D. Richard Cutler

Random Forests for Classification in Ecology

Classification procedures are some of the most widely used statistical methods in ecology. Random forests (RF) is a new and powerful statistical classifier that is well established in other disciplines but is relatively unknown in ecology. Advantages of RF compared to other statistical classifiers include (1) very high classification accuracy; (2) a novel method of determining variable importance; (3) ability to model complex interactions among predictor variables; (4) flexibility to perform several types of statistical data analysis, including regression, classification, survival analysis, and unsupervised learning; and (5) an algorithm for imputing missing values. We compared the accuracies of RF and four other commonly used statistical classifiers using data on invasive plant species presence in Lava Beds National Monument, California, USA, rare lichen species presence in the Pacific Northwest, USA, and nest sites for cavity nesting birds in the Uinta Mountains, Utah, USA. We observed high classification accuracy in all applications as measured by cross-validation and, in the case of the lichen data, by independent test data, when comparing RF to other common classification methods. We also observed that the variables that RF identified as most important for classifying invasive plant species coincided with expectations based on the literature.

Dietary protein intake and risk of osteoporotic hip fracture in elderly residents of Utah

The role of protein intake in osteoporosis is unclear. In a case‐control study in Utah (n = 2501), increasing level of protein intake was associated with a decreased risk of hip fracture in men and women 50–69 years of age but not in those 70–89 years of age. Protein intake may be important for optimal bone health.

Assessing Map Accuracy in a Remotely Sensed, Ecoregion-Scale Cover Map

Abstract Landscape- and ecoregion-based conservation efforts increasingly use a spatial component to organize data for analysis and interpretation. A challenge particular to remotely sensed cover maps generated from these efforts is how best to assess the accuracy of the cover maps, especially when they can exceed 1000 s/km 2 in size. Here we develop and describe a methodological approach for assessing the accuracy of large-area cover maps, using as a test case the 21.9 million ha cover map developed for Utah Gap Analysis. As part of our design process, we first reviewed the effect of intracluster correlation and a simple cost function on the relative efficiency of cluster sample designs to simple random designs. Our design ultimately combined clustered and subsampled field data stratified by ecological modeling unit and accessibility (hereafter a mixed design). We next outline estimation formulas for simple map accuracy measures under our mixed design and report results for eight major cover types and the three ecoregions mapped as part of the Utah Gap Analysis. Overall accuracy of the map was 83.2% (SE= 1.4). Within ecoregions, accuracy ranged from 78.9% to 85.0%. Accuracy by cover type varied, ranging from a low of 50.4% for barren to a high of 90.6% for man modified. In addition, we examined gains in efficiency of our mixed design compared with a simple random sample approach. In regard to precision, our mixed design was more precise than a simple random design, given fixed sample costs. We close with a discussion of the logistical constraints facing attempts to assess the accuracy of large-area, remotely sensed cover maps.

MODEL‐BASED STRATIFICATIONS FOR ENHANCING THE DETECTION OF RARE ECOLOGICAL EVENTS

A common concern when designing surveys for rare species is ensuring sufficient detections for analytical purposes, such as estimating frequency on the landscape or modeling habitat relationships. Strict design-based approaches provide the least biased estimates but often result in low detection rates of rare species. Here, we demonstrate how model-based stratification can improve the probability of detecting five rare epiphytic macrolichens (Nephroma laevigatum, N. occultum, N. parile, Lobaria scrobiculataa, and Psuedocyphelaria rainierensis) in the Pacific Northwest. We constructed classification tree models for four more common lichens (L. oregana, L. pulmonaria, P. anomala, and P. anthraspis) that are associated with the rare species, then used the models to generate strata for sampling for the five lichen species considered rare. The classification tree models were developed using topographic and bio-climatic variables hypothesized to have direct relationships to the presence of the modeled lichen species. When the expected detection rates using the model-based stratification approach was tested on an independent data set, it resulted in two- to fivefold gains in detection compared to the observed detection rates for four of the five tested rare species.

ASSESSING RARITY OF SPECIES WITH LOW DETECTABILITY: LICHENS IN PACIFIC NORTHWEST FORESTS

We show how simple statistical analyses of systematically collected inven- tory data can be used to provide reliable information about the distribution and habitat associations of rare species. Using an existing design-based sampling grid on which epi- phytic macrolichens had been inventoried in the Northwest Forest Plan area of the U.S. Pacific Northwest, we (1) estimate frequencies and standard errors for each of 25 lichen species having special management designation (i.e., Survey and Manage), (2) assess the probability that individual species were associated with specific land allocation and forest stand age classifications, and (3) provide estimates of sample sizes necessary to ensure sufficient detections for these analyses. We conclude with a discussion of management and conservation information needs that extant data can satisfy and identify advantages and limitations of random vs. nonrandom sampling strategies. Combining design-assisted and model-assisted approaches can overcome some of the limitations of either single strategy.

Adjusting the Census of 1990 The Smoothing Model

Considering the difficulties, the Census Bureau does a remarkably good job at counting people. This article discusses techniques for adjusting the census. If there is a large undercount, these techniques may be accurate enough for adjustment. With a small undercount, they are unlikely to improve on the census; instead, adjustment could easily degrade the accuracy of the data. The focus will be sampling error, that is, uncertainty in estimates due to the luck of the draw in choosing the sample. Sampling error is a major obstacle to adjusting the 1990 census, even at the state level. To control sampling error, the Census Bureau used a smoothing model. However, the model does not solve the problem, because its effects are strongly dependent on unverified and implausible assumptions. This story has a broader moral. Statistical models are often defended on grounds of robustness, that is, estimates do not depend strongly on assumptions. But the standard errors, which are internally generated measures of precision, may be critical. Then caution is in order. If the model is at all complicated, the standard errors may turn out to be driven by assumptions not data—the antithesis of robustness.

Surgeon Variation in Patient Quality of Life After Radical Prostatectomy

PURPOSE We assessed variation among surgeons in patient quality of life outcomes. MATERIALS AND METHODS A survey of standard questions used to examine current urinary and sexual function was mailed to 1,500 randomly selected patients from the Utah Cancer Registry who met certain criteria, including prostatectomy for cancer cure more than 1 year previously, current age 70 years or less and no metastatic disease or other cancer therapy. Questionnaire information was linked to cancer registry and hospital discharge abstract information. Hierarchical mixed models were used to examine whether surgeons varied with respect to risk adjusted outcomes. RESULTS The cooperation rate was 64%. Of the 678 qualifying responders 22% reported leaking urine more than once per day, 7% used more than 1 pad per day and 40% reported no erection without medication. Surgeon variation was significant for 3 patient outcomes, including erectile strength, urine leakage and length of hospital stay (each p <0.001). Surgeon risk adjusted erectile outcomes significantly correlated with leakage outcomes (r = 0.84, p <0.0001) and length of stay (r = -0.55, p = 0.0004). Annual surgeon volume significantly correlated with less leakage and shorter length of stay (r = 0.34 and -0.36, respectively, each p = 0.05). Compared to open retropubic surgery, robotic surgery was associated with a shorter stay. The perineal approach was associated with shorter stay, less urine leakage and weaker erection. CONCLUSIONS Patient quality of life outcomes after prostatectomy varies substantially among surgeons. Administering patient surveys through cancer registries may provide valuable data for improving prostatectomy outcomes statewide.

Efficient block designs for comparing test treatments to a control when the errors are correlated

Abstract This paper is concerned with the problem of comparing test treatments to a control in incomplete blocks when the errors in each block follow a stationary, first order autoregressive correlation structure. General optimality theorems are presented as well as A-optimality and construction results for two new families of designs: CNBTIB design when the blocks are circular and ANBIB designs when the blocks are rectangular.

Estimation for U-shaped beta distributions : Minimum hellinger distance and related methods

We compare minimum Hellinger distance and minimum Heiiinger disparity estimates for U-shaped beta distributions. Given suitable density estimates, both methods are known to be asymptotically efficient when the data come from the assumed model family, and robust to small perturbations from the model family. Most implementations use kernel density estimates, which may not be appropriate for U-shaped distributions. We compare fixed binwidth histograms, percentile mesh histograms, and averaged shifted histograms. Minimum disparity estimates are less sensitive to the choice of density estimate than are minimum distance estimates, and the percentile mesh histogram gives the best results for both minimum distance and minimum disparity estimates. Minimum distance estimates are biased and a bias-corrected method is proposed. Minimum disparity estimates and bias-corrected minimum distance estimates are comparable to maximum likelihood estimates when the model holds, and give better results than either method of moments or maximum likelihood when the data are discretized or contaminated, Although our re¬sults are for the beta density, the implementations are easily modified for other U-shaped distributions such as the Dirkhlet or normal generated distribution.