John E. Boyer

Robust fitting of mixture regression models

The existing methods for fitting mixture regression models assume a normal distribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this article, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. A real data application is used to illustrate the success of the proposed robust estimation procedure.

Host-plant-mediated interaction between populations of a true omnivore and its herbivorous prey

Western flower thrips, Frankliniella occidentalis (Pergande) (Thysanoptera: Thripidae), are competitors with twospotted spider mites, Tetranychus urticae Koch (Acari: Tetranychidae), for plant resources and potential predators on spider mites when the opportunity arises. Which interaction predominates may depend on relative population densities and individual species’ responses to the plants on which they co‐occur. We examined interactions between populations of thrips and spider mites on several cultivars of two bedding plants: impatiens (Impatiens wallerana Hook.f) cultivars ‘Impulse Orange’ and ‘Cajun Carmine’, and ivy geranium [Pelargonium peltatum (L.) L’Her ex Aiton] cultivars ‘Sybil Holmes’ and ‘Amethyst 96’. Four combinations of thrips and mite numbers were studied: thrips alone, mites alone, and two densities of thrips and mites together. We compared population numbers after 4 weeks. Overall, mite numbers increased more rapidly than thrips did, but both species increased more rapidly on impatiens than on ivy geraniums. Between impatiens cultivars, thrips and mites increased more slowly on ‘Cajun Carmine’ (i.e., it was more resistant) than on ‘Impulse Orange’. On ivy geraniums, spider mites increased more slowly on ‘Sybil Holmes’ than on ‘Amethyst 96’ but the reverse was the case for thrips. Regardless of plant species or cultivar, thrips had a strong negative effect on spider mites whenever they co‐occurred, suppressing mite population growth by around 50% compared to when mites were alone. However, the effect of spider mites on western flower thrips depended on the quality of the plant species. On impatiens, thrips co‐occurring with spider mites increased slightly more than thrips alone did, while on ivy geranium mites had a small negative effect on thrips. Contrary to expectations, thrips had a larger negative impact on spider mites on plants that were more susceptible to thrips than they did on plants more resistant to thrips. We suggest that host plants mediate the interaction between an omnivore and its herbivorous prey not only by altering individual diet choice but by changing the relative population dynamics of each species.

An Empirical Study of Related Correlation Coefficients

Tests for comparing the strength of association between a variable, X 1, and each of two potential predictor variables, X 2 and X 3, are proposed and examined in a simulation study. The variances of X 2 and X 3 and the correlation between X 2 and X 3 are nuisance parameters. A simple modification of a test proposed by Williams (1959) is found to have reasonable properties for a wide range of parameter values and both normal and nonnormal distributions.

Scarification and Degermination of Sorghum for Grits Production: Effects of Hybrid and Conditioning1

ABSTRACT Three sorghum hybrids were tempered and decorticated with an abrasive-type mill (scarifier) to produce low-ash and low-fat grits. The effects of tempering time and temperature were investigated, and the optimum tempering conditions for obtaining low-ash and low-fat grits were found for each sorghum hybrid. The conditions were 3 min at 30°C for bronze sorghum with heteroyellow endosperm, 40 min at 40°C for white sorghum with white endosperm, and 10 min at 20°C for red sorghum with white endosperm. The grits yields were low using the scarifier, hence, another abrasive-type mill was investigated for improving grits yields. A modified experimental corn decorticator-degerminator was used to dry-mill the three sorghum hybrids tempered to the optimum conditions found with the scarifier. The yields were 45.3% grits with 0.23% ash and 0.18% fat for the bronze/heteroyellow hybrid, 49.1% grits with 0.22% ash and 0.36% fat for white/white hybrid, and 44.2% grits with 0.20% ash and 0.22% fat for red/white hyb...

Nonparametric Estimation of Insect Stage Transition Times

Consider an experiment on an insect where the stages (or stadia) can only be observed by sacrificing the insect or its habitat. Choose a fixed sequence of samples in time. At each sample time, sacrifice a subset of a cohort and record the number of insects in each stage. We review nonparametric point estimators of the time to each stage and evaluate the estimators by computer simulation. The simulation results, under five survival distributions, indicate that overall the estimators provide reasonable estimates of parametric values.

Kansas State University Department of Statistics

The Department of Statistics at Kansas State University came into being under the authorization of the Kansas Board of Regents on July 1, 1959. Holly C. Fryer was named the initial head and there were five faculty members in the department. The department continues to be a vibrant and active entity today, with 14 faculty members, nearly 60 graduate students, and 3 staff positions.

CONDITIONING PLOTS AND DESIGNED EXPERIMENTS

Conditioning plots (coplots) are useful graphics for displaying values of response variables conditional on the values of given (conditioning) variables. We present a principles guide for construction of coplots when the data or statistics come from studies based on designed experiments, and illustrate the usefulness of these coplots in interpreting results. We have found coplots to be useful in our statistical consulting work, and illustrate our approach so that others may find them useful. Coplots in traditional and in trellis displays are provided.