Multivariate Spatio-temporal Model Research Articles

Multivariate spatiotemporal models with low rank coefficient matrix

Multivariate spatiotemporal models with low rank coefficient matrix

Bayesian multivariate spatiotemporal statistical modeling of bus and taxi ridership

Statistical modeling of ridership over both space and time provides valuable insights on transportation planning and policies. Existing spatiotemporal studies, however, predominantly focus on analyzing a single type rather than multiple types of ridership, thus cannot leverage the correlation between different types of ridership. This study proposes a Bayesian multivariate spatiotemporal statistical model to jointly analyze multiple ridership over time. Specifically, the model accounts for correlation between multiple ridership based on different assumptions of space-time interactions (i.e., departures from the main spatial and temporal patterns) between different types of ridership as well as if covariates are included in the model. Using hourly bus and taxi ridership in the city of Wuhu, China as an example, the case study indicates that accounting for the correlation between the space-time interactions of each ridership, beyond the correlation between the main spatial patterns of the two ridership, further improves the statistical inferences of ridership modeling. In addition, the proposed approach enables the detection of spatial and spatiotemporal hotspots of each ridership as well as bus-taxi ratio hotspots using posterior probabilities. It also supports visual inspections regarding how the inclusion of covariates explains these hotspots. The proposed approach not only advances multivariate spatiotemporal statistical modeling of ridership, but can also provide useful insights on space- and time-specific transport policies at a granular resolution.

Applying a Bayesian Spatiotemporal Model to Examine Excess County-Level Cardiovascular Disease Death Rates During the COVID-19 Pandemic.

Amid the COVID-19 pandemic, national cardiovascular disease (CVD) death rates increased, especially among younger adults. County-level variation has not been documented. Using county-level CVD deaths (ICD-10 codes: I00-I99) from the US National Vital Statistics System, we developed a Bayesian multivariate spatiotemporal model to estimate excess CVD death rates in 2020 based on trends from 2010-2019 for adults aged 35-64 and ≥65 years. Among adults aged 35-64 years, 64.7% of counties experienced significant excess CVD death rates. The median county-level CVD death rate in 2020 was 150 per 100,000 persons, which exceeded the predicted rate for 2020 (median excess death rate: 11 per 100,000; median excess rate ratio: 1.08). Among adults aged ≥65 years, 15.2% of counties experienced significant excess CVD death rates. The median county-level CVD death rate was 1,546 per 100,000 in 2020, which exceeded the predicted rate in 2020 (median excess death rate: 48 per 100,000, median excess rate ratio: 1.03). Counties with significant excess death rates in 2020 were geographically dispersed. In 2020, disruptions of county-level CVD death rates were widespread, especially among younger adults, suggesting the continued importance of CVD prevention and treatment in younger adults in communities across the country.

Disentangling bottom-up and top-down controls on fish consumption of key prey in the Northeast US Shelf ecosystem

Abstract Exploited forage fishes serve a dual role in marine ecosystems by supporting directed fisheries and predator productivity, and thus both harvest and predatory removals should be accounted for when developing stock assessments and evaluating management trade-offs. Predator catch and stomach content data collected on the Northeast US Shelf from 1978 to 2019 by two fisheries-independent surveys were combined within multivariate spatiotemporal models to estimate time-series of consumptive removals during spring and fall for four commercially exploited prey; Atlantic herring (Clupea harengus), silver hake (Merluccius bilinearis), butterfish (Peprilus triacanthus), and longfin squid (Doryteuthis pealeii). Seasonal consumption trends were mostly synchronous for Atlantic herring and silver hake, asynchronous for butterfish and longfin squid, and predatory removals were generally greater during fall. Consumption has increased since the 1990s for all prey except Atlantic herring and butterfish during fall, which coincides with the widespread implementation of harvest constraints meant to rebuild predator and prey populations. These time-series were linked to hypothesized drivers using state-space regression models; prey availability (bottom-up; positive relationships) and commercial catch (top-down; primarily negative relationships) were the strongest predictors of consumption. Although the mechanisms underlying these relationships remain unresolved, these linkages highlight connections among the systemic drivers of productivity on the Northeast Shelf.

A multivariate spatial and spatiotemporal ARCH Model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spillovers.

Spatio-temporal species distribution models reveal dynamic indicators for ecosystem-based fisheries management

Abstract Many economic sectors rely on marine ecosystem services, and holistic management is necessary to evaluate trade-offs between sectors and facilitate sustainable use. Integrated ecosystem assessments (IEA) integrate system components so that managers can evaluate pathways to achieve desired goals. Indicators are a central element of IEAs and capture the status and trend of individual components and should be sensitive to changes in the system; however, most indicators are aggregated over space and time as annual values, potentially leading to incomplete or inaccurate inferences about system change. Here, we demonstrate the utility of spatially and temporally explicit ecological indicators by fitting multivariate spatio-temporal models to survey data from the northeast US Shelf Ecosystem, encompassing three distinct ecoregions: Georges Bank, Gulf of Maine, and mid-Atlantic Bight. We evaluate three case studies to explore how these models can help assess ecosystem performance relative to management objectives, such as to: (1) identify dominant modes of variation in zooplankton communities; (2) quantify components of system stability; and (3) assess the density-dependent condition of groundfish over time. Collectively, these three examples demonstrate multiple interesting processes, but particularly highlight the rapid zooplankton changes and associated changes in benthivore condition and stability in the Gulf of Maine. Attributing changes in ecosystem indicators to localized processes is difficult using conventional “regionally aggregated” indicators, so this example highlights the benefits of spatio-temporal methods for integrated ecosystem analysis in this and other regions.

A multivariate spatio-temporal model for the incidence of imported COVID-19 cases and COVID-19 deaths in Cuba

To monitor the COVID-19 epidemic in Cuba, data on several epidemiological indicators have been collected on a daily basis for each municipality. Studying the spatio-temporal dynamics in these indicators, and how they behave similarly, can help us better understand how COVID-19 spread across Cuba. Therefore, spatio-temporal models can be used to analyze these indicators. Univariate spatio-temporal models have been thoroughly studied, but when interest lies in studying the association between multiple outcomes, a joint model that allows for association between the spatial and temporal patterns is necessary. The purpose of our study was to develop a multivariate spatio-temporal model to study the association between the weekly number of COVID-19 deaths and the weekly number of imported COVID-19 cases in Cuba during 2021. To allow for correlation between the spatial patterns, a multivariate conditional autoregressive prior (MCAR) was used. Correlation between the temporal patterns was taken into account by using two approaches; either a multivariate random walk prior was used or a multivariate conditional autoregressive prior (MCAR) was used. All models were fitted within a Bayesian framework.

Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, including symmetry and separability, can reduce the model complexity and facilitate the inference procedure. However, a careful examination of these properties is needed in real applications. In the work presented here, we formally define these properties for multivariate spatio-temporal random fields and use functional data analysis techniques to visualize them, hence, providing intuitive interpretations. We then propose a rigorous rank-based testing procedure to conclude whether the simplified properties of covariance are suitable for the underlying multivariate space-time data. The good performance of our method is illustrated through synthetic data, for which we know the true structure. We also investigate the covariance of bivariate wind speed, a key variable in renewable energy, over a coastal and an inland area in Saudi Arabia. The supplementary material is available online, including the R code for our developed methods.

Incorporating distribution shifts and spatio-temporal variation when estimating weight-at-age for stock assessments: a case study involving the Bering Sea pollock (Gadus chalcogrammus)

AbstractEnvironmental conditions can create spatial and temporal variability in growth and distribution processes, yet contemporary stock assessment methods often do not explicitly address the consequences of these patterns. For example, stock assessments often assume that body weight-at-age (i.e. size) is constant across the stocks’ range, and may thereby miss important spatio-temporal patterns. This is becoming increasingly relevant given climate-driven distributional shifts, because samples for estimating size-at-age can be spatially unbalanced and lead to biases when extrapolating into unsampled areas. Here, we jointly analysed data on the local abundance and size of walleye pollock (Gadus chalcogrammus) in the Bering Sea, to demonstrate a tractable first step in expanding spatially unbalanced size-at-age samples, while incorporating fine-scale spatial and temporal variation for inclusion in stock assessments. The data come from NOAA’s bottom trawl survey data and were evaluated using a multivariate spatio-temporal statistical model. We found extensive variation in size-at-age at fine spatial scales, though specific patterns differed between age classes. In addition to persistent spatial patterns, we also documented year-to-year differences in the spatial patterning of size-at-age. Intra-annual variation in the population-level size-at-age (used to generate the size-at-age matrix in the stock assessment) was largely driven by localized changes in fish size, while shifts in species distribution had a smaller effect. The spatio-temporal size-at-age matrix led to marginal improvement in the stock assessment fit to the survey biomass index. Results from our case study suggest that accounting for spatially unbalanced sampling improved stock assessment consistency. Additionally, it improved our understanding on the dynamics of how local and population-level demographic processes interact. As climate change affects fish distribution and growth, integrating spatiotemporally explicit size-at-age processes with anticipated environmental conditions may improve stock-assessment forecasts used to set annual harvest limits.

Do large‐scale associations in birds imply biotic interactions or environmental filtering?

AbstractAimThere has been a wide interest in the effect of biotic interactions on species' occurrences and abundances at large spatial scales, coupled with a vast development of the statistical methods to study them. Still, evidence for whether the effects of within‐trophic‐level biotic interactions (e.g. competition and heterospecific attraction) are discernible beyond local scales remains inconsistent. Here, we present a novel hypothesis‐testing framework based on joint dynamic species distribution models and functional trait similarity to dissect between environmental filtering and biotic interactions.LocationFrance and Finland.TaxonBirds.MethodsWe estimated species‐to‐species associations within a trophic level, independent of the main environmental variables (mean temperature and total precipitation) for common species at large spatial scale with joint dynamic species distribution (a multivariate spatiotemporal delta model) models. We created hypotheses based on species' functionality (morphological and/or diet dissimilarity) and habitat preferences about the sign and strength of the pairwise spatiotemporal associations to estimate the extent to which they result from biotic interactions (competition, heterospecific attraction) and/or environmental filtering.ResultsSpatiotemporal associations were mostly positive (80%), followed by random (15%), and only 5% were negative. Where detected, negative spatiotemporal associations in different communities were due to a few species. The relationship between spatiotemporal association and functional dissimilarity among species was negative, which fulfils the predictions of both environmental filtering and heterospecific attraction.Main conclusionsWe showed that processes leading to species aggregation (mixture between environmental filtering and heterospecific attraction) seem to dominate assembly rules, and we did not find evidence for competition. Altogether, our hypothesis‐testing framework based on joint dynamic species distribution models and functional trait similarity is beneficial in ecological interpretation of species‐to‐species associations from data covering several decades and biogeographical regions.

A multivariate spatiotemporal model for tracking COVID-19 incidence and death rates in socially vulnerable populations

Recent studies have produced inconsistent findings regarding the association between community social vulnerability and COVID-19 incidence and death rates. This inconsistency may be due, in part, to the fact that these studies modeled cases and deaths separately, ignoring their inherent association and thus yielding imprecise estimates. To improve inferences, we develop a Bayesian multivariate negative binomial model for exploring joint spatial and temporal trends in COVID-19 infections and deaths. The model introduces smooth functions that capture long-term temporal trends, while maintaining enough flexibility to detect local outbreaks in areas with vulnerable populations. Using multivariate autoregressive priors, we jointly model COVID-19 cases and deaths over time, taking advantage of convenient conditional representations to improve posterior computation. As such, the proposed model provides a general framework for multivariate spatiotemporal modeling of counts and rates. We adopt a fully Bayesian approach and develop an efficient posterior Markov chain Monte Carlo algorithm that relies on easily sampled Gibbs steps. We use the model to examine incidence and death rates among counties with high and low social vulnerability in the state of Georgia, USA, from 15 March to 15 December 2020.

Multivariate Bayesian spatio-temporal P-spline models to analyze crimes against women.

Univariate spatio-temporal models for areal count data have received great attention in recent years for estimating risks. However, models for studying multivariate responses are less commonly used mainly due to the computational burden. In this article, multivariate spatio-temporal P-spline models are proposed to study different forms of violence against women. Modeling distinct crimes jointly improves the precision of estimates over univariate models and allows to compute correlations among them. The correlation between the spatial and the temporal patterns may suggest connections among the different crimes that will certainly benefit a thorough comprehension of this problem that affects millions of women around the world. The models are fitted using integrated nested Laplace approximations and are used to analyze four distinct crimes against women at district level in the Indian state of Maharashtra during the period 2001-2013.

Spatiotemporal variable selection and air quality impact assessment of COVID-19 lockdown

During the first wave of the COVID-19 pandemics in 2020, lockdown policies reduced human mobility in many countries globally. This significantly reduces car traffic-related emissions. In this paper, we consider the impact of the Italian restrictions (lockdown) on the air quality in the Lombardy Region. In particular, we consider public data on concentrations of particulate matters (PM10 and PM2.5) and nitrogen dioxide, pre/during/after lockdown. To reduce the effect of confounders, we use detailed regression function based on meteorological, land and calendar information. Spatial and temporal correlations are handled using a multivariate spatiotemporal model in the class of hidden dynamic geostatistical models (HDGM). Due to the large size of the design matrix, variable selection is made using a hybrid approach coupling the well known LASSO algorithm with the cross-validation performance of HDGM.The impact of COVID-19 lockdown is heterogeneous in the region. Indeed, there is high statistical evidence of nitrogen dioxide concentration reductions in metropolitan areas and near trafficked roads where also PM10 concentration is reduced. However, rural, industrial, and mountain areas do not show significant reductions. Also, PM2.5 concentrations lack significant reductions irrespective of zone. The post-lockdown restart shows unclear results.

A MULTIVARIATE SPATIOTEMPORAL CHANGE-POINT MODEL OF OPIOID OVERDOSE DEATHS IN OHIO.

Ohio is one of the states most impacted by the opioid epidemic and experienced the second highest age-adjusted fatal drug overdose rate in 2017. Initially it was believed prescription opioids were driving the opioid crisis in Ohio. However, as the epidemic evolved, opioid overdose deaths due to fentanyl have drastically increased. In this work we develop a Bayesian multivariate spatiotemporal model for Ohio county overdose death rates from 2007 to 2018 due to different types of opioids. The log-odds are assumed to follow a spatially varying change point regression model. By assuming the regression coefficients are a multivariate conditional autoregressive process, we capture spatial dependence within each drug type and also dependence across drug types. The proposed model allows us to not only study spatiotemporal trends in overdose death rates but also to detect county-level shifts in these trends over time for various types of opioids.

Applying a Bayesian multivariate spatio-temporal interaction model based approach to rank sites with promise using severity-weighted decision parameters

Ranking sites with promise is an essential step for cost-effective engineering improvement on roadway traffic safety. This study proposes a Bayesian multivariate spatio-temporal interaction model based approach for ranking sites. The severity-weighted crash frequency and crash rate are used as the decision parameters. The posterior expected rank and posterior mean of the decision parameters are adopted as the statistical criteria. The proposed approach is applied to rank road segments on Kaiyang Freeway in China, which is conducted via programming in the freeware WinBUGS. The results of Bayesian estimation and assessment indicate that incorporating spatio-temporal correlations and interactions into the crash frequency model significantly improves the overall goodness-of-fit performance and affects the identified crash-contributing factors and the estimated safety effects for each severity level. With respect to the ranking results, significant differences are found between those generated from the proposed approach and those generated from the naïve ranking approach and a Bayesian approach based on the multivariate Poisson-lognormal model. Besides, the ranks under the posterior mean criterion are found generally consistent with those under the posterior expected rank criterion.

Quantifying the small-area spatio-temporal dynamics of the Covid-19 pandemic in Scotland during a period with limited testing capacity

Modelling the small-area spatio-temporal dynamics of the Covid-19 pandemic is of major public health importance, because it allows health agencies to better understand how and why the virus spreads. However, in Scotland during the first wave of the pandemic testing capacity was severely limited, meaning that large numbers of infected people were not formally diagnosed as having the virus. As a result, data on confirmed cases are unlikely to represent the true infection rates, and due to the small numbers of positive tests these data are not available at the small-area level for confidentiality reasons. Therefore to estimate the small-area dynamics in Covid-19 incidence this paper analyses the spatio-temporal trends in telehealth data relating to Covid-19, because during the first wave of the pandemic the public were advised to call the national telehealth provider NHS 24 if they experienced symptoms of the virus. Specifically, we propose a multivariate spatio-temporal correlation model for modelling the proportions of calls classified as either relating to Covid-19 directly or having related symptoms, and provide software for fitting the model in a Bayesian setting using Markov chain Monte Carlo simulation. The model was developed in partnership with the national health agency Public Health Scotland, and here we use it to analyse the spatio-temporal dynamics of the first wave of the Covid-19 pandemic in Scotland between March and July 2020, specifically focusing on the spatial variation in the peak and the end of the first wave.

On the spatial and temporal shift in the archetypal seasonal temperature cycle as driven by annual and semi‐annual harmonics

AbstractStatistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the seasonal temperature cycle. However, an often overlooked feature of the climate seasonal cycle is the semi‐annual harmonic, which can account for a significant portion of the variance of the seasonal cycle and varies in amplitude and phase across space. Together, the spatial variation in the annual and semi‐annual harmonics can play an important role in driving processes that are tied to seasonality (e.g., ecological and agricultural processes). We propose a multivariate spatiotemporal model to quantify the spatial and temporal change in minimum and maximum temperature seasonal cycles as a function of the annual and semi‐annual harmonics. Our approach captures spatial dependence, temporal dynamics, and multivariate dependence of these harmonics through spatially and temporally varying coefficients. We apply the model to minimum and maximum temperature over North American for the years 1979–2018. Formal model inference within the Bayesian paradigm enables the identification of regions experiencing significant changes in minimum and maximum temperature seasonal cycles due to the relative effects of changes in the two harmonics.

A Multivariate Spatiotemporal Model of COVID-19 Epidemic Using Ensemble of ConvLSTM Networks

The high R-naught factor of SARS-CoV-2 has created a race against time for mankind, and it necessitates rapid containment actions to control the spread. In such scenario short-term accurate spatiotemporal predictions can help understanding the dynamics of the spread in a geographic region and identify hotspots. However, due to the novelty of the disease there is very little disease-specific data generated yet. This poses a difficult problem for machine learning methods to learn a model of the epidemic spread from data. A proposed ensemble of convolutional LSTM-based spatiotemporal model can forecast the spread of the epidemic with high resolution and accuracy in a large geographic region. The feature construction method creates geospatial frames of features with or without temporal component based on latitudes and longitudes thus avoiding the need of location specific adjacency matrix. The model has been trained with available data for USA and Italy. It achieved 5.57% and 0.3% mean absolute percent error for total number of predicted infection cases in a 5-day prediction period for USA and Italy, respectively.

A multivariate spatio-temporal model of the opioid epidemic in Ohio: A factor model approach.

Opioid misuse is a significant public health issue and a national epidemic with a high prevalence of associated morbidity and mortality. The epidemic is particularly severe in Ohio which has some of the highest overdose rates in the country. It is important to understand spatial and temporal trends of the opioid epidemic to learn more about areas that are most affected and to inform potential community interventions and resource allocation. We propose a multivariate spatio-temporal model to leverage existing surveillance measures, opioid-associated deaths and treatment admissions, to learn about the underlying epidemic for counties in Ohio. We do this using a temporally varying spatial factor that synthesizes information from both counts to estimate common underlying risk which we interpret as the burden of the epidemic. We demonstrate the use of this model with county-level data from 2007-2018 in Ohio. Through our model estimates, we identify counties with above and below average burden and examine how those regions have shifted over time given overall statewide trends. Specifically, we highlight the sustained above average burden of the opioid epidemic on southern Ohio throughout the 12 years examined.

Air Conditioning and Heat-related Mortality: A Multi-country Longitudinal Study.

Air conditioning has been proposed as one of the key factors explaining reductions of heat-related mortality risks observed in the last decades. However, direct evidence is still limited. We used a multi-country, multi-city, longitudinal design to quantify the independent role of air conditioning in reported attenuation in risk. We collected daily time series of mortality, mean temperature, and yearly air conditioning prevalence for 311 locations in Canada, Japan, Spain, and the USA between 1972 and 2009. For each city and sub-period, we fitted a quasi-Poisson regression combined with distributed lag non-linear models to estimate summer-only temperature-mortality associations. At the second stage, we used a novel multilevel, multivariate spatio-temporal meta-regression model to evaluate effect modification of air conditioning on heat-mortality associations. We computed relative risks and fractions of heat-attributable excess deaths under observed and fixed air conditioning prevalences. Results show an independent association between increased air conditioning prevalence and lower heat-related mortality risk. Excess deaths due to heat decreased during the study periods from 1.40% to 0.80% in Canada, 3.57% to 1.10% in Japan, 3.54% to 2.78% in Spain, and 1.70% to 0.53% in the USA. However, increased air conditioning explains only part of the observed attenuation, corresponding to 16.7% in Canada, 20.0% in Japan, 14.3% in Spain, and 16.7% in the USA. Our findings are consistent with the hypothesis that air conditioning represents an effective heat adaptation strategy, but suggests that other factors have played an equal or more important role in increasing the resilience of populations.