Robert L. Schaefer

Alternative estimators in logistic regression when the data are collinear

Logistic regression using conditional maximum likelihood estimation has recently gained widespread use. Many of the applications of logistic regression have been in situations in which the independent variables are collinear. It is shown that collinearity among the independent variables seriously effects the conditional maximum likelihood estimator in that the variance of this estimator is inflated in much the same way that collinearity inflates the variance of the least squares estimator in multiple regression. Drawing on the similarities between multiple and logistic regression several alternative estimators, which reduce the effect of the collinearity and are easy to obtain in practice, are suggested and compared in a simulation study.

Trail corridors as habitat and conduits for movement of plant species in Rocky Mountain National Park, Colorado, USA

Ground-layer vegetation was sampled along selected trail corridors to determine whether corridors provide habitat for certain species and act as conduits for species movement. Patterns of plant species composition were analyzed in relation to distance from trail edge, level of trail use, and distance from trailheads, junctions, and campgrounds. Species composition was significantly affected by distance from trail edge and level of trail use, as species were favored or inhibited by the corridor, depending upon their growth habits. Species composition was also affected by distance from trailheads. These findings, along with the presence of exotic species, indicate that trail corridors in Rocky Mountain National Park function as habitat and conduits for movement of plant species.

Temporal variation in the woody understory of an old-growth Fagus-Acer forest and implications for overstory recruitment

Abstract. Changes in woody vegetation were examined over eight years, using a 1.05-ha permanent plot in which the location of every shrub and tree > 1m height was mapped. There was little change in the overstory vegetation, as expected for an old-growth forest. Much greater change occurred in the understory, primarily related to a 40 % increase in density. Differences occurred among species in the under-story, as Acer saccharum and Prunus serotina increased and Fraxinus americana and Fagus grandifolia decreased. Canopy gap dynamics are implicated in differences among species in the establishment and growth of individuals in the understory and their recruitment into the overstory. It is concluded that because understory is temporally variable, overstory recruitment from the understory may take different courses at different times in the same forest.

Behavioural suppression of female pine voles after replacement of the breeding male

Examination of the mechanism of reproductive suppression includes determining which cues are involved and the context in which they occur. We studied groups of pine voles, Microtus pinetorum, that were disrupted by the replacement of the breeding male and compared them with intact family groups. If reproductive suppression is mediated by chemical cues, then soiled bedding should be sufficient to prevent production of litters by daughters. If reproductive suppression involves a behavioural component, we should observe aggressive behaviours or those indicative of dominance interactions directed from the mother towards the daughter or the replacement male. If replacement of the breeding male leads to conflict between the breeding female and her daughter, then more aggression or dominance interactions would be expected in disrupted than in intact families. The presence of the mother decreased reproduction by daughters, but chemical cues alone were not sufficient to prevent the daughter from mating with the replacement male. Rather, this decrease in reproduction seemed to be mediated by behavioural interactions. We propose that the mothers tugging on the daughter may lead to subordination of the daughter. The mothers presence may also alter the behaviour patterns of the male and daughter, which could delay reproductive activation of the daughter, prevent the formation of pair bonds or inhibit sexual behaviour. These behavioural interactions appear to depend on the presence of an unfamiliar male, because tugging, for example, was less frequent in intact family groups. Copyright 1998 The Association for the Study of Animal Behaviour Copyright 1998 The Association for the Study of Animal Behaviour.

A Pooled Response Strategy for Combining Multiple Lines of Evidence to Quantitatively Estimate Impact

The impacts of sediment contaminants can be evaluated by different lines of evidence, including toxicity tests and ecological community studies. Responses from 10 different toxicity assays/tests were combined to arrive at a “site score.” We employed a relatively simple summary measure, pooled P-values where we quantify a potential decrement in response in a contaminated site relative to nominally clean reference sites. The response-specific P-values were defined relative to a “null” distribution of responses in reference sites, and were then pooled using standard meta-analytic methods. Ecological community data were also evaluated using an analogous strategy. A distribution of distances of the reference sites from thecentroid of the reference sites was obtained. The distance from each of the test sites from the centroid of the reference sites was then calculated, and the proportion of reference distances that exceed the test site difference was used to define an empirical P-value for that test site. A plot of the toxicity P-value versus the community P-value was used to identify sites based on both alteration in community structure and toxicity, that is, by weight-of-evidence. This approach provides a useful strategy for examining multiple lines of evidence that should be accessible to the broader scientific community. The use of a large collection of reference sites to empirically define P-values is appealing in that parametric distribution assumptions are avoided, although this does come at the cost of assuming the reference sites provide an appropriate comparison group for test sites.

THE ROLE OF CHELIPED AUTOTOMY IN THE TERRITORIAL BEHAVIOR OF THE FRESHWATER PRAWN MACROBRACHIUM LAR

Abstract The role of cheliped autotomy in the territorial behavior of the freshwater prawn Macrobrachium lar was analyzed to determine whether or not prawns modified their defended territory size based on cheliped autotomy. Territory size measurements were recorded for captive prawns interacting in artificial tank habitats and were logged according to the locations where agonistic encounters occurred and aggressive pressures were equal. All prawns used in this study were mid-intermolt males in the size class 9.0 ± 1.5 cm, with staged encounters occurring under three treatment conditions in which fully intact prawns were matched against animals possessing no chelipeds, one cheliped, or two chelipeds (fully intact). Separate experiments for each condition were completed with four prawns per tank per 14-day trial and were run a total of three times each. The defended territory size mean for the Control prawns (matched only against other intact animals) did not differ significantly from one quarter of the total tank area. The mean territory sizes for prawns within or between each treatment condition was significantly different. Prawns with one or two chelipeds autotomized each defended significantly smaller territories than other male prawns of equal size, but with both chelipeds intact. Our results show that the presence of chelipeds allowed the defense of larger territories compared with the territories defended by prawns with one or both chelipeds autotomized.

The effect of withdrawal censoring on two-sample tests

A simulation study was performed to examine the effects of withdrawal censoring and fixed right censoring on the level of significance and power of two-sample tests. Statistics based on Gehan, logrank, and Peto-Prentice scores are used. It is demonstrated that the performance of these tests can be adversely affected by a high percenage of withdrawals and/or unequal sample sizes

An Introduction to Computational Statistics: Regression Analysis

1. A Quick Look at a Typical Regression Program. 2. Simple Linear Regression. 3. Applying Simple Linear Regression. 4. Multiple Linear Regression. 5. Computer Assisted Model Building. 6. The General Linear Model. 7. Analysis of Variance and Covariance. 8. Nonlinear Regression. 9. Maximum Likelihood Analysis and Robust Estimation.

Using default tests in repeated measures: how bad can it get?

In the typical repeated measures analysis, the subject effect is assumed to be random and the error terms random and uncorrelated. (One could assume that the subject effect is fixed while the errors are correlated.) In many statistical packages, unless the user specifically requests that otherMean Squares be used for tests, the MSE is used by default. A simulation study investigates the magnitude of the errors that result if the inappropriate tests are performed. It is found that both the Type I and Type II errors can be greatly affected

Effects of withdrawals on tests involving censored data in toxicology experiments

Censoring can occur with some response variables that are frequently of interest in toxicology studies (for example, time to maturation or lifetime). This censoring can be in the form of fixed right censoring or a withdrawal, and its presence can have a major impact on the analysis of the data. In this paper we consider the effect of censoring on statistical procedures that are commonly used in toxicology experiments. The tests examined in this study are the Gehan and log rank tests which are available on the major statistical packages (SAS, SPSSX, and BMDP). The application of these tests for k ≥ 2 samples and for multiple comparisons is considered. The effect of withdrawals on the performance of these tests is found to be quite different than the effect of fixed right censored observations. Our study results indicate that these tests can lead to incorrect or misleading inferences when there is a high percentage of withdrawals. The tests may have very poor sensitivity to treatment differences, and the actual significance levels may be quite different from what the user specifies.