantities of interest when switching to a noncanonical link. In particular, the rate of misspeci cations becomes considerably large, when the inverse information value associated with the underlying parametric link model increases. This shows that the classical tests are often too sensitive, in particular, when the number of observations is large. The consideration of a generalized p-value function is proposed instead, which a l l o ws the exact quanti cation of a suitable distance to the canonical model at a controlled error rate. Corresponding tests for validating or discriminating the canonical model can easily performed by means of this function. keywords: generalized linear models, goodness of link tests, logistic regression, link function, parametric links, model validation and discrimination, p-value curve.

In fitting production models and age-structured models to an index of the relative abundance of a fish population, errors are usually assumed to follow a log-normal or normal distribution, without any diagnostic analyses. A generalized linear model can readily deal with many types of error structures. In this paper, a generalized linear model is coupled with a production model and a sequential population model to assess the stock of the Atlantic cod (Gadus morhua) 2J3KL. This study suggests that the parameter estimates in these models can be greatly influenced by the assumption about the error structures in the estimation and that log-normal and gamma distributions are appropriate for the production model in assessing the Atlantic cod 2J3KL stock, whereas gamma distribution is appropriate for the sequential population model. We recommend that generalized linear models should be used to identify the appropriate error structure in modeling fish population dynamics.

Timely effective cost management requires reliable cost estimates at every stage of project development. While underestimation of transportation costs seems to be a global trend, improving early cost prediction accuracy in estimates is difficult. This paper presents a parametric estimating technique applied to Texas highway projects using a set of project characteristics. Generalized linear models (GLM) of early quantity prediction for geometry-related work activities, namely earthwork, pavement and traffic control were developed for continuous project cost tracking. The approach of cost breakdown demonstrates the potential to separate quantity uncertainty from price uncertainty for highway construction. The benefit of this approach is to provide a platform for evolving the preliminary parametric cost estimates to a fully detailed cost management as further information becomes available as the project progresses. During project execution, managers are given opportunities to review the associated work activities and make better decisions from the developed GLM-based estimating system. Compared to typical practice of applying a gross cost per lane length during pre-project planning phase, the proposed approach with the aid of the developed expert system provides more detailed basis and efficiency for tracking the effects of changes within the project life cycle.

We review three leading stochastic optimization methods-simulated annealing, genetic algorithms, and tabu search. In each case we analyze the method, give the exact algorithm, detail advantages and disadvantages, and summarize the literature on optimal values of the inputs. As a motivating example we describe the solution-using Bayesian decision theory, via maximization of expected utility-of a variable selection problem in generalized linear models, which arises in the cost-effective construction of a patient sickness-at-admission scale as part of an effort to measure quality of hospital care.

Equality and proportionality of the ordinary least-squares estimator (OLSE), the weighted least-squares estimator (WLSE), and the best linear unbiased estimator (BLUE) for Xb in the general linear (Gauss-Markov) model M ¼ fy; Xb; s 2 Rg are investigated through the matrix rank method. r

Aim Numerous functions have been proposed to describe the species-area relationship but despite almost a century of curve-fitting there is little agreement on which is best. We aimed to rationalize the list of proposed functions and to discuss appropriate methodology for fitting and comparing the alternatives.

We analyze in a regression setting the link between a scalar response and a functional predictor by means of a Functional Generalized Linear Model. We first give a theoretical framework and then discuss identifiability of the model. The functional coefficient of the model is estimated via penalized likelihood with spline approximation. The L 2 rate of convergence of this estimator is given under smoothness assumption on the functional coefficient. Heuristic arguments show how these rates may be improved for some particular frameworks. r

Missingness frequently complicates the analysis of longitudinal data. A popular solution for dealing with incomplete longitudinal data is the use of likelihood-based methods, when, for example, linear, generalized linear, or non-linear mixed models are considered, due to their validity under the assumption of missing at random (MAR). Semi-parametric methods such as generalized estimating equations (GEE) offer another attractive approach but require the assumption of missing completely at random (MCAR). Weighted GEE (WGEE) has been proposed as an elegant way to ensure validity under MAR. Alternatively, multiple imputation (MI) can be used to pre-process incomplete data, after which GEE is applied (MI-GEE). Focusing on incomplete binary repeated measures, both methods are compared using the so-called asymptotic, as well as small-sample, simulations, in a variety of correctly specified as well as incorrectly specified models. In spite of the asymptotic unbiasedness of WGEE, results provide striking evidence that MI-GEE is both less biased and more accurate in the small to moderate sample sizes which typically arise in clinical trials.

The purpose of this study is to examine the number of DIF items detected by HGLM at different sample sizes.
Eight different sized data files have been composed. The population of the study is 798307 students who had
taken the 2006 OKS Examination. 10727 students of 798307 are chosen by random sampling method as the
sample of the study. Turkish, science, and social studies subtests, all composed of 25 items and applied in the
OKS-2006, are used as data gathering instruments in this study. It has been concluded that varieties in sample
sizes have a great effect on DIF detection in test items

The control and management of non-indigenous plant species (NIS) can be conceptually divided into three phases: inventory/survey, monitoring and management. Here we focus on phase one, determining which species are present and where they are located within the environment. Sampling for NIS is inherently time-consuming and thus costly. Many management areas are large and therefore can only be surveyed (partial observation of the total area by sampling) and not inventoried (total observation of area). Survey data should reflect the spatial distribution of the target species populations over the landscape. Such data can then be used in combination with environmental data, to create probability maps of target species occurrence for the entire area of interest. We used a GIS model to evaluate seven different survey methods for consistency and reliability of intersecting NIS species' patches and producing samples which reflect the spatial distribution of the population, and which can be performed in a cost and time-efficient manner. The GIS model was developed to create NIS populations which were then sampled using the different survey methods, and the results recorded. To improve the applicability of the model, four patch sizes and levels of occurrence were used, along with random and weighted distribution patterns in relation to patch proximity to roads and trails. Grid and random points, and targeted (stratified continuous) transects (starting on a road or trail (rights of way (RoW)) and finishing 2 km from any RoW) methods provided the most consistent samples of the population. Logistically, point methods required an unrealistic distance and time commitment in comparison with transect methods. The importance of collecting information on the size of NIS patches was demonstrated as more small patches were intersected than larger ones when the area infested was held constant. Thus, if frequency of patches is used to explain the results of a survey then comparisons between species and methods are difficult to interpret thus leading to erroneous conclusions. However, use of percentage of area infested estimates provides for easier comparison between species and sample methods. The targeted transect method provided the most reliable, efficient and consistent sample with the expected spatial distribution. Abbreviations: NIS-non-indigenous plant species; perp.RoW-perpendicular to rights of way transect survey method; RoW-rights of way e.g. roads and trails; SaD-Seek and destroy survey method; YNP-Yellowstone National Park

Historical longline catch per unit effort (CPUE) constitutes the major time series used in tuna stock assessment to follow the trend in abundance since the beginning of the large-scale tuna fisheries. The efficiency and species composition of a longline fishing operations essentially depends on the overlap in the vertical and spatial distribution between hooks and species habitat. Longline catchability depends on the vertical distribution of hooks and the aim of our paper was to analyse principal factors affecting the deviation of observed longline hook depths from predicted values. Since observed hook depth is usually shallower than predicted, this deviation is called longline shoaling. We evaluate the accuracy of hook depth distribution estimated from a theoretical catenary model commonly used in longline CPUE standardizations. Temperature-depth recorders (TDRs) were deployed on baskets of a monitored longline. Mainline shapes and maximum fishing depths were similar to gear configurations commonly used to target both yellowfin and bigeye tuna by commercial longliners in the central part of the South Pacific Ocean. Our working hypothesis assumes that the maximum fishing depth reached by the mainline depends on the gear configuration (sag ratio, mainline length per basket), the fishing tactics (bearing of the setting) and environmental variables characterizing water mass dynamics (wind stress, current velocity and shear). Based on generalized additive models (GAMs) simple transformations are proposed to account for the non-linearity between the shoaling and explanatory variables. Then, generalized linear models (GLMs) were fit to model the effects of explanatory variables on the longline shoaling. Results indicated that the shoaling (absolute as well as relative) was significantly influenced by (1) the shape of the mainline (i.e., the tangential angle), which is the strongest predictor, and (2) the current shear and the direction of setting. Geometric forcing (i.e. transverse versus in-line) between the environment and the longline set is shown for the first time from in situ experimental fishing data. Results suggest that a catenary model that does not take these factors into consideration provides a biased estimate of the vertical distribution of hooks and must be used with caution in CPUEs standardization methods. Since catchability varies in time and space we discuss how suitable data could be routinely collected onboard commercial fishing vessels in order to estimate longline catchability for stock assessments. (P. Bach). catch rates as an index of abundance, and the ability to adequately standardize catch rates, has been the subject of much debate Maunder et al., 2006a,b). For a passive longline fishing, this hypothesis is further complicated by the fact that longline catchability is influenced by a number of factors related to gear configuration . Thus while variables such as area, year, and season are commonly considered in CPUE standardization, many others factors such as bait, fishing materials, day vs. night fishing period, soaking time, and fishing depth which are known to influence CPUE and are often not taken into account in such standardizations

Information criteria form an important class of model/variable selection methods in statistical analysis. Parametric likelihood is a crucial part of these methods. In some applications such as the generalized linear models, the models are only specified by a set of estimating functions. To overcome the non-availability of well defined likelihood function, the information criteria under empirical likelihood are introduced. Under this setup, we successfully solve the existence problem of the profile empirical likelihood due to the over constraint in variable selection problems. The asymptotic properties of the new method are investigated.

Grid gates with multiple sharp-crested rectangular orifices are used to control manually water discharge from branch channels to semi-intensive aquaculture ponds. Experimental and analytical analysis related to the discharge characteristics of these grid gates under submerged flow conditions have been presented in this paper with the objective to integrate the results in an support system to control the water exchange management. Experimental analysis was carried out in the laboratory using a scaled model. Steady-state hydraulic data were measured and collected for each tested grid gate considering different orifices number and flow rates. Multiple linear regression (MLR), factorial regression (FR), polynomial regression (PR), hybrid model (PR + FR) and generalized linear model (GLM) were evaluated to determine the relationship between the coefficient of discharge C d and the non-dimensional parameters x=h 2 1 , b/h 1 and h 3 /h 1 (x is the total cross section of discharge; h 1 is the upstream water level of the grid gate; h 3 is the downstream water level of the grid gate; and b is the width of the channel) which were obtained by the analysis dimensional. Of all these approaches, the best fits were obtained using a FR + PR hybrid model and a GLM model with only two non-dimensional parameters x=h 2 1 and h 3 /h 1 as independent variables. These models produced errors not higher than ±3%. The best GLM model and the aquaculturist knowledge in relation to the management of water exchange were integrated in a computer program namely 'Gate management' which was implemented in the ACUIGES system.

Whereas previous studies have investigated correlates of extinction risk either at global or regional scales, our study explicitly models regional effects of anthropogenic threats and biological traits across the globe. Using phylogenetic comparative methods with a newly-updated supertree of 5020 extant mammals, we investigate the impact of species traits on extinction risk within each WWF ecoregion. Our analyses reveal strong geographical variation in the influence of traits on risk: notably, larger species are at higher risk only in tropical regions. We then relate these patterns to current and recent-historical human impacts across ecoregions using spatial modelling. The body–mass results apparently reflect historical declines of large species outside the tropics due to large-scale land conversion. Narrow-ranged and rare species tend to be at high risk in areas of high current human impacts. The interactions we describe between biological traits and anthropogenic threats increase understanding of the processes determining extinction risk.

In the paper we propose nonparametric approaches for e-learning data. In particular we want to supply a measure of the relative exercises importance, to estimate the acquired Knowledge for each student and finally to personalize the e-learning platform. The methodology employed is based on a comparison between nonparametric statistics for kernel density classification and parametric models such as generalized linear models and generalized additive models.

1 An important goal of community ecology is the assessment of factors that are likely to influence the spatio-temporal distribution of species assemblages and diversity. Surprisingly, most statistical methods devoted to this have remained poorly interconnected, as well as poorly connected with the popular metrics of diversity estimation. In the present paper we show that important questions related to determinants of species diversity can be specified through a simple multivariate linear model and explored, in common diversity metrics, using standard methods and routines of variance/covariance decomposition. 2 Thanks to an unusual form of presentation of taxonomic data into a table of species occurrences , which considers the individuals as data units, Shannon and Simpson indices as well as species richness can all be expressed as a (weighted) sum of squares. Subsequent apportionments into explained and residual sum of squares provide direct estimates of the beta-and alpha-diversity components with respect to either categorical habitat types or continuous gradient variables. Appropriate statistics and non-parametric tests are available to assess the significance of these components. 3 Explicit analytical relationships exist between the linear approximation of the table of species occurrences by sampling sites, and the more classical table of species abundances by sites. Therefore, direct links with methods of ordination in reduced space, such as correspondence analysis and canonical correspondence analysis, provide opportunities for partitions that preserve consistency with usual diversity indices. The sum of squares of the approximated occurrence table provides measures of intersites beta-diversity, from which measures of dissimilarity with explicit references to diversity indices can be derived. Such measures are amenable to distance-based apportionments through multivariate variograms and multiscale ordination. 4 What are the relative effects of the biological, environmental and anthropogenic factors and of their potential interactions on species diversity? Are these effects stable across scales, from landscape to region, between regions and across ecosystems? The methodological integration proposed in our analytical framework enables one to address these questions using standard statistical tools, and opens new prospects for quantitative biodiversity studies. This also paves the way towards refined models for predicting species diversity at unsampled locations.

To manage or control nonindigenous species (NIS), we need to know where they are located in the landscape. However, many natural areas are large, making it unfeasible to inventory the entire area and necessitating surveys to be performed on smaller areas. Provided appropriate survey methods are used, probability of occurrence predictions and maps can be generated for the species and area of interest. The probability maps can then be used to direct further sampling for new populations or patches and to select populations to monitor for the degree of invasiveness and effect of management. NIS occurrence (presence or absence) data were collected during 2001 to 2003 using transects stratified by proximity to rights-of-way in the northern range of Yellowstone National Park. In this study, we evaluate the use of environmental and remotely sensed (LANDSAT Enhanced Thematic Mapper ϩ) data, separately and combined, for developing probability maps of three target NIS occurrence. Canada thistle, dalmation toadflax, and timothy were chosen for this study because of their different dispersal mechanisms and frequencies, 5, 3, and 23%, respectively, in the surveyed area. Data were analyzed using generalized linear regression with logit link, and the best models were selected using Akaike's Information Criterion. Probability of occurrence maps were generated for each target species, and the accuracies of the predictions were assessed with validation data excluded from the model fitting. Frequencies of occurrence of the validation data were calculated and compared with predicted probabilities. Agreement between the observed and predicted probabilities was reasonably accurate and consistent for timothy and dalmation toadflax but less so for Canada thistle.

Count data are usually modeled using the Poisson generalized linear model. The Poisson model requires that the variance be a deterministic function of the mean. This assumption may not be met for a particular data set, that is, the model may not adequately capture the variability in the data. The extra-variability in the data may be accommodated using overdispersion models, such as the negative binomial distribution. In addition to the overdispersion outliers may be present in the data as indicated by the model residuals or some functions of the model residuals. A variance shift outlier model (VSOM) for count data is introduced. The model is used to detect potential outliers in the data, and to downweight them in the analysis if desired. In this model the overdispersion is modeled using an observation-specific random effect. The status of a given observation as an outlier is indicated by the size of the associated shift in variance for that observation. The model is then extended to longitudinal count data for the detection of outliers at the subject level. We illustrate the methodology using a real data set taken from the literature. Extensions of the VSOM for count data to other non-normal responses are discussed.

Widespread conversion of deciduous forests to agriculture in the midwestern United States has resulted in landscapes whose remaining native habitats are highly fragmented, with well-documented consequences for wildlife community structure. We analyzed trap data for 5 forest rodent species from 525 sites in 35 study landscapes throughout the upper Wabash River basin, which is dominated by agricultural use and drains >20% of Indiana. We used a recently developed likelihood approach and multi-model inference to obtain unbiased estimates of occurrence probabilities for a species when detection rates are <1, and we used hierarchical generalized linear modeling to evaluate random effects associated with nested data structure. Inclusion of a spatial autocovariate term had important effects on model selection results for 4 of 5 species and improved fit of models. Eastern chipmunks (Tamias striatus), although previously described as sensitive to fragmentation, were nearly ubiquitous in our study region and had greater occupancy rates in smaller woodlots. Fox squirrels (Sciurus niger) are well adapted to patchy landscapes, and their occupancy rates actually increased with patch isolation. Gray squirrels (S. carolinensis) are adversely affected by forest fragmentation; we observed a threshold decline in occupancy rates beyond ∼15 km from the Wabash River, which harbors the only source of contiguous habitat within the entire river basin. Red squirrels (Tamiasciurus hudsonicus) exhibited greater abundance in sites without gray squirrels. Moreover, their occupancy rates were positively related to habitat and landscapes considered suboptimal (e.g., lower basal area of hard-mast bearing trees, more isolated patches); this was further evidence for negative effects of gray squirrels on red squirrel populations. White-footed mice (Peromyscus leucopus) were nearly ubiquitous; although occurrence rates in less forested landscapes increased with distance from edge and greater volume of woody debris.

A resource selection function (RSF) is any model that yields values proportional to the probability of use of a resource unit. RSF models often are fitted using generalized linear models (GLMs) although a variety of statistical models might be used. Information criteria such as the Akaike Information Criteria (AIC) or Bayesian Information Criteria (BIC) are tools that can be useful for selecting a model from a set of biologically plausible candidates. Statistical inference procedures, such as the likelihood-ratio test, can be used to assess whether models deviate from random null models. But for most applications of RSF models, usefulness is evaluated by how well the model predicts the location of organisms on a landscape. Predictions from RSF models constructed using presence/absence (used/ unused) data can be evaluated using procedures developed for logistic regression, such as confusion matrices, Kappa statistics, and Receiver Operating Characteristic (ROC) curves. However, RSF models estimated from presence/ available data create unique problems for evaluating model predictions. For presence/available models we propose a form of k -fold cross validation for evaluating prediction success. This involves calculating the correlation between RSF ranks and area-adjusted frequencies for a withheld sub-sample of data. A similar approach can be applied to evaluate predictive success for out-of-sample data. Not all RSF models are robust for application in different times or different places due to ecological and behavioral variation of the target organisms. #

Evidence for severe declines in large predatory fishes is increasing around the world. Because of its long history of intense fishing, the Mediterranean Sea offers a unique perspective on fish population declines over historical timescales. We used a diverse set of records dating back to the early 19th and mid 20th century to reconstruct long-term population trends of large predatory sharks in the northwestern Mediterranean Sea. We compiled 9 time series of abundance indices from commercial and recreational fishery landings, scientific surveys, and sighting records. Generalized linear models were used to extract instantaneous rates of change from each data set, and a meta-analysis was conducted to compare population trends. Only 5 of the 20 species we considered had sufficient records for analysis. Hammerhead (Sphyrna spp.), blue (Prionace glauca), mackerel (Isurus oxyrinchus and Lamna nasus), and thresher sharks (Alopias vulpinus) declined between 96 and 99.99% relative to their former abundance. According to World Conservation Union (IUCN) criteria, these species would be considered critically endangered. So far, the lack of quantitative population assessments has impeded shark conservation in the Mediterranean Sea. Our study fills this critical information gap, suggesting that current levels of exploitation put large sharks at risk of extinction in the Mediterranean Sea. Possible ecosystem effects of these losses involve a disruption of top-down control and a release of midlevel consumers.

Selassie AW, Varma A, Saunders LL. Current trends in venous thromboembolism among persons hospitalized with acute traumatic spinal cord injury: does early access to rehabilitation matter? Arch Phys Med Rehabil 2011;92:1534-41. Objective: To determine the incidence of venous thromboembolism (VTE) among patients with traumatic spinal cord injury (TSCI) in acute care settings that is attributable to extended length of stay (LOS), insurance status, and access to rehabilitation. Design: Population-based, retrospective cohort study. Setting: Levels I through III and undesignated trauma centers. Participants: Patients with acute TSCI (Nϭ3389) discharged from all acute care hospitals in South Carolina from 1998 through 2009, and a representative sample of patients with TSCI (nϭ186) interviewed 1 year later. Interventions: Not applicable. Main Outcome Measure: VTE while in acute care. Results: Annual incidence of TSCI is 67.2 per million in the state of South Carolina, while the cumulative incidence of VTE is 4.1%. Patients with TSCI who developed VTE were nearly 4 times more likely (odds ratio [OR], 3.98; 95% confidence interval [CI], 2.57-6

Resource selection functions (RSF) have contributed to the conservation of species negatively affected by human activities. Despite these applications, two assumptions frequent many studies: the assumption of independence among groups in social species, and that selection is proportional to resource availability. This latter case is known as a functional response in resource selection, and may be especially important in human-wildlife relationships where there is a fitness cost of proximity to humans. 2. Recent advances in generalized linear mixed models offer new ways to account for resource selection in social species and functional responses by accommodating correlations within hierarchical groups with random intercepts, and functional responses with random coefficients. 3. We illustrate the application of mixed-effects RSF models using a case study of resource selection by individual wolves Canis lupus living in packs as a function of human activity. 4. In areas of low human activity, wolf resource selection was independent of proximity to humans. As human activity increased, wolves displayed a functional response selecting areas closer to human activity. With increasing human activity, however, wolves displayed spatio-temporal avoidance of human activity during daylight. This could lead to behaviourally induced trophic cascades mediated by wolf avoidance of human activity, and fits within the framework of attractive sink habitats. 5. Accounting for the hierarchical social structure of wolves clearly showed that the response of wolves to human disturbance was strongly correlated, but different, within packs, and that the correlation was strongest during winter and weakest during summer. 6. Syntheses and applications . Failure to consider the social structure of wolves and the functional response to human activity would result in mistaken conclusions about wolf-human relationships. Our approach provides a unifying framework to understand the contradictory results of previous studies of wolf-human relationships and a template for future studies to evaluate effects of increasing human activity on wildlife.

Th e aim of this research is to determine diff erential item functioning (DIF) by hierarchical
linear modeling (HGLM) on test items and comparing these results by the DIF results
determined by logistic regression (LR) and IRT-likelihood ratio (IRT-LR) techniques.
Investigating the concordance between the techniques in determining the items
with DIF, we have found significant relations between items with DIF determined in
Turkish and Science sub-tests using LR and IRT-LR. In Social Studies test, we have
found significant relation between the results of the HGLM and LR, HGLM and IRTLR,
LR and IRT-LR techniques. Th e number of items with DIF per gender determined
by all three diff erent techniques has been found to be almost half of the number of test
items. Th ough all the level of the items determined by LR technique have been negligible,
with IRT-LR technique only a very few of the items have been found with negligible
DIF. Comparing the Social Studies and Science sub-tests with Turkish sub-test using
HGLM technique, more than half of the items have been found to have DIF. Turkish
sub-test has the maximum number of item with DIF.

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order n^-1, where n is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected Pearson residuals.

We introduce the Hinde-Demétrio (HD) regression models in order to analyze overdispersed count data. We mainly investigate the effect of the dispersion parameter. The HD distributions are discrete additive exponential dispersion models (depending on canonical and dispersion parameters) with a third real index parameter p. They have been characterized by the unit variance function µ + µ p. For p equal to 2, 3,. .. , the corresponding distributions are concentrated on non-negative integers, overdispersed and zero-inflated with respect to a Poisson distribution having the same mean. The negative binomial (p = 2), strict arcsine (p = 3) and Poisson (p → ∞) distributions are particular count HD families. In a generalized linear modelling framework, the effect of the dispersion parameter in the HD regression models is, among other things, pointed out through the two parametrizations for the mean: unit and standard means. In this particular additive model, this effect must be negligible within an adequate HD model for fixed p. The estimation of the integer p is also examined separately. The results are illustrated and discussed on a horticultural data set.

The paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases. The paper develops jackknife theory for the important, but so far neglected, prediction problem for the general mixed model. For estimation of fixed parameters, a jackknife method is considered for a general class of M-estimators which includes the maximum likelihood, residual maximum likelihood and ANOVA estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models. For both the prediction and estimation problems, a jackknife method is used to obtain estimators of the mean squared errors (MSE). Asymptotic unbiasedness of the MSE estimators is shown to hold essentially under certain moment conditions. Simulation studies undertaken support our theoretical results.

Between 1991 and the present, we have had observers stationed at the port of San Juan in southern Peru to interview fishers as they landed their catch. They observed the landings of 922 Humboldt Penguins ( Spheniscus humboldti ), 510 dusky dolphins ( Lagenorhynchus obscurus ), 214 Burmeister's porpoises ( Phocaena spinnipinnis ), and 75 bottlenose dolphins ( Tursiops truncatus ) between November 1991 and June 1998, although the retention of penguins and small cetaceans is banned by Peruvian law. Most of these animals were captured in [1992][1993][1994], when the fishers were mainly using surface-drift gillnets to target a pelagic schooling fish called cojinova ( Seriolella violacea ). Capture rates were much lower in 1995-1998, when fishers were mostly using fixed demersal gillnets and shellfish diving, due apparently to a lack of surface-schooling cojinova in the vicinity. We used generalized linear models to examine the effect of year, gear type, area, and target fish species on the probability of capturing either penguins or dolphins. We found that the probability of a fishing vessel capturing a penguin or a dolphin increased when drift gillnets were used instead of fixed gillnets. Fishing area, year, and the species of fish caught also significantly affected the probability of capture. A population model ( Vortex) applied to Humboldt Penguins showed that the high levels of mortality seen in the early 1990s are not sustainable and could lead to local extinction in a few years. The mortality levels seen in the late 1990s are more likely to be sustainable, but a return to the use of drift gillnets would rapidly result in unsustainable levels of mortality.

Given a number of different studies estimating the same effect size, it is often desired to explain heterogeneity of outcomes using concomitant covariates. For very large sample sizes, effect size estimates are approximately normally distributed and a straightforward application of weighted least squares is appropriate. However in practice within study sample variances are often small to moderate, casting doubt on the normality assumption for effect sizes and results based on weighted least squares. One can alternatively variance stabilize the effect size estimates and adopt a generalized linear model. Both methods are compared on two examples when effect sizes are the standardized difference of means. Then simulation studies are conducted to compare the coverage and width of confidence intervals for the meta-regression coefficients. These simulations show that the coverage probability associated with weighted least squares can be well below the nominated level for small to moderate sample sizes. Further empirical investigations reveal a bias in estimation due to using estimated weights which were assumed to be known. For these models, the generalized linear model approach resulted in much improved coverage probabilities.

In the United States, the number of Phasor Measurement Units (PMU) will increase from 166 networked devices in 2010 to 1043 in 2014. According to the Department of Energy, they are being installed in order to "evaluate and visualize reliability margin (which describes how close the system is to the edge of its stability boundary)." However, there is still a lot of debate in academia and industry around the usefulness of phase angles as unambiguous predictors of dynamic stability. In this paper, using 4-year of actual data from Hydro-Québec EMS, it is shown that phase angles enable satisfactory predictions of power transfer and dynamic security margins across critical interface using random forest models, with both explanation level and R-squares accuracy exceeding 99%.