Unmodeled Heterogeneity Research Articles

A Monte Carlo resampling framework for implementing goodness‐of‐fit tests in spatial capture‐recapture models

Abstract Spatial capture‐recapture (SCR) models provide estimates of animal density from spatially referenced encounter data and has become the most widely adopted approach for estimating density. Despite the rapid growth in the development and application of spatial capture‐recapture methods, approaches for assessing model fit have received very little attention when compared to other classes of hierarchical models in ecology. Here, we develop an approach for testing goodness‐of‐fit (GoF) for frequentist SCR models using Monte Carlo simulations. We derive probability distributions of activity centres from the fitted model. From these, we calculate the expected encounters in the capture history based on the SCR parameter estimates, propagating the uncertainty of the estimates and the activity centre locations via Monte Carlo simulations. Aggregating these test statistics result in count data, allowing us to test fit with Freeman‐Tukey tests. These tests are based on summary statistics of the total encounters of each individual at each trap (FT‐ind‐trap), total encounters of each individual (FT‐individuals) and total encounters at each trap (FT‐traps). We assess the ability of these GoF tests to diagnose lack of fit under a range of assumption violating scenarios. FT‐traps had the strongest response to unmodelled spatial and trap heterogeneity in detection probability (power = 0.53–0.56), while FT‐ind‐traps had the strongest responses to random individual variation in detectability (power = 0.88) and non‐spatial discrete variation in (power = 0.35). The tests, designed to diagnose poor fit in the detection parameters, were insensitive to unmodelled heterogeneity in density (power = <0.001). They also demonstrated low false positive rates (<0.001) when the correct models were fitted; therefore, it is very unlikely that they will provide false indications of poor model fit. We demonstrate that these GoF tests are capable of detecting lack‐of‐fit when unmodelled heterogeneity is present in the detection sub‐model. When used jointly, the combinations of test results are also able to infer the type of lack‐of‐fit in certain cases. Our Monte Carlo sampling methods may be extended to a wider range of GoF tests, thereby providing a platform for developing more GoF methods for SCR.

Evaluating two small-sample corrections for fixed-effects standard errors and inferences in multilevel models with heteroscedastic, unbalanced, clustered data

Multilevel modeling (MLM) is commonly used in psychological research to model clustered data. However, data in applied research usually violate one of the essential assumptions of MLM—homogeneity of variance. While the fixed-effect estimates produced by the maximum likelihood method remain unbiased, the standard errors for the fixed effects are misestimated, resulting in inaccurate inferences and inflated or deflated type I error rates. To correct the bias in fixed effects standard errors and provide valid inferences, small-sample corrections such as the Kenward-Roger (KR) adjustment and the adjusted cluster-robust standard errors (CR-SEs) with the Satterthwaite approximation for t tests have been used. The current study compares KR with random slope (RS) models and the adjusted CR-SEs with ordinary least squares (OLS), random intercept (RI) and RS models to analyze small, heteroscedastic, clustered data using a Monte Carlo simulation. Results show the KR procedure with RS models has large biases and inflated type I error rates for between-cluster effects in the presence of level 2 heteroscedasticity. In contrast, the adjusted CR-SEs generally yield results with acceptable biases and maintain type I error rates close to the nominal level for all examined models. Thus, when the interest is only in within-cluster effect, any model with the adjusted CR-SEs could be used. However, when the interest is to make accurate inferences of the between-cluster effect, researchers should use the adjusted CR-SEs with RS to have higher power and guard against unmodeled heterogeneity. We reanalyzed an example in Snijders & Bosker (2012) to demonstrate the use of the adjusted CR-SEs with different models.

A simple framework for maximizing camera trap detections using experimental trials

Camera trap data are biased when an animal passes through a camera’s field of view but is not recorded. Cameras that operate using passive infrared sensors rely on their ability to detect thermal energy from the surface of an object. Optimal camera deployment consequently depends on the relationship between a sensor array and an animal. Here, we describe a general, experimental approach to evaluate detection errors that arise from the interaction between cameras and animals. We adapted distance sampling models and estimated the combined effects of distance, camera model, lens height, and vertical angle on the probability of detecting three different body sizes representing mammals that inhabit temperate, boreal, and arctic ecosystems. Detection probabilities were best explained by a half-normal-logistic mixture and were influenced by all experimental covariates. Detection monotonically declined when proxies were ≥6 m from the camera; however, models show that body size and camera model mediated the effect of distance on detection. Although not a focus of our study, we found that unmodeled heterogeneity arising from solar position has the potential to bias inferences where animal movements vary over time. Understanding heterogeneous detection probabilities is valuable when designing and analyzing camera trap studies. We provide a general experimental and analytical framework that ecologists, citizen scientists, and others can use and adapt to optimize camera protocols for various wildlife species and communities. Applying our framework can help ecologists assess trade-offs that arise from interactions among distance, cameras, and body sizes before committing resources to field data collection.

Accounting for heterogeneous density and detectability in spatially explicit capture–recapture studies of carnivores

AbstractReliable estimates of population density are fundamental for managing and conserving wildlife. Spatially explicit capture–recapture (SECR) models in combination with information‐theoretic model selection criteria are frequently used to estimate population density. Variation in density and detectability is inevitable and, when unmodeled, can lead to erroneous estimates. Despite this knowledge, the performance of SECR models and information‐theoretic criteria remain relatively untested for populations with realistic levels of variation in density and detectability. We addressed this issue using simulations of American black bear (Ursus americanus) populations with variable density and detectability between sexes and across study areas. We first assessed the reliability of Akaike information criterion adjusted for small sample sizes (AICc) to correctly identify the true data generating model or a good approximating model. We then assessed the bias, accuracy, and precision of density estimates when such a model was selected or not. We demonstrated that unmodeled heterogeneity in detection and, more importantly, density can lead to pronounced bias. However, when a good approximating model is included in the candidate set, models with lower AICc included important forms of variation and yielded accurate estimates. We encourage researchers and practitioners to consider the impact of unmodeled variation in SECR models when making inferences and to strive to include covariates likely to be the most influential based on the species biology and ecology in candidate model sets. Doing so can improve the robustness of wildlife density estimation methods that can be leveraged to make more sound conservation and management decisions.

Integrating multiple sign types to improve occupancy estimation for inconspicuous species.

Standard occupancy models enable unbiased estimation of occupancy by accounting for observation errors such as missed detections (false negatives) and, less commonly, incorrect detections (false positives). Occupancy models are fitted to data from repeated site visits in which surveyors record evidence of species presence. Use of indirect sign (e.g., scat, tracks) as evidence of presence can vastly improve survey efficiency for inconspicuous species but can also introduce additional sources of error. We developed a "multi-sign" occupancy approach to model the detection process separately for unique sign types and used this method to improve estimates of occupancy dynamics for an inconspicuous species, the American pika (Ochotona princeps). We investigated how estimates of pika occupancy and environmental drivers differed under four increasingly realistic representations of the observation process: (1) perfect detection (commonly assumed for modeling pika occupancy), (2) standard occupancy model (single observation process without possibility of false detection), (3) multi-sign with no false detections (non-false positive model), and (4) multi-sign with false detections (full model). For the multi-sign occupancy models, we modeled the detection of each sign type (fresh scat, fresh haypiles, pika calls, and pika sightings) separately as a function of climatic and environmental covariates. Estimates of occupancy processes and inferences about environmental drivers were sensitive to different detection models. Simplified representations of the detection processes generally resulted in higher occupancy estimates and higher turnover rates than the full multi-sign model. Environmental drivers also varied in their influence on occupancy models, where (e.g.) forb cover was estimated to more strongly influence occupancy in the full multi-sign model than the simpler models. As has been reported previously in other contexts, unmodeled heterogeneity in the observation process can lead to biases in occupancy processes and uncertainty in the relationships between occupancy and environmental covariates. Overall, our multi-sign approach to dynamic occupancy modeling, which accounts for spatio-temporal variation in reliability among sign types, has strong potential to generate more realistic estimates of occupancy dynamics for inconspicuous species.

An evaluation of multistate occupancy models for estimating relative abundance and population trends

Detecting spatiotemporal changes in the abundances of organisms is key to effectively conserving species. While indices of abundance have long been used, there has been a shift toward model-based estimators that account for the detection process. Popular approaches including traditional occupancy models and N-mixture models entail tradeoffs. The traditional occupancy approach requires the researcher coarsen the characterization of abundance to the probability that a site is occupied or unoccupied. Conversely, N-mixture models make use of variation in counts, but perform poorly when individuals have low detectability or move into or out of sites between visits. Multistate occupancy models that differentiate relatively abundant from non-abundant states have the potential to fill this gap but have been underexplored. We conducted a simulation study to test whether multistate occupancy models could capture spatial abundance patterns and detect population declines in the face of low individual detection probability (p ≤ 0.3) and unmodeled heterogeneity (e.g., that arising from individual movement). We considered 10,773 scenarios to examine the effects of differing amounts of heterogeneity as well as alternative study designs, population parameters, and modeling choices. We tracked bias in the proportion of sites estimated to be in the abundant state for single-season models, and power to detect a declining trend across multiple years. We also evaluated data diagnostic metrics to provide guidance to users. Multistate occupancy models were able to differentiate sites with higher abundances from sites with lower abundances when there were at least medium levels of spatial heterogeneity in true abundances. If different sites were randomly selected each year, power to detect even large population declines (65%) was poor (power < 0.8). However, if the same sites were surveyed each year, and a dynamic multistate occupancy was used, multistate occupancy models could detect (power ≥ 0.8) relatively small declines (5-40%) in 20% of scenarios, and frequently detect large declines of 45-60% (mean power = 0.92). Conservation decisions rely on detecting change reliably, rarely needing absolute abundance information. Multistate occupancy models can improve our ability to detect changing abundance while accommodating low individual detection probability and heterogeneity in count monitoring data.

Pooling robustness in distance sampling: Avoiding bias when there is unmodelled heterogeneity.

The pooling robustness property of distance sampling results in unbiased abundance estimation even when sources of variation in detection probability are not modeled. However, this property cannot be relied upon to produce unbiased subpopulation abundance estimates when using a single pooled detection function that ignores subpopulations. We investigate by simulation the effect of differences in subpopulation detectability upon bias in subpopulation abundance estimates. We contrast subpopulation abundance estimates using a pooled detection function with estimates derived using a detection function model employing a subpopulation covariate. Using point transect survey data from a multispecies songbird study, species-specific abundance estimates are compared using pooled detection functions with and without a small number of adjustment terms, and a detection function with species as a covariate. With simulation, we demonstrate the bias of subpopulation abundance estimates when a pooled detection function is employed. The magnitude of the bias is positively related to the magnitude of disparity between the subpopulation detection functions. However, the abundance estimate for the entire population remains unbiased except when there is extreme heterogeneity in detection functions. Inclusion of a detection function model with a subpopulation covariate essentially removes the bias of the subpopulation abundance estimates. The analysis of the songbird point count surveys shows some bias in species-specific abundance estimates when a pooled detection function is used. Pooling robustness is a unique property of distance sampling, producing unbiased abundance estimates at the level of the study area even in the presence of large differences in detectability between subpopulations. In situations where subpopulation abundance estimates are required for data-poor subpopulations and where the subpopulations can be identified, we recommend the use of subpopulation as a covariate to reduce bias induced in subpopulation abundance estimates.

A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure

Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in the presence of unmodeled coefficient heterogeneity. We illustrate some implications for the case where the research design takes advantage of variation across units (say, US states) in exposure to some treatment (say, a policy change). In this case, the TWFE can fail to estimate the average (or even a weighted average) of the units’ coefficients. Under some conditions, there exists no estimator that is guaranteed to estimate even a weighted average. Building on the literature, we note that when there is a unit totally unaffected by treatment, it is possible to estimate an average effect by replacing the TWFE with an average of difference-in-differences estimators.

Estimating animal abundance at multiple scales by spatially explicit capture-recapture.

Information about how animal abundance varies across landscapes is needed to inform management action but is costly and time-consuming to obtain; surveys of a single population distributed over a large area can take years to complete. Surveys employing small, spatially replicated sampling units improve efficiency, but statistical estimators rely on assumptions that constrain survey design or become less reasonable as larger areas are sampled. Efficient methods that avoid assumptions about similarity of detectability or density among replicates are therefore appealing. Using simulations and data from >3500 black bears sampled on 73 independent study areas in Ontario, Canada, we (1) quantified bias induced by unmodeled spatial heterogeneity in detectability and density; (2) evaluated novel, design-based estimators of average density across replicate study areas; and (3) evaluated two estimators of the variance of average density across study areas: an analytic estimator that assumed an underlying homogeneous spatial Poisson point process for the distribution of animals' activity centers, and an empirical estimator of variance across study areas. In simulations where detectability varied in space, assuming spatially constant detectability yielded density estimates that were negatively biased by 20% to 30%; estimating local detectability and density from local data and treating study areas as independent, equal replicates when estimating average density across study areas using the design-based estimator yielded unbiased estimates at local and landscape scales. Similarly, detectability of black bears varied among study areas and estimates of bear density at landscape scales were higher when no information was shared across study areas when estimating detectability. This approach also maximized precision (relative SEs of estimates of average black bear density ranged from 7% to 18%) and computational efficiency. In simulations, the analytic variance estimator was robust to threefold variation in local densities but the empirical estimator performed poorly. Conducting multiple, similar SECR surveys and treating them as independent replicates during analyses allowed us to efficiently estimate density at multiple scales and extents while avoiding biases caused by pooling spatially heterogeneous data. This approach enables researchers to address a wide range of ecological or management-related questions and is applicable with most types of SECR data.

Statistical modelling of vignette data in psychology.

Vignette methods are widely used in psychology and the social sciences to obtain responses to multi-dimensional scenarios or situations. Where quantitative data are collected this presents challenges to the selection of an appropriate statistical model. This depends on subtle details of the design and allocation of vignettes to participants. A key distinction is between factorial survey experiments where each participant receives a different allocation of vignettes from the full universe of possible vignettes and experimental vignette studies where this restriction is relaxed. The former leads to nested designs with a single random factor and the latter to designs with two crossed random factors. In addition, the allocation of vignettes to participants may lead to fractional or unbalanced designs and a consequent loss of efficiency or aliasing of the effects of interest. Many vignette studies (including some factorial survey experiments) include unmodeled heterogeneity between vignettes leading to potentially serious problems if traditional regression approaches are adopted. These issues are reviewed and recommendations are made for the efficient design of vignette studies including the allocation of vignettes to participants. Multilevel models are proposed as a general approach to handling nested and crossed designs including unbalanced and fractional designs. This is illustrated with a small vignette data set looking at judgements of online and offline bullying and harassment.

Assessing vegetation recovery from energy development using a dynamic reference approach.

Ecologically relevant references are useful for evaluating ecosystem recovery, but references that are temporally static may be less useful when environmental conditions and disturbances are spatially and temporally heterogeneous. This challenge is particularly acute for ecosystems dominated by sagebrush (Artemisia spp.), where communities may require decades to recover from disturbance. We demonstrated application of a dynamic reference approach to studying sagebrush recovery using three decades of sagebrush cover estimates from remote sensing (1985–2018). We modelled recovery on former oil and gas well pads (n = 1200) across southwestern Wyoming, USA, relative to paired references identified by the Disturbance Automated Reference Toolset. We also used quantile regression to account for unmodelled heterogeneity in recovery, and projected recovery from similar disturbance across the landscape. Responses to weather and site‐level factors often differed among quantiles, and sagebrush recovery on former well pads increased more when paired reference sites had greater sagebrush cover. Little (<5%) of the landscape was projected to recover within 100 years for low to mid quantiles, and recovery often occurred at higher elevations with cool and moist annual conditions. Conversely, 48%–78% of the landscape recovered quickly (within 25 years) for high quantiles of sagebrush cover. Our study demonstrates advantages of using dynamic reference sites when studying vegetation recovery, as well as how additional inferences obtained from quantile regression can inform management.

Consequences of ignoring variable and spatially autocorrelated detection probability in spatial capture-recapture

ContextSpatial capture-recapture (SCR) models are increasingly popular for analyzing wildlife monitoring data. SCR can account for spatial heterogeneity in detection that arises from individual space use (detection kernel), variation in the sampling process, and the distribution of individuals (density). However, unexplained and unmodeled spatial heterogeneity in detectability may remain due to cryptic factors, both intrinsic and extrinsic to the study system. This is the case, for example, when covariates coding for variable effort and detection probability in general are incomplete or entirely lacking.ObjectivesWe identify how the magnitude and configuration of unmodeled, spatially variable detection probability influence SCR parameter estimates.MethodsWe simulated SCR data with spatially variable and autocorrelated detection probability. We then fitted an SCR model ignoring this variation to the simulated data and assessed the impact of model misspecification on inferences.ResultsHighly-autocorrelated spatial heterogeneity in detection probability (Moran’s I = 0.85–0.96), modulated by the magnitude of the unmodeled heterogeneity, can lead to pronounced negative bias (up to 65%, or about 44-fold decrease compared to the reference scenario), reduction in precision (249% or 2.5-fold) and coverage probability of the 95% credible intervals associated with abundance estimates to 0. Conversely, at low levels of spatial autocorrelation (median Moran’s I = 0), even severe unmodeled heterogeneity in detection probability did not lead to pronounced bias and only caused slight reductions in precision and coverage of abundance estimates.ConclusionsUnknown and unmodeled variation in detection probability is liable to be the norm, rather than the exception, in SCR studies. We encourage practitioners to consider the impact that spatial autocorrelation in detectability has on their inferences and urge the development of SCR methods that can take structured, unknown or partially unknown spatial variability in detection probability into account.

Spatial correlation structures for detections of individuals in spatial capture-recapture models.

Spatial capture-recapture (SCR) models are commonly used to estimate animal density from surveys on which detectors passively detect animals without physical capture, for example, using camera traps, hair snares, or microphones. An individual is more likely to be recorded by detectors close to its activity center, the centroid of its movement throughout the survey. Existing models to account for this spatial heterogeneity in detection probabilities rely on an assumption of independence between detection records at different detectors conditional on the animals' activity centers, which are treated as latent variables. In this paper, we show that this conditional independence assumption may be violated due to the way animals move around the survey region and encounter detectors, such that additional spatial correlation is almost inevitable. We highlight the links between the well-studied issue of unmodeled temporal heterogeneity in nonspatial capture-recapture and this variety of unmodeled spatial heterogeneity in SCR, showing that the latter causes predictable bias in the same way as the former. We address this by introducing a latent detection field into the model, and illustrate the resulting approach with a simulation study and an application to a camera-trap survey of snow leopards Panthera uncia. Our method is a unifying model for several existing SCR approaches, with special cases including standard SCR, models that account for nonspatial individual heterogeneity, and models with overdispersed detection counts.

Bayesian non-parametric detection heterogeneity in ecological models

Detection heterogeneity is inherent to ecological data, arising from factors such as varied terrain or weather conditions, inconsistent sampling effort, or heterogeneity of individuals themselves. Incorporating additional covariates into a statistical model is one approach for addressing heterogeneity, but there is no guarantee that any set of measurable covariates will adequately address the heterogeneity, and the presence of unmodelled heterogeneity has been shown to produce biases in the resulting inferences. Other approaches for addressing heterogeneity include the use of random effects, or finite mixtures of homogeneous subgroups. Here, we present a non-parametric approach for modeling detection heterogeneity for use in a Bayesian hierarchical framework. We employ a Dirichlet process mixture which allows a flexible number of population subgroups without the need to pre-specify this number of subgroups as in a finite mixture. We describe this non-parametric approach, then consider its use for modeling detection heterogeneity in two common ecological motifs: capture–recapture and occupancy modeling. For each, we consider a homogeneous model, finite mixture models, and the non-parametric approach. We compare these approaches using simulation, and observe the non-parametric approach as the most reliable method for addressing varying degrees of heterogeneity. We also present two real-data examples, and compare the inferences resulting from each modeling approach. Analyses are carried out using the nimble package for R, which provides facilities for Bayesian non-parametric models.

Imaging upper mantle anisotropy with teleseismicP-wave delays: insights from tomographic reconstructions of subduction simulations

SUMMARYDespite the well-established anisotropic nature of Earth’s upper mantle, the influence of elastic anisotropy on teleseismic P-wave imaging remains largely ignored. Unmodelled anisotropic heterogeneity can lead to substantial isotropic velocity artefacts that may be misinterpreted as compositional heterogeneities. Recent studies have demonstrated the possibility of inverting P-wave delay times for the strength and orientation of seismic anisotropy. However, the ability of P-wave delay times to constrain complex anisotropic patterns, such as those expected in subduction settings, remains unclear as synthetic testing has been restricted to the recovery of simplified block-like structures using ideal self-consistent data (i.e. data produced using the assumptions built into the tomography algorithm). Here, we present a modified parametrization for imaging arbitrarily oriented hexagonal anisotropy and test the method by reconstructing geodynamic simulations of subduction. Our inversion approach allows for isotropic starting models and includes approximate analytic finite-frequency sensitivity kernels for the simplified anisotropic parameters. Synthetic seismic data are created by propagating teleseismic waves through an elastically anisotropic subduction zone model created via petrologic-thermomechanical modelling. Delay times across a synthetic seismic array are measured using conventional cross-correlation techniques. We find that our imaging algorithm is capable of resolving large-scale features in subduction zone anisotropic structure (e.g. toroidal flow pattern and dipping fabrics associated with the descending slab). Allowing for arbitrarily oriented anisotropy also results in a more accurate reconstruction of isotropic slab structure. In comparison, models created assuming isotropy or only azimuthal anisotropy contain significant isotropic and anisotropic imaging artefacts that may lead to spurious interpretations. We conclude that teleseismic P-wave traveltimes are a useful observable for probing the 3-D distribution of upper mantle anisotropy and that anisotropic inversions should be explored to better understand the nature of isotropic velocity anomalies particularly in subduction settings.

Estimating abundance based on time‐to‐detection data

AbstractMany studies in ecology and management aim at quantifying absolute abundance based on counts at a set of surveyed sites. As time for data collection is typically limited, methods for reliable estimation of occupancy or abundance from low‐cost data are desirable. Time‐to‐detection (TTD) models have shown promise for the estimation of occupancy. However, they remain heavily underutilized, and restricted to inference about occupancy, rather than abundance.We developed a binomial N‐mixture model for species‐level TTD protocols that allows estimation of abundance with multiple‐ or single‐visit data. An extension of the multi‐visit version allows estimating availability per visit, given temporary emigration is random. We provide JAGS code and a new function (nmixTTD) in the R packageunmarkedfor fitting a variety of such models.Simulations showed accurate parameter estimation from single‐visit species‐level TTD data if individual detection probability is high (≥~0.7) and the number of visited sites is in the hundreds (≥~300). Additional visits improved the accuracy of estimates considerably. A comparison with the Royle‐Nichols‐ and the classic binomial N‐mixture‐model revealed that the performance of our model is between these two, but requires data that are less expensive and less error‐prone than count data required for binomial N‐mixture‐models. In a case study, we found similar results when analysing data with the Royle‐Nichols‐, the binomial N‐mixture‐model or the multi‐visit version of our TTD model. Analysing single‐visit data with our model yielded lower abundance and higher detectability estimates. Presumably these differences are due to temporary emigration, as the single‐visit method estimates the abundance of individuals available at one sampling occasion, whereas the multi‐visit methods refer to the superpopulation, that is, the number of individuals present over the study period.Our new TTD‐N‐mixture model shows promise because it enables estimation of abundance, corrected for imperfect detection, for single‐ and multiple‐visit data, based on data that are less expensive and that will be available in large quantities in the near future thanks to technical advances like autonomous recording units. The effects of unmodelled heterogeneity in detection rate and imperfect availability require further study.

Does Proximity to Nazi Concentration Camps Make Germans Intolerant? Modeling Spatial Heterogeneity and Historical Persistence

In a recent article in the American Political Science Review entitled “Legacies of the Third Reich: Concentration Camps and Out-group Intolerance,” Jonathan Homola, Miguel M. Pereira, and Margit Tavits argue that Germans who live nearer to former Nazi concentration camps are more likely to display out-group intolerance. We argue that their statistical findings are the product of unobserved regional heterogeneity. Using publicly available European Values Survey data and electoral results from 2017, we replicate their results, and then extend them using simple fixed effects specifications as well as more elaborate multilevel models. Our approach finds no consistent evidence that distance to camps is related to contemporary values. We also preregister our plan to replicate and extend their analyses using restricted-access data from the German General Social Survey. Our findings have important implications for the new literatures on historical persistence and the deep origins of contemporary politics, as well as for the fields of Holocaust studies, German politics, and out-group tolerance. Our approach to modeling spatial heterogeneity in historical persistence studies—investigating spatial variation and diagnosing why unmodeled heterogeneity can produce misleading inferences—can serve as a template for future studies.

Identifying Heterogeneity in Dynamic Panel Models with Individual Parameter Contribution Regression

Dynamic panel models are a popular approach to study interrelationships between repeatedly measured variables. Often, dynamic panel models are specified and estimated within a structural equation modeling (SEM) framework. An endemic problem threatening the validity of such models is unmodelled heterogeneity. Recently, individual parameter contribution (IPC) regression was proposed as a flexible method to study heterogeneity in SEM parameters as a function of observed covariates. In the present paper, we derive how IPCs can be calculated for general maximum likelihood estimates and evaluate the performance of IPC regression to estimate group differences in dynamic panel models in discrete and continuous time. We show that IPC regression can be slightly biased in samples with large group differences and present a bias correction procedure. IPC regression showed generally promising results for discrete time models. However, due to highly nonlinear parameter constraints, caution is indicated when applying IPC regression to continuous time models.

The importance of simulation assumptions when evaluating detectability in population models

AbstractPopulation monitoring is important for investigating a variety of ecological questions, and N‐mixture models are increasingly used to model population size (N) and trends (λ) while estimating detectability (p) from repeated counts within primary periods (when populations are closed to changes). Extending these models to dynamic processes with serial dependence across primary periods may relax the closure assumption, but simulations to evaluate models and inform effort (e.g., number of repeated counts) typically assume p is constant or random across sites and years. Thus, it is unknown how these models perform under scenarios where trends in p confound inferences on N and λ, and conclusions regarding effort may be overoptimistic. Here, we used global positioning system data from greater sage‐grouse (Centrocercus urophasianus) to inform simulations of the detection process for lek counts of this species, and we created scenarios with and without linear annual trends in p. We then compared estimates of N and λ from hierarchical population models either fit with single maximum counts or with detectability estimated from repeated counts (dynamic N‐mixture models). We also explored using auxiliary data to correct counts for variation in detectability. Uncorrected count models consistently underestimated N by &gt;50%, whereas N‐mixture models without auxiliary data underestimated N to a lesser degree due to unmodeled heterogeneity in p such as age. Nevertheless, estimates of λ from both types of models were unbiased and similar for scenarios without trends in p. When p declined systematically across years, uncorrected count models underestimated λ, whereas N‐mixture models estimated λ with little bias when all sites were counted repeatedly. Auxiliary data also reduced bias in parameter estimates. Evaluating population models using scenarios with systematic variation in p may better reveal potential biases and inform effort than simulations that assume p is constant or random. Dynamic N‐mixture models can distinguish between trends in p and N, but also require repeated counts within primary periods for accurate estimates. Auxiliary data may be useful when researchers lack repeated counts, wish to monitor more sites less intensively, or require unbiased estimates of N.

Did You Miss Something? Inattentive Respondents in Discrete Choice Experiments

Stated preference practitioners are increasingly relying on internet panels to gather data, but emerging evidence suggests potential limitations with respect to respondent and response quality in such panels. We identify groups of inattentive respondents who have failed to watch information videos provided in the survey to completion. Our results show that inattentive respondents have a higher cost sensitivity, are more likely to have a small scale parameter, and are more likely to ignore the non-cost attributes. These results are largely driven by respondents failing to watch the information video about the discrete choice experiment, attributes and levels, which underlines the importance of information provision and highlights possible implications of inattentiveness. We develop a modeling framework to simultaneously address preference, scale and attribute processing heterogeneity. We find that when we consider attribute non-attendance—scale differences disappear, which suggests that the type of heterogeneity detected in a model could be the result of un-modeled heterogeneity of a different kind. We discuss implications of our results.