Generalized Least Squares Model Research Articles

Eutrophication trends in the coastal region of the Great Tokyo area based on long-term trends of Secchi depth.

The coastal ocean's environment has changed owing to human activity, with eutrophication becoming a global concern. However, oligotrophication occurs locally and decreases fish production. Historically, the Secchi depth has been used as an index of primary productivity. We analyzed the results of over-a-half-century routine observations conducted in Sagami Bay and Tokyo Bay to verify the eutrophication/oligotrophication trend based on Secchi depth observations in a temperate coastal region near the Greater Tokyo area, which is highly affected by human activities. Data recorded in the Kanagawa Prefecture from 1963 to 2018 were used in this study. After quality control, the observation area was divided into Tokyo Bay, the Uraga Channel (outer part of Tokyo Bay), Sagami Bay (northern part), and Sagami Nada (southern part of Sagami Bay) based on temperature and salinity at a depth of 10 m. Because the environmental parameters showed autocorrelation, time-series and correlation analyses were conducted using generalized least squares (GLS) models with a Prais-Winsten estimator. The Secchi depth was the shallowest in Tokyo Bay, followed by the Uraga Channel, Sagami Bay, and Sagami Nada, and was deep in winter (December and January), and shallow in summer (July) in all regions. The correlated analyses using the GLS model indicated that the shallowing of Secchi depth was significantly associated with decreases in temperature, salinity, and phosphate concentration. However, time-series analyses using GLS models indicated that the Secchi depth was significantly shallower, except in Tokyo Bay, where the surface temperature was significantly warming and the surface phosphate and nitrite concentrations decreased everywhere. A significant shallowing trend of the Secchi depth was mostly observed during the light-limiting season (January-March). Correlation analyses suggested the importance of horizontal advective transport, particularly from Tokyo Bay, which has cold and less saline eutrophic water. However, long-term shallowing of the Secchi depth was associated with warming, and changes in salinity were not significant in most months when the Secchi depth trend was significant. Thus, horizontal advection is not the primary cause of long-term eutrophication. Because the eutrophication trend was primarily observed in winter, when light is the major limiting factor of primary production, we concluded that warming provides a better photoenvironment for phytoplankton growth and induces eutrophication. As a decline in anthropogenic nutrient input after 1990s was reported in the investigated area, the long-term eutrophication trend was most likely caused due to global warming, which is another alarming impact resulting from human activities.

Checking for model consistency in optimal fingerprinting: a comment

Allen and Tett (1999, herein AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change for attribution purposes and proposed the “Residual Consistency Test” (RCT) to check the GLS specification. Their methodology has been widely used and highly influential ever since, in part because subsequent authors have relied upon their claim that their GLS model satisfies the conditions of the Gauss-Markov (GM) Theorem, thereby yielding unbiased and efficient estimators. But AT99 stated the GM Theorem incorrectly, omitting a critical condition altogether, their GLS method cannot satisfy the GM conditions, and their variance estimator is inconsistent by construction. Additionally, they did not formally state the null hypothesis of the RCT nor identify which of the GM conditions it tests, nor did they prove its distribution and critical values, rendering it uninformative as a specification test. The continuing influence of AT99 two decades later means these issues should be corrected. I identify 6 conditions needing to be shown for the AT99 method to be valid.

Intraday analysis of regulation change in microstructure: evidence from an emerging market

PurposeThis study investigates the impact of simultaneously replacing both midday single-price call auction and lunch break with multi-price continuous trading on intraday volatility–volume patterns as well as the intraday volatility–volume nexus.Design/methodology/approachThe analysis utilises 150 m tick-by-tick transaction data related to 333 stocks traded on Borsa Istanbul Equity Market covering a period of 2 months prior to and following the change. In addition to graphic comparisons, the study uses difference in mean tests, panel-fixed generalized least squares (GLS), panel-random GLS and random-effects linear models with AR(1) disturbance regression estimations.FindingsThe results show that intraday volatility and trading volume form an inverse J-shape and are positively correlated. It is observed that the implementation of the regulation change decreased intraday volatility and increased trading volume. Additionally, the results indicate a negative volatility–liquidity and a positive volume–liquidity relationship, supporting the mixture of distribution hypothesis.Research limitations/implicationsEnhanced market efficiency provides greater opportunity for investment and risk management. Investors can benefit from the findings on the intraday volatility–volume nexus, which is an indicator of informed trading, and regulatory authorities can use volume to oversight volatility.Originality/valueThis very rare regulation change of the simultaneous replacement of the lunch break and midday call auction with continuous trading is investigated in the context of intraday volume and volatility. This study also expands upon some important findings on the volume–volatility nexus for the Turkish Stock Market.

Spatial Externalities of Income Inequality on Security in Latin America

The aim of this research is to analyse the effect of income inequality on the homicide rate. The study is carried out in 18 Latin American countries for the period 2005–2018. The methodology used is the Generalized Least Squares (GLS) model and the data were obtained from World Development Indicators, the World Health Organization and the Inter-American Development Bank. Thus, the dependent variable is the homicide rate and the independent variable is income inequality. In addition, some control variables are included, such as: poverty, urban population rate, unemployment, schooling rate, spending on security and GDP per capita, which improve the consistency of the model. The results obtained through GLS model determine that inequality has a negative and significant effect on the homicide rate for high-income countries (HIC) and lower-middle-income countries (LMIC), whereas it is positive and significant for upper-middle-income countries (UMIC). On the other hand, the control variables show different results by group of countries. In the case of unemployment, it is not significant in any group of countries. Negative spatial dependence was found regarding spatial models such as: the spatial lag (SAR) and spatial error (SEM) method. In the spatial Durbin model (SDM), positive spatial dependence between the variables was corroborated. However, spatial auto-regressive moving average (SARMA) identified no spatial dependence. Under these results it is proposed: to improve productivity, education and improve the efficiency of security-oriented resources.

Long-term effects of fish biomanipulation and macrophyte management on zooplankton functional diversity and production in a temperate shallow lake

Eutrophication still is one of the greatest anthropogenic impacts affecting aquatic ecosystems. Food web manipulations to reverse eutrophic conditions have been applied, mainly by reducing fish stocks. However, the long-term results of biomanipulation are still ambiguous. The objective of this study was to evaluate biomanipulation effects on zooplankton functional diversity and production during 24 years of monitoring a shallow temperate lake. Temporal variation in crustacean biomass (CB), zooplankton resource use efficiency (RUE), limnological variables, functional diversity indices and functional traits were assessed using the Mann–Kendall test. The effects of the limnological and functional variables on zooplankton production (CB and RUE) were analyzed by generalized least squares models (GLSs). We found decreasing trends for almost all the limnological variables, indicating a reduction in lake eutrophic conditions. We also observed a decreasing trend in functional traits related to pelagic habitat, filter-feeding mode, herbivore feeding preference and body size. The GLS results showed that functional dispersion and chlorophyll a are important determinants of zooplankton production. The effects of fish biomanipulation produced no significant temporal trends in zooplankton biomass. In fact, the increase in submerged macrophytes promoted littoral food webs, which was likely the main determining factor of the changes in zooplankton functional traits and production.

Habitat productivity is a poor predictor of body size in rodents.

The “resource availability hypothesis” predicts occurrence of larger rodents in more productive habitats. This prediction was tested in a dataset of 1,301 rodent species. We used adult body mass as a measure of body size and normalized difference vegetation index (NDVI) as a measure of habitat productivity. We utilized a cross-species approach to investigate the association between these variables. This was done at both the order level (Rodentia) and at narrower taxonomic scales. We applied phylogenetic generalized least squares (PGLS) to correct for phylogenetic relationships. The relationship between body mas and NDVI was also investigated across rodent assemblages. We controlled for spatial autocorrelation using generalized least squares (GLS) analysis. The cross-species approach found extremely low support for the resource availability hypothesis. This was reflected by a weak positive association between body mass and NDVI at the order level. We find a positive association in only a minority of rodent subtaxa. The best fit GLS model detected no significant association between body mass and NDVI across assemblages. Thus, our results do not support the view that resource availability plays a major role in explaining geographic variation in rodent body size.

Spatial patterns in habitat specialization of European bird communities

Abstract The level of habitat specialization is informative in terms of animals’ population status and conservation concern. Therefore, identifying the areas where specialist species are aggregated and understanding the ecological constrains that might shape their distribution has become an important issue. In this sense, we tested whether specialist communities are more likely to succeed in milder and stable environments or in more extreme and less predictable environments. For that purpose, we used data from the EBCC atlas of European breeding birds and for each of 50 × 50 km grid cells calculated community specialization index (CSI). We expressed CSI in two ways: as a mean (CSIMEAN) and a standard deviation (CSISD) across species in a given cell. We used generalized least squares (GLS) models to relate these measures to geographic variables (latitude, longitude and altitude) and climatic variables (temperature and rainfall) across Europe controlling for possible confounding effects of habitat heterogeneity and human-induced land cover conversion. We identified two areas, Scandinavian Peninsula and the steppe regions north of Caucasus, where bird communities are highly specialised. GLS models showed that habitat specialization generally increased with altitude and this pattern was broadly shared by the CSIMEAN and CSISD. Concerning climatic variables, we found that specialist spatial distribution was significantly related to extreme temperatures and lower level of precipitation. Our results thus suggest that European specialist birds are found mostly in strongly seasonal, dry and cold environments. Thereby, preserving these sensible environments from further perturbations might be the key for the specialist conservation.

Identifying the Main Factors Contributing to the Spatial Variability of Soil Saline–Sodic Properties in a Reclaimed Coastal Area

Core Ideas A spatial model was used for identifying the main factors affecting spatial variability of soil salt. Land‐use pattern was the most influential factor that affected spatial variation of soil salt. The generalized least squares model was suitable for soil salt content in Transect 2. This study is helpful for agronomic management practices in coastal reclamation areas. Studies on changes in soil saline–sodic characteristics have important reference value for reclamation planning and agricultural utilization of coastal regions. The objective of this study was to investigate the spatial distribution of the soil salt content (SSC) and sodium adsorption ratio (SAR) in two transects, which extended through different reclamation areas along a reclaimed coastal area of China. A total of 54 sampling points along Transect 1 were collected to study soil saline–sodic characteristics of a recently reclaimed farmland in 2007, and 50 sampling points were collected along Transect 2 that ran through six farmland areas reclaimed at different times (2007, 1981, 1960, 1950, 1940, and 1916). A spatial model, generalized least squares (GLS), was used to conduct multiple regression equations on SSC or SAR and explanatory variables. The results showed that land‐use pattern was the most influential factor that affected spatial variation of SSC and SAR. The parametric Levene's test and Moran's I test showed that heterogeneity and autocorrelated residuals could only be found for SSC in Transect 2, so the GLS model was suitable for SSC in Transect 2. The GLS method did not perform better than the nonspatial model (ordinary least squares) by incorporating exhaustive ancillary variables but was more suitable when autocorrelation and heteroscedasticity existed in the errors of a model. Using these methods, we obtained information on the spatial variation of soil saline–sodic characteristics and its controlling factors. This information is helpful for land‐use planning, soil partition management, and agronomic management practices in coastal reclamation areas.

Achieving Good Glycemic Control Early After Onset of Diabetes: A Cost-Effectiveness Analysis in Patients with Type 1 Diabetes in Sweden.

IntroductionSweden has amongst the highest incidence rates of type 1 diabetes (T1D) in Europe. The high incidence and chronic nature of T1D result in high prevalence and economic burden. Improving glycemic control reduces the incidence of microvascular complications, which in turn reduces medical costs. The present study aimed to quantify the reductions in cost and improvements in quality-adjusted life expectancy with varying reductions in HbA1c in the T1D population.MethodsThe IQVIA CORE Diabetes Model was used to simulate a typical Swedish population of patients with T1D experiencing HbA1c reductions from 0.1% to 0.8% (in 0.1% increments) from 7.9% at baseline. Analyses were conducted in simulated cohorts based on data from the Swedish National Diabetes Register (NDR) and in subgroups by sex, smoking status, and body mass index (BMI), with different sets of quality-of-life utilities included. Generalized least squares (GLS) models were used to test for significant differences between subgroups. Analyses were also performed to investigate the effect of the duration of HbA1c control. Analyses were run over 50 years and outcomes discounted at 3% per annum.ResultsIn the reference case analysis, reducing HbA1c lowered the incidence of microvascular and macrovascular complications and improved quality-adjusted life expectancy. GLS models identified a significantly larger benefit of reducing HbA1c in women over men, but found no significant differences in the magnitude of quality of life improvements with decreasing HbA1c when segregating by smoking status or BMI.ConclusionsReducing HbA1c in a population with T1D would reduce the incidence of microvascular complications, improve life expectancy and quality of life. Larger quality-of-life benefits were observed in younger and female adult patients, but no notable differences were observed in the benefits of glycemic control in smokers versus non-smokers or in patients with low or high BMI.FundingNovo Nordisk Scandinavia AB, Malmö, Sweden.

Factors controlling the three-decade long rise in cyanobacteria biomass in a eutrophic shallow lake

We aimed at quantifying the importance of limnological variables in the decadal rise of cyanobacteria biomass in shallow hemiboreal lakes. We constructed estimates of cyanobacteria (blue-green algae) biomass in a large, eutrophic lake (Estonia, Northeastern Europe) from a database comprising 28 limnological variables and spanning more than 50years of monitoring. Using a dual-model approach consisting in a boosted regression trees (BRT) followed by a generalized least squares (GLS) model, our results revealed that six variables were most influential for assessing the variance of cyanobacteria biomass. Cyanobacteria response to nitrate concentration and rotifer abundance was negative, whereas it was positive to pH, temperature, cladoceran and copepod biomass. Response to total phosphorus (TP) and total phosphorus to total nitrogen ratio was very weak, which suggests that actual in-lake TP concentration is still above limiting values. The most efficient GLS model, which explained nearly two thirds (r2=0.65) of the variance of cyanobacteria biomass included nitrate concentration, water temperature and pH. The very high number of observations (maximum n=525) supports the robustness of the models. Our results suggest that the decadal rise of blue-green algae in shallow lakes lies in the interaction between cultural eutrophication and global warming which bring in-lake physical and chemical conditions closer to cyanobacteria optima.

The rainfall erosivity factor in the Czech Republic and its uncertainty

Abstract. In the present paper, the rainfall erosivity factor (R factor) for the area of the Czech Republic is assessed. Based on 10 min data for 96 stations and corresponding R factor estimates, a number of spatial interpolation methods are applied and cross-validated. These methods include inverse distance weighting, standard, ordinary, and regression kriging with parameters estimated by the method of moments and restricted maximum likelihood, and a generalized least-squares (GLS) model. For the regression-based methods, various statistics of monthly precipitation as well as geographical indices are considered as covariates. In addition to the uncertainty originating from spatial interpolation, the uncertainty due to estimation of the rainfall kinetic energy (needed for calculation of the R factor) as well as the effect of record length and spatial coverage are also addressed. Finally, the contribution of each source of uncertainty is quantified. The average R factor for the area of the Czech Republic is 640 MJ ha−1 mm h−1, with values for the individual stations ranging between 320 and 1520 MJ ha−1 mm h−1. Among various spatial interpolation methods, the GLS model relating the R factor to the altitude, longitude, mean precipitation, and mean fraction of precipitation above the 95th percentile of monthly precipitation performed best. Application of the GLS model also reduced the uncertainty due to the record length, which is substantial when the R factor is estimated for individual sites. Our results revealed that reasonable estimates of the R factor can be obtained even from relatively short records (15–20 years), provided sufficient spatial coverage and covariates are available.

Toward optimal model averaging in regression models with time series errors

Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However, GLS estimators, depending on the unknown inverse covariance matrix of the errors, are usually infeasible. We therefore construct feasible generalized least squares (FGLS) estimators using a consistent estimator of the unknown inverse matrix. Based on this inverse covariance matrix estimator and FGLS estimators, we develop a feasible autocovariance-corrected Mallows model averaging criterion to select weights, thereby providing an FGLS model averaging estimator of the true regression function. We show that the generalized squared error loss of our averaging estimator is asymptotically equivalent to the minimum one among those of GLS model averaging estimators with the weight vectors belonging to a continuous set, which includes the discrete weight set used in Hansen (2007) as its proper subset.

Host abundance, durability, basidiome form and phylogenetic isolation determine fungivore species richness

Species with close associations to a specific host species, such as parasites and phytophages, make immense contributions to biodiversity. Hence, factors determining the variation in species richness among hosts are a main focus of ecological research. Investigations of determining factors of fungivorous species among host species are still scarce. Based on ecological patterns of parasites and phytophages, we hypothesized that the species richness of tree-fungus beetles of the family Ciidae (Coleoptera) would increase with increasing basidiome size, niche diversity of the growth form, durability, increasing abundance and decreasing phylogenetic isolation of the host fungus. Our generalized least-squares model, controlled by host phylogeny, revealed that Ciidae species richness increases with host abundance, but decreases with host phylogenetic isolation. In contrast with our prediction, Ciidae species richness was higher in annual basidiomes than in perennials. Pileate basidiomes revealed higher species richness than resupinate and stipitate basidiomes, which may be interpreted as being a result of their higher host niche diversity. The importance of host abundance, measured on the landscape scale, corroborates that fungivore species richness among macrofungal hosts is determined by factors similar to those that determine parasite and phytophage species richness among their hosts. © 2015 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114, 699–708.

Spatial variability of soil electrical conductivity in a small watershed on the Loess Plateau of China

Knowledge of soil electrical conductivity of saturated paste extract (ECe) pattern is important to effectively managing farmland and improving crop productivity. The objectives of this study were (1) to characterize the spatial patterns of ECe and electrical conductivity of saturated paste (ECs) and (2) to determine the factors that affect significantly in the estimation of soil ECe. Soil samples were taken at various soil depths (0.1, 0.2, 0.4, 0.6, and 0.8m) of 124 locations in a small watershed. Besides ECe and ECs, various soil, topographical, and vegetation properties were measured. Geostatistical techniques were used to characterize the spatial patterns of ECe and ECs. Ordinary least squares (OLS) and generalized least squares (GLS) models were used to perform multiple regression analyses between ECe and other properties. The OLS model belongs to a non-spatial regression, whereas the GLS model is a spatial regression which considers the autocorrelation in the residuals. Results showed that both ECe and ECs presented moderate variability at the watershed scale. The ECe presented weak to moderate spatial dependency, whereas the ECs presented moderate to strong spatial dependency. The ratio of ECe to ECs differed with soil texture, and it was greater for sand texture than for loam texture. A fair to moderate spatial agreement existed between ECe and ECs at all depths except for 0.2m, where ECe presented a more random distribution. Heteroscedasticity in the residuals between two land uses (grass land and shrub land) and autocorrelation in the residuals only existed at 0.4m soil layer where the GLS model did not improve significantly over the OLS model in terms of explaining variations in ECe. Electrical conductivity of saturated paste was the dominant factor in explaining ECe variation for all depths, while soil separate significant affected the estimation of ECe at 0.1m as well. It is concluded that ECs may be used as a surrogate for ECe especially for homogeneous soil textures. This would greatly reduce the work involved in ECe measurement due to the easier availability of ECs. Our study implies that ECe can be used as an index of soil fertility condition in this area. In addition, OLS model can be accurate enough to describe the relationships between ECe and other properties due to the absence of strong spatial dependency of ECe in this area.

Regionalisation of the parameters of the log-Pearson 3 distribution: a case study for New South Wales, Australia

The index flood method is widely used in regional flood frequency analysis (RFFA) but explicitly relies on the identification of ‘acceptable homogeneous regions’. This paper presents an alternative RFFA method, which is particularly useful when ‘acceptably homogeneous regions’ cannot be identified. The new RFFA method is based on the region of influence (ROI) approach where a ‘local region’ can be formed to estimate statistics at the site of interest. The new method is applied here to regionalize the parameters of the log-Pearson 3 (LP3) flood probability model using Bayesian generalized least squares (GLS) regression. The ROI approach is used to reduce model error arising from the heterogeneity unaccounted for by the predictor variables in the traditional fixed-region GLS analysis. A case study was undertaken for 55 catchments located in eastern New South Wales, Australia. The selection of predictor variables was guided by minimizing model error. Using an approach similar to stepwise regression, the best model for the LP3 mean was found to use catchment area and 50-year, 12-h rainfall intensity as explanatory variables, whereas the models for the LP3 standard deviation and skewness only had a constant term for the derived ROIs. Diagnostics based on leave-one-out cross validation show that the regression model assumptions were not inconsistent with the data and, importantly, no genuine outlier sites were identified. Significantly, the ROI GLS approach produced more accurate and consistent results than a fixed-region GLS model, highlighting the superior ability of the ROI approach to deal with heterogeneity. This method is particularly applicable to regions that show a high degree of regional heterogeneity. Copyright © 2014 John Wiley & Sons, Ltd.

Independent Contrasts and PGLS Regression Estimators Are Equivalent

We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.

Estimating Riparian Understory Vegetation Cover with Beta Regression and Copula Models

Abstract Understory vegetation communities are critical components of forest ecosystems. As a result, the importance of modeling understory vegetation characteristics in forested landscapes has become more apparent. Abundance measures such as shrub cover are bounded between 0 and 1, exhibit heteroscedastic error variance, and are often subject to spatial dependence. These distributional features tend to be ignored when shrub cover data are analyzed. The beta distribution has been used successfully to describe the frequency distribution of vegetation cover. Beta regression models ignoring spatial dependence (BR) and accounting for spatial dependence (BRdep) were used to estimate percent shrub cover as a function of topographic conditions and overstory vegetation structure in riparian zones in western Oregon. The BR models showed poor explanatory power (pseudo-R2 ≤ 0.34) but outperformed ordinary least-squares (OLS) and generalized least-squares (GLS) regression models with logit-transformed response in terms of mean square prediction error and absolute bias. We introduce a copula (COP) model that is based on the beta distribution and accounts for spatial dependence. A simulation study was designed to illustrate the effects of incorrectly assuming normality, equal variance, and spatial independence. It showed that BR, BRdep, and COP models provide unbiased parameter estimates, whereas OLS and GLS models result in slightly biased estimates for two of the three parameters. On the basis of the simulation study, 93–97% of the GLS, BRdep, and COP confidence intervals covered the true parameters, whereas OLS and BR only resulted in 84–88% coverage, which demonstrated the superiority of GLS, BRdep, and COP over OLS and BR models in providing standard errors for the parameter estimates in the presence of spatial dependence.

A Rapid Generalized Least Squares Model for a Genome-Wide Quantitative Trait Association Analysis in Families

Genome-wide association studies (GWAS) using family data involve association analyses between hundreds of thousands of markers and a trait for a large number of related individuals. The correlations among relatives bring statistical and computational challenges when performing these large-scale association analyses. Recently, several rapid methods accounting for both within- and between-family variation have been proposed. However, these techniques mostly model the phenotypic similarities in terms of genetic relatedness. The familial resemblances in many family-based studies such as twin studies are not only due to the genetic relatedness, but also derive from shared environmental effects and assortative mating. In this paper, we propose 2 generalized least squares (GLS) models for rapid association analysis of family-based GWAS, which accommodate both genetic and environmental contributions to familial resemblance. In our first model, we estimated the joint genetic and environmental variations. In our second model, we estimated the genetic and environmental components separately. Through simulation studies, we demonstrated that our proposed approaches are more powerful and computationally efficient than a number of existing methods are. We show that estimating the residual variance-covariance matrix in the GLS models without SNP effects does not lead to an appreciable bias in the p values as long as the SNP effect is small (i.e. accounting for no more than 1% of trait variance).

Attributable Costs of Enterococcal Bloodstream Infections in a Nonsurgical Hospital Cohort

Vancomycin-resistant Enterococcus (VRE) bloodstream infections (BSIs) are associated with increased morbidity and mortality. To determine the hospital costs and length of stay attributable to VRE BSI and vancomycin-sensitive Enterococcus (VSE) BSI and the independent effect of vancomycin resistance on hospital costs. A retrospective cohort study was conducted of 21,154 nonsurgical patients admitted to an academic medical center during the period from 2002 through 2003. Using administrative data, attributable hospital costs (adjusted for inflation to 2007 US dollars) and length of stay were estimated with multivariate generalized least-squares (GLS) models and propensity score-matched pairs. The cohort included 94 patients with VRE BSI and 182 patients with VSE BSI. After adjustment for demographics, comorbidities, procedures, nonenterococcal BSI, and early mortality, the costs attributable to VRE BSI were $4,479 (95% confidence interval [CI], $3,500-$5,732) in the standard GLS model and $4,036 (95% CI, $3,170-$5,140) in the propensity score-weighted GLS model, and the costs attributable to VSE BSI were $2,250 (95% CI, $1,758-$2,880) in the standard GLS model and $2,023 (95% CI, $1,588-$2,575) in the propensity score-weighted GLS model. The median values of the difference in costs between matched pairs were $9,949 (95% CI, $1,579-$24,693) for VRE BSI and $5,282 (95% CI, $2,042-$8,043) for VSE BSI. The costs attributable to vancomycin resistance were $1,713 (95% CI, $1,338-$2,192) in the standard GLS model and $1,546 (95% CI, $1,214-$1,968) in the propensity score-weighted GLS model. Depending on the statistical method used, attributable length of stay estimates ranged from 2.2 to 3.5 days for patients with VRE BSI and from 1.1 to 2.2 days for patients with VSE BSI. VRE BSI and VSE BSI were independently associated with increased hospital costs and increased length of stay. Vancomycin resistance was associated with increased costs.

Combining site and regional flood information using a Bayesian Monte Carlo approach

Regression‐based methods are widely used in flood regionalization. Since the generalized least squares (GLS) regression model properly accounts for both model and sampling errors, realistic estimates of uncertainty can be obtained. This study presents a general Bayesian approach for inferring the GLS regional regression model and for combining with any available site information to obtain the most accurate flood quantiles. A robust block Metropolis scheme is developed to sample the posterior distribution of the GLS regression model parameters. A particular feature of the sampler is the use of a uniform proposal for the regional model error variance to avoid convergence difficulties. A simple but general procedure, based on importance sampling, is developed to combine any kind of site information with regional information. The benefit of this approach is that all available information is fully exploited, and uncertainty is rigorously quantified as well as being minimized. Two case studies are presented. A synthetic case study illustrates the complex nature of the posterior distribution for the regional model error variance with its shape dependent on how much sampling error dominates the total error in the regional GLS model. A second case study involving 24 sites from the east coast of Australia is presented for the log Pearson III model. It demonstrates the significant benefit of combining site and regional information and the quantification of uncertainty.