John J. Beauchamp

Bayesian Variable Selection in Linear Regression

Abstract This article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable. It is based on a Bayesian approach, intended to be as objective as possible. A probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model. The method is not fully Bayesian, however, because the ultimate choice of prior distribution from this family is affected by the data. It is assumed that the predictors represent distinct observables; the corresponding regression coefficients are assigned independent prior distributions. For each regression coefficient subject to deletion from the model, the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere, that is, a “spike and slab” distribution. The random error component is assigned a normal distribution with mean 0 and standard deviation ...

Corrections for Bias in Regression Estimates After Logarithmic Transformation

Experience with biological data, such as dimensions of organisms, often confirms that logarithmic transformations should precede the testing of hypotheses about regression relations. However, estimates also may be needed in terms of untransformed variables. Just taking antilogarithms of values from a log—log regression line or function leads to biased estimates. This note compares corrections for this bias, and includes an example relating mass of tree parts (bole, branches, and leaves) to tree diameter of tulip poplar (Liriodendron tulipifera L.) in Oak Ridge, Tennessee, forests. An Appendix summarizes derivation of exact and approximate unbiased estimators of expected values from log—antilog regression, and of variance around the unbiased regression line. See full-text article at JSTOR

Regression Analysis of Poisson-Distributed Data

Abstract The principle of maximum likelihood is used to obtain estimates of the parameters in a regression model when the experimental observations are assumed to follow the Poisson distribution. The maximum likelihood estimates are shown to be equivalent to those obtained by minimization of a quadratic form which reduces to a modified chi square under the Poisson assumption. Computationally, both of these estimation procedures are equivalent to a properly weighted least squares analysis. Approximate tests of the assumed Poisson variation and “goodness of fit” of the data to the model are proposed. Applications of the estimation procedure to linear and nonlinear regression models are discussed, and numerical examples are presented.

Farming in Rondônia

Abstract We study economic and environmental aspects of farming practices of a sample of 91 family farms around the city of Ouro Preto, in Brazils state of Rondonia, in western Amazonia, from four overlapping perspectives. First, we estimate production functions for six activities on multiproduct farms, finding evidence of increasing returns to scale in cattle activity and possible evidence of nonindependence of profit and utility maximization in severalsubsistence crops. Second, we examine determinants of overall current farm revenue and wealth, finding possible evidence of overuse of land and underinvestment in cattle, decapitalization of farms over time, overpopulation, and trade-off between children and capital accumulation. Third, we study interactions between burning strategies, diversification of farm activities, locational choice, length of tenure on a farm, and soil quality. Longer tenure on a farm and large area in perenial crops appear to reduce the frequency of burning, while greater area in annual crops increases the frequency. Larger pasture area tends to reduce the frequency of burning below an annual periodicity. Less frequent burning appears to be accompanied by greater diversification of farm income sources. Fourth, we study the determinants of deforestation on lots, finding a negative effect of clearance costs and productivity of land and in cultivation on the clearance of new land. However, the evidence for the relationship between cattle activity and deforestation is mixed: a larger number of cattle increases the absolute amount of land deforested on a lot, but a higher proportion of income from cattle increases the ratio of cultivated land to pasture on a farm. There is also evidence of a trade-off between land quality and the quantity of land deforested.

Grain size and depth constraints on microbial variability in coastal plain subsurface sediments

We have examined the effects of sediment grain size and depth on the abundance and activity of aerobic bacteria at two coastal plain sites in Virginia. Samples were collected at centimeter intervals as well as meter intervals because fine‐scale sampling can be essential to assess microbial variability. At the Oyster site, grain size varied from 0.12 to 0.25 mm below 1.5 m depth and did not correlate with either bacterial abundance or activity. Perhaps due to the fairly uniform grain size at this site, variations in bacterial numbers were less than fivefold between replicate samples of 0,1 to 100 g and generally less than 15‐fold among closely spaced intervals (∼5 cm). At the Abbott Pit site, grain size was about threefold greater (0.50 ± 0.17mm) in an interval of 4.35 to 5.0m below land surface than grain size in the surrounding sediments. In the same interval, bacterial abundance increased by 11‐fold and activity increased by 217‐fold relative to the surrounding sediments. Overall, grain size correlated ...

Evaluation of caging designs and a fingernail clam for use in an in situ bioassay

Two cage designs and fingernail clams(Sphaerium fabale) were evaluated for theirsuitability for use in in situ bioassays toassess the ecological condition of a stream andpredict ecological recovery potential. One design(referred to as tray design) was a modified plastictray about one-fourth full of small gravels andcovered with 1 mm fiberglass mesh. The second design(referred to as tube-plates) consisted of shortplexiglass tubes about one-third full of small gravelsand attached horizontally to a plexiglass plate. Oneend of each tube faced into the current; both endswere covered with mesh. Cages containing clams weredeployed at reference and impacted (test) sites forperiods of 70 to 135 d. Growth and survival were theprimary endpoints evaluated, but the tube-platesallowed isolation of individual clams so that natalityalso could be evaluated as an endpoint. Results ofbenthic macroinvertebrate surveys, performed foranother study, were included to help validate bioassayresults. Both cage designs yielded good quantitative,site-specific results for clam survival and growth;results for natality, though, were less conclusive. Clam survival and growth results were in good generalagreement with the results for the benthicmacroinvertebrate community surveys. At a site wherethe macroinvertebrate community was the mostdepauperate, clam mortality was always rapid. At asite where the condition of the macroinvertebratecommunity was only slightly less impacted than themost impacted site, clam growth was almost alwayssignificantly lower than at reference sites. Survivalof clams was significantly reduced in <25 d at thissite in some trials, but in other trials there waslittle mortality. At a minimally impacted site, clamsurvival was similar to that found at reference sites,and differences in clam growth were not detectableuntil after 40 to 50 d of exposure. The tube-platedesign was easier to use, allowed more flexibility inselection of response parameters, and required lesshandling time of test animals, thus, this was thepreferred design. Our results demonstrated thateither in situ bioassay design can be used toaugment monitoring and assessment programs. Their useas a predictor of ecological recovery, however,requires further evaluation.

MAXIMUM LIKELIHOOD ESTIMATION OF SURVIVAL CURVE PARAMETERS.

SUMMARY A maximum likelihood procedure is presented for the estimation of the parameters in a survival curve which is used in the quantitative investigation of cytological damage resulting from ionizing radiation. This estimation procedure is developed under the assumption that the observations are distributed as independent Poisson random variables. In addition, a weighted least squares procedure, which gives estimates equivalent to the maximum likelihood estimates, is presented. Tests of the model and of the assumed distribution of the observations are given. Two illustrative examples are included.

Integrated and individual biochemical responses of rainbow trout (Salmo gairdneri) to varying durations of acidification stress

Abstract 1. Rainbow trout displayed a variety of biochemical responses when exposed to pH 4.5 for periods of 6–48 hr. 2. Some adaptive or recovery responses occur in rainbow trout after 12–24hr of continuous exposure to reduced pH, with most biochemical variables returning to near control levels following 48 hr of nonexposure. 3. The integrated biochemical response of trout to acidification stress was determined by incorporating all 10 measured biochemical variables into a discriminant analysis procedure. 4. Measures of electrolyte homeostasis (sodium), carbohydrate metabolism (glucose), lipid metabolism (triglycoride) and amino acid metabolism (serum glutamate oxaloacetate transaminase) provide the best indicators of individual biochemical responses of trout to reduced pH. 5. Determination and interpretation of fish response to reduced pH can differ, depending on whether individual or multiple biochemical variables are being evaluated.

Spatial and Temporal Variations of Microbial Properties at Different Scales in Shallow Subsurface Sediments

Microbial abundance, activity, and community-level physiological profiles (CLPP) were examined at centimeter and meter scales in the subsurface environment at a site near Oyster, VA. At the centimeter scale, variations in aerobic culturable heterotrophs (ACH) and glucose mineralization rates (GMR) were highest in the water table zone, indicating that water availability has a major effect on variations in microbial abundance and activity. At the meter scale, ACH and microaerophiles decreased significantly with depth, whereas anaerobic GMR often increased with depth; this may indicate low redox potentials at depth caused by microbial consumption of oxygen. Data of CLPP indicated that the microbial community (MC) in the soybean field exhibited greater capability to utilize multiple carbon sources than MC in the corn field. This difference may reflect nutrient availability associated with different crops (soybean vs corn). By using a regression model, significant spatial and temporal variations were observed for ACH, microaerophiles, anaerobic GMR, and CLPP. Results of this study indicated that water and nutrient availability as well as land use could have a dominant effect on spatial and temporal variations in microbial properties in shallow subsurface environments.

Determining regional water quality patterns and their ecological relationships

A multivariate statistical method for analyzing spatial patterns of water quality in Georgia and Kansas was tested using data in the US Environmental Protection Agencys STORET data system. Water quality data for Georgia and Kansas were organized by watersheds. We evaluated three questions: (a) can distinctive regional water quality patterns be detected and predicted using only a few water quality variables, (b) are regional water quality patterns correlated with terrestrial biotic regions, and (c) are regional water quality patterns correlated with fish distributions? Using existing data, this method can distinguish regions with water quality very different from the average conditions (as in Georgia), but it does not discriminate well between regions that do not have diverse water quality conditions (as in Kansas). Data that are spatially and temporally adequate for representing large regions and for multivariate statistical analysis are available for only a few common water quality parameters. Regional climate, lithology, and biotic regimes all have the potential to affect water quality, and terrestrial biotic regions and fish distributions do compare with regional water quality patterns, especially in a state like Georgia, where watershed characteristics are diverse. Thus, identifiable relationships between watershed characteristics and water quality should allow the development of an integrated landaquatic classification system that would be a valuable tool for resource management. Because geographical distributions of species may be limited by Zoogeographic and environmental factors, the recognition of patterns in fish distributions that correlate with regional water quality patterns could influence management strategies and aid regional assessments.