Search

We develop hierarchical models and methods in a fully parametric approach to generalized linear mixed models for any patterned covariance matrix. The Laplace approximation is used to marginally estimate covariance parameters by integrating over all fixed and latent random effects. The Laplace approximation relies on Newton–Raphson updates, which also leads to predictions for the latent random effects. We develop methodology for complete marginal inference, from estimating covariance parameters and fixed effects to making predictions for unobserved data. The marginal likelihood is developed for six distributions that are often used for binary, count, and positive continuous data, and our framework is easily extended to other distributions. We compare our methods to fully Bayesian methods, automatic differentiation, and integrated nested Laplace approximations (INLA) for bias, mean‐squared (prediction) error, and interval coverage, and all methods yield very similar results. However, our methods are much faster than Bayesian methods, and more general than INLA. Examples with binary and proportional data, count data, and positive‐continuous data are used to illustrate all six distributions with a variety of patterned covariance structures that include spatial models (both geostatistical and areal models), time series models, and mixtures with typical random intercepts based on grouping. [ABSTRACT FROM AUTHOR]

We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each of these goals can present different challenges when analyzing large spatial data sets. Current research uses a variety of methods, including spatial basis functions (reduced rank), covariance tapering, etc, to achieve these goals. However, spatial indexing, which is very similar to composite likelihood, offers some advantages. We develop a simple framework for all four goals listed above by using indexing to create a block covariance structure and nearest-neighbor predictions while maintaining a coherent linear model. We show exact inference for fixed effects under this block covariance construction. Spatial indexing is very fast, and simulations are used to validate methods and compare to another popular method. We study various sample designs for indexing and our simulations showed that indexing leading to spatially compact partitions are best over a range of sample sizes, autocorrelation values, and generating processes. Partitions can be kept small, on the order of 50 samples per partition. We use nearest-neighbors for kriging and block kriging, finding that 50 nearest-neighbors is sufficient. In all cases, confidence intervals for fixed effects, and prediction intervals for (block) kriging, have appropriate coverage. Some advantages of spatial indexing are that it is available for any valid covariance matrix, can take advantage of parallel computing, and easily extends to non-Euclidean topologies, such as stream networks. We use stream networks to show how spatial indexing can achieve all four goals, listed above, for very large data sets, in a matter of minutes, rather than days, for an example data set. [ABSTRACT FROM AUTHOR]

Spatio-temporal models are widely used in many research areas from ecology to epidemiology. However, a limited number of computational tools are available for modeling river network datasets in space and time. In this paper, we introduce the R package SSNbayes for fitting Bayesian spatio-temporal models and making predictions on branching stream networks. SSNbayes provides a linear regression framework with multiple options for incorporating spatial and temporal autocorrelation. Spatial dependence is captured using stream distance and flow connectivity while temporal autocorrelation is modelled using vector autoregression approaches. SSNbayes provides the functionality to make predictions across the whole network, compute exceedance probabilities, and other probabilistic estimates, such as the proportion of suitable habitat. We illustrate the functionality of the package using a stream temperature dataset collected in the Clearwater River Basin, USA. [ABSTRACT FROM AUTHOR]

spmodel is an R package used to fit, summarize, and predict for a variety spatial statistical models applied to point-referenced or areal (lattice) data. Parameters are estimated using various methods, including likelihood-based optimization and weighted least squares based on variograms. Additional modeling features include anisotropy, non-spatial random effects, partition factors, big data approaches, and more. Model-fit statistics are used to summarize, visualize, and compare models. Predictions at unobserved locations are readily obtainable. [ABSTRACT FROM AUTHOR]

We developed spatial Bayesian hierarchical models to assess potential climate change impacts on suitable habitat for five important tree species in the Pacific northwestern United States (California, Oregon, and Washington). Individual‐species models were fit with presence–absence data from forest inventory field plots and spatial relationships were specified through a conditional autoregressive model. This modeling approach allowed us to visualize uncertainty in response curves, map current and future prediction uncertainty, and provide interval estimates for change. Upward elevational or northward latitudinal shifts in climatically suitable habitat were projected for all species. Climate change impacts were the most damaging for noble fir (Abies procera), for which 79%–100% of the current range was projected to become climatically unsuitable by the 2080s. Although coastal Douglas‐fir (Pseudotsuga menziesii var. menziesii) has been projected by others to gain habitat in Canada, within our study area we projected a net loss of climatically suitable habitat (ca. 8000–31,400 km2) under three of four future climate scenarios. A net loss in habitat was also projected for Oregon white oak (Quercus garryana) under three of four scenarios, with 40%–60% of the current range becoming unsuitable. Although there was no net loss of habitat for forest land blue oak under any scenario, other factors like competition may inhibit blue oak (Quercus douglasii) and white oak from occupying areas projected to increase in climatic suitability. Additionally, between 13% and 32% of blue oak's current range was projected to become unsuitable; some of these areas aligned with dieback following the 2012–2015 California drought, which our data set predates. Unlike the other four species, we projected a 17%–25% increase in climatically suitable habitat for California black oak (Quercus kelloggii), although 1%–20% of the current range was still projected to become unsuitable. Our findings indicate that, although some species will face more pressure in tracking climatically suitable habitat than others, climate change will impact the location of suitable habitat for many species. [ABSTRACT FROM AUTHOR]

Spatio‐temporal maps of organismal density or relative abundance are fundamental to many applications in conservation and ecology. There are often a number of data sources to inform species maps, including citizen science monitoring programs, remote sensing, geolocation data from satellite‐tagged animals and formal scientific surveys. In these cases, it may be desirable to come up with a single map integrating all data sources.We introduce a novel two‐step method for combining inference about relative abundance maps using multiple data sources. Log‐scale relative abundance surfaces are first estimated from individual data sets, and resultant surfaces are then treated as 'data' within a generalized linear mixed model framework with a spatially autocorrelated mean process. We also introduce generalizations allowing data misalignment and predictive processes to decrease computational burden.Using simulation, we show that our approach frequently outperfoms other approaches, including basing inference on a single surface, or taking a simple arithmetic mean (although the arithmetic mean performs well when there are few surfaces). We then demonstrate our method using citizen science and satellite‐tracking data of Steller sea lions in Alaska. In this case, relative abundance surfaces consisted of an effort‐adjusted map developed from platform‐of‐opportunity sightings and a utilization distribution developed from geolocation records. The resulting combined surface represented a compromise between single‐data source predictions.Our approach should be useful for ecologists seeking to reconcile alternative species distribution maps, particularly when individual surfaces are prone to bias, when there is no obvious common currency (e.g. point process), or when computational demands preclude a fully integrated analysis. [ABSTRACT FROM AUTHOR]

1. The design-based and model-based approaches to frequentist statistical inference rest on fundamentally different foundations. In the design-based approach, inference relies on random sampling. In the model-based approach, inference relies on distributional assumptions. We compare the approaches in a finite population spatial context. 2. We provide relevant background for the design-based and model-based approaches and then study their performance using simulated data and real data. The real data are from the United States Environmental Protection Agency's 2012 National Lakes Assessment. A variety of sample sizes, location layouts, dependence structures, and response types are considered. The population mean is the parameter of interest, and performance is measured using statistics like bias, squared error and interval coverage. 3. When studying the simulated and real data, we found that regardless of the strength of spatial dependence in the data, the generalized random tessellation stratified (GRTS) algorithm, which explicitly incorporates spatial locations into sampling, tends to outperform the simple random sampling (SRS) algorithm, which does not explicitly incorporate spatial locations into sampling. We also found that model-based inference tends to outperform design-based inference, even for skewed data where the model-based distributional assumptions are violated. The performance gap between design-based inference and model-based inference is small when GRTS samples are used but large when SRS samples are used, suggesting that the sampling choice (whether to use GRTS or SRS) is most important when performing design-based inference. 4. There are many benefits and drawbacks to the design-based and model-based approaches for finite population spatial sampling and inference that practitioners must consider when choosing between them. We provide relevant background contextualizing each approach and study their properties in a variety of scenarios, making recommendations for use based on the practitioner's goals. [ABSTRACT FROM AUTHOR]

Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time & day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods. Key words: covariates; generalized linear models; harbor seals; iteratively weighted least squares; overdispersion; quasi models.

Models for spatial autocorrelation and cross-correlation depend on the distance and direction separating two locations, and are constrained so that for all possible sets of locations, the covariance matrices implied [...]

Spatial confounding, that is, collinearity between fixed effects and random effects in a spatial generalized linear mixed model, can adversely affect estimates of the fixed effects. Restricted spatial regression methods have been proposed as a remedy for spatial confounding. Such methods replace inference for the fixed effects of the original model with inference for those effects under a model in which the random effects are restricted to a subspace orthogonal to the column space of the fixed effects model matrix; thus, they "deconfound" the two types of effects. We prove, however, that frequentist inference for the fixed effects of a deconfounded linear model is generally inferior to that for the fixed effects of the original spatial linear model; in fact, it is even inferior to inference for the corresponding nonspatial model. We show further that deconfounding also leads to inferior predictive inferences, though its impact on prediction appears to be relatively small in practice. Based on these results, we argue that deconfounding a spatial linear model is bad statistical practice and should be avoided. [ABSTRACT FROM AUTHOR]

The population of harbor seals (Phoca vitulina vitulina) along the coast of Maine, U.S.A., has experienced rapid growth in abundance following passage of the Marine Mammal Protection Act in 1972 but current information on trends in abundance is lacking. In this study, we apply a Bayesian hierarchical model to aerial survey data of nonpups and pups. Prior to 2001, estimates of growth rates from 8‐year moving averages reached a high of 2.1% and 9.4% per year with posterior probabilities of positive growth of.97 and >.99 for nonpups and pups, respectively. Between 2001 and 2012, estimated growth rates for nonpups decreased to a low of −1.9% per year with a posterior probability of negative growth of.95. Between 2012 and 2018, posterior estimates of growth were close to zero suggesting little change in abundance of nonpups. Estimates of growth for pups were close to zero between 2001 and 2012 but reached a low of −2.5% per year with a posterior probability of negative growth of 0.94 at the end of the time series suggesting a decrease in pup abundance between 2012 and 2018. The total abundance estimate for 2018 is 61,336 (CV = 0.08). [ABSTRACT FROM AUTHOR]

This paper presents a collaboration with Indigenous Nlaka'pamux communities to develop a study to address the effects of mining dust on soapberry (Shepherdia canadensis), which is an important medicinal and food resource for local Nlaka'pamux people. The objectives were to compare element concentrations in samples of washed and unwashed leaves and berries relative to soil samples collected around the mine and in a reference area. Samples were analyzed for metal concentrations using inductively coupled plasma mass spectrometry (ICP‐MS). Spatial models showed that six metals (Al, Ba, Cu, Fe, Pb, and Sr) had significant elevated concentrations near the mine compared to farther away, though concentrations were generally within ranges reported for human consumption. There was no correspondence with soil metal concentrations, suggesting that elevated metal concentrations in leaves and berries near the mine were due to dust rather than uptake from local soils. Washing of leaves and berries reduced concentrations by between 13 and 48%, depending on the metal. The study illustrates a model with global relevance for how mines can work with communities to address complex social–ecological problems. [ABSTRACT FROM AUTHOR]

With the advent of technology for data gathering and storage, opportunistic citizen science data are proliferating. Species distribution models (SDMs) aim to use species occurrence or abundance for ecological insights, prediction and management. We analysed a massive opportunistic dataset with over 100,000 records of incidental shipboard observations of marine mammals. Our overall goal was to create maps of species density from massive opportunistic data by using spatial regression for count data with an effort offset. We illustrate the method with two marine mammals in the Gulf of Alaska and Bering Sea.We counted the total number of animals in 11,424 hexagons based on presence‐only data. To decrease bias, we first estimated a spatial density surface for ship‐days, which was our proxy variable for effort. We used spatial considerations to create pseudo‐absences, and left some hexagons as missing values. Next, we created SDMs that used modelled effort to create pseudo‐absences, and included the effort surface as an offset in a second stage analysis of two example species, northern fur seals and Steller sea lions.For both effort and species counts, we used spatial count regression with random effects that had a multivariate normal distribution with a conditional autoregressive (CAR) covariance matrix, providing 2.5 million Markov chain Monte Carlo (MCMC) samples (1,000 were retained) from the posterior distribution. We used a novel MCMC scheme that maintained sparse precision matrices for observed and missing data when batch sampling from the multivariate normal distribution. We also used a truncated normal distribution to stabilize estimates, and used a look‐up table for sampling the autocorrelation parameter. These innovations allowed us to draw several million samples in just a few hours.From the posterior distributions of the SDMs, we computed two functions of interest. We normalized the SDMs and then applied an overall abundance estimate obtained from the literature to derive spatially explicit abundance estimates, especially within subsetted areas. We also created 'certain hotspots' that scaled local abundance by standard deviation and using thresholds. Hexagons with values above a threshold were deemed as hotspots with enough evidence to be certain about them. [ABSTRACT FROM AUTHOR]

A finite population version of block kriging (FPBK) estimates a total or a mean when there is perfect detection of population units. However, many environmental datasets challenge the assumption of perfect detection. We consider two extensions of FPBK that incorporate imperfect detection. Spatial population estimator with detection: ratio then add (SPEDRA) adjusts observed counts by the estimated detection probability prior to spatial modeling. Spatial population estimator with detection: add then ratio (SPEDAR) uses spatial modeling on observed counts and then adjusts by mean detection probability. Unlike classical sampling approaches such as simple random sampling, SPEDRA and SPEDAR allow for spatial correlation among counts, and, being moment‐based, are less computationally intensive than a fully Bayesian model. Both SPEDRA and SPEDAR perform similarly in some simulation settings and give comparable estimates for a moose population total when applied to data from Togiak National Wildlife Refuge (AK). In settings where detection probability varies widely across sites, however, SPEDRA outperforms SPEDAR in reducing root mean square prediction error. We recommend SPEDRA in surveys with imperfect detection because it is more theoretically sound and generally performs better. [ABSTRACT FROM AUTHOR]

Streams and rivers are biodiverse and provide valuable ecosystem services. Maintaining these ecosystems is an important task, so organisations often monitor the status and trends in stream condition and biodiversity using field sampling and, more recently, autonomous in-situ sensors. However, data collection is often costly, so effective and efficient survey designs are crucial to maximise information while minimising costs. Geostatistics and optimal and adaptive design theory can be used to optimise the placement of sampling sites in freshwater studies and aquatic monitoring programs. Geostatistical modelling and experimental design on stream networks pose statistical challenges due to the branching structure of the network, flow connectivity and directionality, and differences in flow volume. Geostatistical models for stream network data and their unique features already exist. Some basic theory for experimental design in stream environments has also previously been described. However, open source software that makes these design methods available for aquatic scientists does not yet exist. To address this need, we present SSNdesign, an R package for solving optimal and adaptive design problems on stream networks that integrates with existing open-source software. We demonstrate the mathematical foundations of our approach, and illustrate the functionality of SSNdesign using two case studies involving real data from Queensland, Australia. In both case studies we demonstrate that the optimal or adaptive designs outperform random and spatially balanced survey designs implemented in existing open-source software packages. The SSNdesign package has the potential to boost the efficiency of freshwater monitoring efforts and provide much-needed information for freshwater conservation and management. [ABSTRACT FROM AUTHOR]

From 1992 to 2017, two different monitoring methods were used to assess abundance and trends of seals in Glacier Bay National Park, Alaska: shore-based counts by observers (1992-2002) and aerial photographic surveys (2007-2017). GLO:69VH/01jul20:bes21716-fig-0001.jpg PHOTO (COLOR): Harbor seals (Phoca vitulina richardii) resting on icebergs in Johns Hopkins Inlet in Glacier Bay National Park in southeastern Alaska, USA. [Extracted from the article]

Close‐kin mark–recapture (CKMR) is a method for estimating abundance and vital rates from kinship relationships observed in genetic samples. CKMR inference only requires animals to be sampled once (e.g., lethally), potentially widening the scope of population‐level inference relative to traditional monitoring programs.One assumption of CKMR is that, conditional on individual covariates like age, all animals have an equal probability of being sampled. However, if genetic data are collected opportunistically (e.g., via hunters or fishers), there is potential for spatial variation in sampling probability that can bias CKMR estimators, particularly when genetically related individuals stay in close proximity.We used individual‐based simulation to investigate consequences of dispersal limitation and spatially biased sampling on performance of naive (nonspatial) CKMR estimators of abundance, fecundity, and adult survival. Population dynamics approximated that of a long‐lived mammal species subject to lethal sampling.Naive CKMR abundance estimators were relatively unbiased when dispersal was unconstrained (i.e., complete mixing) or when sampling was random or subject to moderate levels of spatial variation. When dispersal was limited, extreme variation in spatial sampling probabilities negatively biased abundance estimates. Reproductive schedules and survival were well estimated, except for survival when adults could emigrate out of the sampled area. Incomplete mixing was readily detected using Kolmogorov–Smirnov tests.Although CKMR appears promising for estimating abundance and vital rates with opportunistically collected genetic data, care is needed when dispersal limitation is coupled with spatially biased sampling. Fortunately, incomplete mixing is easily detected with adequate sample sizes. In principle, it is possible to devise and fit spatially explicit CKMR models to avoid bias under dispersal limitation, but development of such models necessitates additional complexity (and possibly additional data). We suggest using simulation studies to examine potential bias and precision of proposed modeling approaches prior to implementing a CKMR program. [ABSTRACT FROM AUTHOR]

Environmental data may be "large" due to number of records, number of covariates, or both. Random forests has a reputation for good predictive performance when using many covariates with nonlinear relationships, whereas spatial regression, when using reduced rank methods, has a reputation for good predictive performance when using many records that are spatially autocorrelated. In this study, we compare these two techniques using a data set containing the macroinvertebrate multimetric index (MMI) at 1859 stream sites with over 200 landscape covariates. A primary application is mapping MMI predictions and prediction errors at 1.1 million perennial stream reaches across the conterminous United States. For the spatial regression model, we develop a novel transformation procedure that estimates Box-Cox transformations to linearize covariate relationships and handles possibly zero-inflated covariates. We find that the spatial regression model with transformations, and a subsequent selection of significant covariates, has cross-validation performance comparable to random forests. We also find that prediction interval coverage is close to nominal for each method, but that spatial regression prediction intervals tend to be narrower and have less variability than quantile regression forest prediction intervals. A simulation study is used to generalize results and clarify advantages of each modeling approach. [ABSTRACT FROM AUTHOR]

The impact of low-level military jet overflights on caribou during the calving season is described. Short-term response to overflights was generally mild in comparison to caribou reactions to predators or perceived predators.

Noel Cressie, FAA is Director of the Centre for Environmental Informatics in the National Institute for Applied Statistics Research Australia (NIASRA) and Distinguished Professor in the School of Mathematics and Applied Statistics at the University of Wollongong, Australia. He is also Adjunct Professor at the University of Missouri (USA), Affiliate of Org 398, Science Data Understanding, at NASA’s Jet Propulsion Laboratory (USA), and a member of the Science Team for NASA’s Orbiting Carbon Observatory-2 (OCO-2) satellite. Cressie was awarded a B.Sc. with First Class Honours in Mathematics in 1972 from the University of Western Australia, and an M.A. and Ph.D. in Statistics in 1973 and 1975, respectively, from Princeton University (USA). Two brief postdoctoral periods followed, at the Centre de Morphologie Mathématique, ENSMP, in Fontainebleau (France) from April 1975-September 1975, and at Imperial College, London (UK) from September 1975-January 1976. His past appointments have been at The Flinders University of South Australia from 1976-1983, at Iowa State University (USA) from 1983-1998, and at The Ohio State University (USA) from 1998-2012. He has authored or co-authored four books and more than 280 papers in peer-reviewed outlets, covering areas that include spatial and spatio-temporal statistics, environmental statistics, empirical-Bayesian and Bayesian methods including sequential design, goodness-of-fit, and remote sensing of the environment. Many of his papers also address important questions in the sciences. Cressie is a Fellow of the Australian Academy of Science, the American Statistical Association, the Institute of Mathematical Statistics, and the Spatial Econometrics Association, and he is an Elected Member of the International Statistical Institute. Noel Cressie’s refereed, unrefereed, and other publications are available at: https://niasra.uow.edu.au/cei/people/UOW232444.html. [ABSTRACT FROM AUTHOR]