Regression calibration and maximum likelihood inference for measurement error models

Regression calibration inference seeks to estimate regression models with measurement error in explanatory variables by replacing the mismeasured variable by its conditional expectation, given a surrogate variable, in an estimation procedure that would have been used if the true variable were available. This study examines the effect of the uncertainty in the estimation of the required conditional expectation on inference about regression parameters, when the true explanatory variable and its surrogate are observed in a calibration dataset and related through a normal linear model. The exact sampling distribution of the regression calibration estimator is derived for normal linear regression when independent calibration data are available. The sampling distribution is skewed and its moments are not defined, but its median is the parameter of interest. It is shown that, when all random variables are normally distributed, the regression calibration estimator is equivalent to maximum likelihood provided a natural estimate of variance is non-negative. A check for this equivalence is useful in practice for judging the suitability of regression calibration. Results about relative efficiency are provided for both external and internal calibration data. In some cases maximum likelihood is substantially more efficient than regression calibration. In general, though, a more important concern when the necessary conditional expectation is uncertain, is that inferences based on approximate normality and estimated standard errors may be misleading. Bootstrap and likelihood-ratio inferences are preferable.Keywords: Measurement error, Regression calibration, Validation study, Errors-in-variable

Evidence of Tree Species’ Range Shifts in a Complex Landscape

Climate change is expected to change the distribution of species. For long-lived, sessile species such as trees, tracking the warming climate depends on seedling colonization of newly favorable areas. We compare the distribution of seedlings and mature trees for all but the rarest tree species in California, Oregon and Washington, United States of America, a large, environmentally diverse region. Across 46 species, the mean annual temperature of the range of seedlings was 0.120°C colder than that of the range of trees (95% confidence interval from 0.096 to 0.144°C). The extremes of the seedling distributions also shifted towards colder temperature than those of mature trees, but the change was less pronounced. Although the mean elevation and mean latitude of the range of seedlings was higher than and north of those of the range of mature trees, elevational and latitudinal shifts run in opposite directions for the majority of the species, reflecting the lack of a direct biological relationship between species’ distributions and those variables. The broad scale, environmental diversity and variety of disturbance regimes and land uses of the study area, the large number and exhaustive sampling of tree species, and the direct causal relationship between the temperature response and a warming climate, provide strong evidence to attribute the observed shifts to climate change

Short and long-term effects of prescribed underburning on nitrogen availability in ponderosa pine stands in central Oregon

The effects of prescribed underburning on soil total C pools, total and inorganic N pools, and in situ net N mineralization were examined during a 1-year study in ponderosa pine (Pinus ponderosa Dougl. ex P. & C. Laws.) sites that had been experimentally burned 4 months, 5 years, or 12 years earlier. At the sites burned 4 months previously, total C concentration and inorganic N concentration increased significantly (p < 0.1) after prescribed burning, compared with unburned controls. However, inorganic N concentration declined during the 1-year duration of this study to reach the levels of the control plots at the end of the second growing season. At the site burned 5 years previously, total C and N concentrations, inorganic N concentration, and net N mineralization decreased significantly after prescribed burning. At the sites burned 12 years previously, N and C pools were not affected, but net N mineralization decreased significantly after burning. The decrease in net N mineralization is likely caused by a decrease in substrate quantity 5 years after burning, and by changes in substrate quality 12 years after burning. A long-term decrease in net N mineralization in the N-poor ponderosa pine stands of central Oregon may result in a decrease in long-term site productivity and may explain the observed pattern of long-term decrease in stand growth after prescribed burning.Keywords: mineralization, inorganic nitrogen, ponderosa pine (Pinus ponderosa), underburning, soil nitrogen, prescribed fire, soil carbon pool

Relating Forest Attributes with Area- and Tree-Based Light Detection and Ranging Metrics for Western Oregon

Three sets of linear models were developed to predict several forest attributes, using stand-level and single-tree remote sensing (STRS) light detection and ranging (LiDAR) metrics as predictor variables. The first used only area-level metrics (ALM) associated with first-return height distribution, percentage of cover, and canopy transparency. The second alternative included metrics of first-return LiDAR intensity. The third alternative used area-level variables derived from STRS LiDAR metrics. The ALM model for Lorey’s height did not change with inclusion of intensity and yielded the best results in terms of both model fit (adjusted R² = 0.93) and cross-validated relative root mean squared error (RRMSE = 8.1%). The ALM model for density (stems per hectare) had the poorest precision initially (RRMSE = 39.3%), but it improved dramatically (RRMSE = 27.2%) when intensity metrics were included. The resulting RRMSE values of the ALM models excluding intensity for basal area, quadratic mean diameter, cubic stem volume, and average crown width were 20.7, 19.9, 30.7, and 17.1%, respectively. The STRS model for Lorey’s height showed a 3% improvement in RRMSE over the ALM models. The STRS basal area and density models significantly underperformed compared with the ALM models, with RRMSE values of 31.6 and 47.2%, respectively. The performance of STRS models for crown width, volume, and quadratic mean diameter was comparable to that of the ALM models.Keywords: single-tree remote sensing, area-level metrics, LiDAR intensity, georeferenceKeywords: single-tree remote sensing, area-level metrics, LiDAR intensity, georeferenc

A comparison of small-area estimation techniques to estimate selected stand attributes using LiDAR-derived auxiliary variables

One of the challenges often faced in forestry is the estimation of forest attributes for smaller areas of interest within a larger population. Small-area estimation (SAE) is a set of techniques well suited to estimation of forest attributes for small areas in which the existing sample size is small and auxiliary information is available. Selected SAE methods were compared for estimating a variety of forest attributes for small areas using ground data and light detection and ranging (LiDAR) derived auxiliary information. The small areas of interest consisted of delineated stands within a larger forested population. Four different estimation methods were compared for predicting forest density (number of trees/ha), quadratic mean diameter (cm), basal area (m2/ha), top height (m), and cubic stem volume (m3/ha). The precision and bias of the estimation methods (synthetic prediction (SP), multiple linear regression based composite prediction (CP), empirical best linear unbiased prediction (EBLUP) via Fay–Herriot models, and most similar neighbor (MSN) imputation) are documented. For the indirect estimators, MSN was superior to SP in terms of both precision and bias for all attributes. For the composite estimators, EBLUP was generally superior to direct estimation (DE) and CP, with the exception of forest density

Amount and distribution of coarse woody debris in pine ecosystems of north-western Spain, Russia and the United States

The quantity and characteristics of coarse woody debris (CWD) were examined in four distinct pine ecosystems of north-western (NW) Spain, NW Russia and the NW USA. The average CWD volume and biomass ranged from 3.76 m³ ha⁻¹, 1.55 Mg ha⁻¹ in pine plantations in NW Spain to 24.86 m3 ha⁻¹, 6.69 Mg ha⁻¹ in Scots pine forest in NW Russia to 55.35 m³ ha⁻¹, 20.38 Mg ha⁻¹ and 77.04 m³ ha⁻¹, 28.84 Mg ha⁻¹ in ponderosa and lodgepole pine forests in the NW USA. Despite differences in species, ecological conditions and management histories, in all four ecosystems the mean snag volume was less than that of logs, most of the CWD mass was in an intermediate degree of decay, and mature stands had the greatest amount of CWD mass, followed by middle-age and then young stands. The CWD ratio (ratio of dead to live wood volume) ranged from 2.8% to 126.6%, depending on pine ecosystem and stand age, and was influenced by the type of natural and human disturbance. The difference in CWD amount and distribution among the regions studied reflected differences in disturbance history and management practices. Only in NW USA was the sample size large enough to examine the effect of disturbance type on CWD amount and distribution. There, fire and insect damage were found to considerably influence the amount of CWD in both lodgepole and ponderosa pine forests. Comparison of how different factors affect the amount and distribution of CWD in different ecosystems could be useful in developing ecologically sustainable forest management guidelines.Keywords: Ponderosa Pine, Dead Wood, Lodgepole Pine, Disturbance, Scots PineKeywords: Ponderosa Pine, Dead Wood, Lodgepole Pine, Disturbance, Scots Pin

Using an epiphytic moss to identify previously unknown sources of atmospheric cadmium pollution

Urban networks of air-quality monitors are often too widely spaced to identify sources of air pollutants, especially if they do not disperse far from emission sources. The objectives of this study were to test the use of moss bioindicators to develop a fine-scale map of atmospherically-derived cadmium and to identify the sources of cadmium in a complex urban setting.We collected 346 samples of the moss Orthotrichum lyellii from deciduous trees in December, 2013 using a modified randomized grid-based sampling strategy across Portland, Oregon.We estimated a spatial linear model of moss cadmium levels and predicted cadmium on a 50 m grid across the city. Cadmium levels in moss were positively correlated with proximity to two stained-glass manufacturers, proximity to the Oregon– Washington border, and percent industrial land in a 500 m buffer, and negatively correlated with percent residential land in a 500 m buffer. The maps showed very high concentrations of cadmium around the two stained-glass manufacturers, neither of which were known to environmental regulators as cadmium emitters. In addition, in response to our findings, the Oregon Department of Environmental Quality placed an instrumental monitor 120 m from the larger stained-glass manufacturer in October, 2015. The monthly average atmospheric cadmium concentration was 29.4 ng/m3,which is 49 times higher than Oregon\u27s benchmark of 0.6 ng/m3, and high enough to pose a health risk from even short-term exposure. Both stained-glass manufacturers voluntarily stopped using cadmium after the monitoring results were made public, and the monthly average cadmium levels precipitously dropped to 1.1 ng/m3 for stained-glass manufacturer #1 and 0.67 ng/m3 for stained-glass manufacturer #2

Using an epiphytic moss to identify previously unknown sources of atmospheric cadmium pollution

Urban networks of air-quality monitors are often too widely spaced to identify sources of air pollutants, especially if they do not disperse far from emission sources. The objectives of this study were to test the use of moss bioindicators to develop a fine-scale map of atmospherically-derived cadmium and to identify the sources of cadmium in a complex urban setting.We collected 346 samples of the moss Orthotrichum lyellii from deciduous trees in December, 2013 using a modified randomized grid-based sampling strategy across Portland, Oregon.We estimated a spatial linear model of moss cadmium levels and predicted cadmium on a 50 m grid across the city. Cadmium levels in moss were positively correlated with proximity to two stained-glass manufacturers, proximity to the Oregon– Washington border, and percent industrial land in a 500 m buffer, and negatively correlated with percent residential land in a 500 m buffer. The maps showed very high concentrations of cadmium around the two stained-glass manufacturers, neither of which were known to environmental regulators as cadmium emitters. In addition, in response to our findings, the Oregon Department of Environmental Quality placed an instrumental monitor 120 m from the larger stained-glass manufacturer in October, 2015. The monthly average atmospheric cadmium concentration was 29.4 ng/m3,which is 49 times higher than Oregon\u27s benchmark of 0.6 ng/m3, and high enough to pose a health risk from even short-term exposure. Both stained-glass manufacturers voluntarily stopped using cadmium after the monitoring results were made public, and the monthly average cadmium levels precipitously dropped to 1.1 ng/m3 for stained-glass manufacturer #1 and 0.67 ng/m3 for stained-glass manufacturer #2

Long-term effects of prescribed fire on nitrogen availability in ponderosa pine stands in central Oregon

The effects of prescribed burning on the rates of recent litter decomposition, nitrogen and phosphorus release from litter, soil total and inorganic nitrogen pools, and net nitrogen mineralization were determined in ponderosa pine sites that had been burned 0.3, 5 or 12 years earlier. Prescribed burning decreased litter decomposition rates significantly (p >0.1), in the sites burned 0.3 and 12 years previously, although the differences in litter decomposition rates between burned and control plots were small. Nitrogen and P release from recent litter was significantly higher in the plots burned 5 years previously, but there were no significant differences in the plots burned 0.3 or 12 years earlier. Soil inorganic N concentration significantly increased shortly after prescribed burning, but declined thereafter to reach the levels of the control plots at the end of the next growing season. Both inorganic and total soil N pools in soil were significantly lower in the plots burned 5 years previously, and there were no differences in any of the N pools measured for the sites burned 12 years earlier. Prescribed burning did not significantly affect annual net nitrogen mineralization 0.3 years after burning, but net N mineralization decreased significantly in the 5 and 12 year burned plots. The decrease in net nitrogen mineralization is probably caused by a decrease in substrate quantity 5 years after burning, and by changes in substrate quality 12 years after burning. A long-term decrease in net N mineralization in the N-poor ponderosa pine stands of Central Oregon may result in a decrease in long-term site productivity and may explain the observed pattern of long-term decrease in stand growth following prescribed burning