Restricted Spatial Regression Methods: Implications for Inference

Khan, Kori; Calder, Catherine A.

doi:10.1080/01621459.2020.1788949

Cited by 41 publications

(36 citation statements)

References 32 publications

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“…Hodges and Reich (2010) suggest using restricted spatial regression in which one constructs spatial random effects that are orthogonal to the fixed effects to combat this problem. However, Khan and Calder (2020) suggest that a non‐spatial model and an unrestricted spatial model should be fitted. We have used both a non‐spatial model and an unrestricted spatial model and made our comparisons.…”

Section: Methodsmentioning

confidence: 99%

What are the associations between thinning and fire severity?

2021

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There has been concern globally about the impacts of wildfires on lives, property and biodiversity. Mechanical thinning has been proposed as a way to reduce fire severity. However, its effectiveness appears to vary between regions and ecosystems. Here, we sought to answer the question: Does thinning reduce the severity of wildfire in managed eucalypt forests? We did this by completing an empirical study of the factors affecting two levels of fire severity – crown burn and crown burn/crown scorch in lowland and wet/damp forest burned in 2019‐2020 in East Gippsland, Australia. We found complex interactions between thinning, forest type and time since the last major disturbance in the best‐fitting models for crown burn and crown burn/crown scorch. The probability of a crown burn was higher in younger stands of thinned forest than in unthinned forest. Crown burn risk in thinned forest was characterised by an inverse relationship with increasing time since the last disturbance; there were no such effects in unthinned forest. We found that the probability of crown burn/crown scorch increased with time since last disturbance in both thinned and unthinned lowland forest. The probability of crown burn/crown scorch also increased over time in wet/damp forest, but the patterns were different between unthinned and thinned stands. Risk of crown burn/crown scorch was lower in young thinned forest relative to unthinned forest, but this pattern reversed with increasing time since the last disturbance. Our analyses showed the efficacy of thinning was variable, depending on fire severity, type of forest targeted for management and the age of that forest (as reflected by the time since the last major disturbance). Therefore, thinning interventions to mitigate fire severity should not be implemented without consideration of these factors and are unlikely to be a viable management option in many circumstances. This is because, in some cases, thinning can lead to elevated fire severity (e.g. soon after thinning for crown burn and in older forests for crown burn/crown scorch) and hence have opposite effects to those intended from such activities.

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Section: Methodsmentioning

confidence: 99%

What are the associations between thinning and fire severity?

2021

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“…Additionally to leading to a loss of computational efficiency, these models cannot be naturally extended to other spatial models than the conditional autoregressive ones. Khan and Calder (2020) also note that their use may entail an increased type-S error for both correctly and incorrectly specified…”

Section: Investigating Spatial Confounding: a Bayesian Alternative To Spatial+mentioning

confidence: 99%

“…We explore different prior specifications for these local latent effects, ranging from independent to spatially structured ones. It is known that the inclusion of spatially structured latent effects can affect the estimation of the fixed effects (Reich et al, 2006;Khan and Calder, 2020;Dupont et al, 2021); this is known in the literature of Spatial Statistics as spatial confounding. We fit a Bayesian version of the Spatial+ approach proposed by Dupont et al (2021) to investigate if there is spatial confounding in the fitted models.…”

Section: Motivationmentioning

confidence: 99%

A joint hierarchical model for the number of cases and deaths due to COVID-19 across the boroughs of Montreal

Michal

Vanciu

Schmidt

2021

Preprint

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Montreal has been the epicentre of the COVID-19 pandemic in Canada with the highest number of deaths in the country. The cumulative numbers of cases and deaths, as of July 25th, 2021, recorded in the 33 areas of Montreal are modelled through a bivariate hierarchical Bayesian model using Poisson distributions. The Poisson means are decomposed in the log scale as the sums of fixed effects and latent effects. The areal median age, the educational level, and the number of beds in long-term care homes are included in the fixed effects. To explore the correlation between cases and deaths inside each area and across areas, three bivariate models are considered for the latent effects, namely an independent one, a conditional autoregressive model, and one that allows for both spatially structured and unstructured sources of variability. As the inclusion of spatial effects change some of the fixed effects, we extend the Spatial+ approach to a Bayesian areal set up to investigate the presence of spatial confounding. Results show that the cumulative totals of cases and deaths are negatively correlated inside and across the boroughs of Montreal. The covariates are not associated in a similar manner for the cases and deaths due to COVID-19. The educational level and the median age seem spatially confounded for the cases and deaths across the boroughs of Montreal.

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“…An important difference between the classical and this spatial IV approach is that in the spatial version the fitted values will not be strictly orthogonal to the errors U⊂i. A potential remedy is the use of restricted spatial regression (Reich et al, 2006;Hodges & Reich, 2010;Hughes & Haran, 2013;Hanks et al, 2015), although these methods should be used with caution in light of the recent work of Khan & Calder (2020).…”

Section: Instrumental Variablesmentioning

confidence: 99%

“…One way to resolve this conflict is to restrict the spatial random effects to be orthogonal to the observed treatment variables (Reich et al, 2006;Hughes & Haran, 2013;Hanks et al, 2015;Page et al, 2017;Prates et al, 2019). However, Khan & Calder (2020) showed that this can lead to poor performance for treatment estimates. A motivation for the orthogonal regression approach is that it is easier to interpret a regression model if the signal is attributed to known quantities (e.g.…”

Section: Summary and Future Workmentioning

confidence: 99%

A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications

Reich

Yang

Guan

et al. 2021

Int Statistical Rev

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The scientific rigor and computational methods of causal inference have had great impacts on many disciplines but have only recently begun to take hold in spatial applications. Spatial causal inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided.

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Restricted Spatial Regression Methods: Implications for Inference

Cited by 41 publications

References 32 publications

What are the associations between thinning and fire severity?

What are the associations between thinning and fire severity?

A joint hierarchical model for the number of cases and deaths due to COVID-19 across the boroughs of Montreal

A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications

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