Walter W. Stroup

A unified approach to mixed linear models

Abstract The mixed model equations as presented by C. R. Henderson offers the base for a methodology that provides flexibility of fitting models with various fixed and random elements with the possible assumption of correlation among random effects. The advantage of teaching analysis of variance applications from this methodology is presented. Particular emphasis is placed upon the relationship between choice of estimable function and inference space.

Measuring the development of executive control with the shape school.

Although several neurodevelopmental and psychiatric disorders can emerge during the preschool period, there are comparatively few instruments to assess executive control. Evidence for validity of the Shape School (K. A. Espy, 1997) was examined in a sample of 219 typically developing young children. There was good evidence for validity, as Shape School performance variables were interrelated and were associated to other criterion measures considered to measure aspects of executive control. Also suggesting validity, the Shape School variables varied as a function of whether the task demands (a) were executive, (b) required inhibition of a prepotent response or context-controlled selection among relevant stimulus-response sets, and (c) included unitary or concurrent processing. The Shape School may be an effective tool by which to measure executive control in young children who have atypical developmental patterns.

Power analysis based on spatial effects mixed models: A tool for comparing design and analysis strategies in the presence of spatial variability

Spatial variability among experimental units is known to exist in many designed experiments. Agronomic field trials are a particularly well-known example, but there are others. Historically, spatial variability has been dealt with in one of two ways: either though design, by blocking to account for spatial effects, or though analysis, by nearest neighbor adjustment. More recently, mixed models with spatial covariance structures such as those used in geostatistics have been proposed. These mixed model procedures have tempted some to conclude—to the dismay of many consulting statisticians—that design principles may be bypassed, since spatial covariance models can recover any lost information. Although design principles clearly should not be ignored, spatial procedures do raise questions. Are traditional notions of appropriate design affected? If so, how? How do spatial effects mixed models compare to conventional analysis of variance used in conjunction with blocked designs? This article presents mixed model methods to assess power and precision of proposed designs in the presence of spatial variability and to compare competing design and analysis strategies. The main conclusion is that, if anything, spatial models reinforce the need for sound design principles, particularly the use of incomplete block designs.

Isolated wheat microspore culture

The use of doubled haploid plants in a wheat breeding program requires an efficient haploid production system. While the techniques for producing doubled haploids from anther culture are well established, those for isolated microspores are complicated and inefficient. Four methods of isolating microspores from anthers (blending, stirring, macerating, and floating) were compared. Isolated microspores were washed and cultured in liquid medium. The effects of pre-isolation mannitol conditioning, cell density, culture dilution, and sucrose centrifugation on microspore viability were evaluated. Isolation by blending gave the highest initial microspore viability (75%). Mannitol conditioning and purification by sucrose centrifugation had a detrimental effect on initial viability. An initial microspore density of 2 × 105 microspores per ml was necessary for continued microspore viability. One hundred and nine haploid or spontancously doubled haploid plants were regenerated from microspores isolated without mannitol conditioning using the blending method. Based on this research, blender isolation with an initial density of 2 × 105 microspores per ml is recommended for isolated microspore culture.

Nearest Neighbor Adjusted Best Linear Unbiased Prediction

Abstract Statistical inference for linear models has classically focused on either estimation or hypothesis testing of linear combinations of fixed effects or of variance components for random effects. A third form of inference—prediction of linear combinations of fixed and random effects—has important advantages over conventional estimators in many applications. None of these approaches will result in accurate inference if the data contain strong, unaccounted for local gradients, such as spatial trends in field-plot data. Nearest neighbor methods to adjust for such trends have been widely discussed in recent literature. So far, however, these methods have been developed exclusively for classical estimation and hypothesis testing. In this article a method of obtaining nearest neighbor adjusted (NNA) predictors, along the lines of “best linear unbiased prediction,” or BLUP, is developed. A simulation study comparing “NNABLUP” to conventional NNA methods and to non-NNA alternatives suggests considerable pot...

Dryland Maize Development and Yield Resulting From Tillage and Nitrogen Fertilization Practices

Conservation tillage ( > 30% residue cover) has proven to be very effective in reducing runoff and erosion and in increasing soil water storage. In dryland cropping situations, the latter fact should result in a greater yield potential for conservation than for conventional tillage. In practice, however, this theoretical advantage has not consistently realized. The objective of this study was to determine the influence of tillage and N-fertilization management on growth and yield of maize (Zea mays L.) under dryland conditions in the western Corn Belt (U.S.A.). The experiment was conducted from 1977 through 1983 on a Crete-Butler silty clay loam (Pachic Arguistolls-Abruptic Argiaquolls). Whole-plot treatments were moldboard plow, disk, chisel plow, no-till, disk plus manure and no-till plus manure. Sub-plot treatments were N fertilization (NH4NO3) at 0, 70 or 140 kg ha−1N. Grain yield and yield components were not affected by the tillage × N-fertilization interaction. The response both to tillage and to N fertilization was influenced by yearly climatic variation. Generally, grain yield was maximum at 90 kg ha−1 N and, in dry years, yields usually declined at N rates > 90 kg ha−1 N. In only one year (1978) did tillage influence yield; the chisel plow treatment produced less grain than the moldboard plow or disk. The no-till treatment did not differ from the mean of the other 3 tillage practices in any year. The interaction of yearly weather variation with phenology and the development of the crop appeared to be a greater determinant of yield than tillage.

Pattern Recognition of Longitudinal Trial Data with Nonignorable Missingness: An Empirical Case Study

Methods for identifying meaningful growth patterns of longitudinal trial data with both nonignorable intermittent and drop-out missingness are rare. In this study, a combined approach with statistical and data mining techniques is utilized to address the nonignorable missing data issue in growth pattern recognition. First, a parallel mixture model is proposed to model the nonignorable missing information from a real-world patient-oriented study and concurrently to estimate the growth trajectories of participants. Then, based on individual growth parameter estimates and their auxiliary feature attributes, a fuzzy clustering method is incorporated to identify the growth patterns. This case study demonstrates that the combined multi-step approach can achieve both statistical gener ality and computational efficiency for growth pattern recognition in longitudinal studies with nonignorable missing data.

Renovation of seeded warm-season pastures with atrazine

Numerous warm-se8son p8stures b8ve been established in the last 30 years in the centr81 Great Plains. Some of these p8stures 8re old enough to verify that they can be 8bused by overgrizing 8s easily 8s native t8llgms.s prairies. Overgrazed warm-season pastures are invaded 8nd domirurted by cool-tuason grasses such 8s smooth brome (Bromus inermis Leyaa.) and Kentucky bluegrass (Poaprate~ L.), which diminishes the pasture productivity during the hot summer months. Since established warm-season grasses have greater tolennce to the herbicide ntrazine than coolseason grasses, the effectiveness of atrrzine applications in renovating invrded warm-season pastures was evaluated. A single, early spring application of atrazine (3.3 kg/ha) killed or suff~Gently suppressed the cool-season grasses so that surviving warmseason remnants were able to effectively re-establish the warmseason pasture in a single growing season without any loss in total pasture forage production. Lower rates of atrazine were not as effective, particularly if smooth brome ~8s the primary coolseason gr8ss. The single rtrazine application cost was 8pproximutely 25% of the seed cost associated with more conventional renovation. Pastures should not be grazed the treatment year but c8n be hayed rt the end of the growing season. The success of the practice is dependent on the presence of warm-season grass remnants. Spraying test strips in small fenced areas would be advisable before treating entire pastures. The eastern one-third of Nebraska was historically warm-season dominated True Prairie (Weaver 1965). Much of this land was plowed when the area was homesteaded for production of grain crops. Many of these areas have been seeded into warm-season pastures during the last 30 years. Usual seed mixtures consist of big bluestem (Andropogon gerardii Vitman), switchgrass (Panicurn virgatum L.), indiangrass (Sorghastrum nutans Nash.), sideoats grama [Boureloua curripendula (Michx.) Torr.], and little bluestern [Schizachyrium scoparium (Michx.) Nash]. These pastures and native rangeland are used primarily for spring and summer grazing for cow-calf herds. Some of the seeded pastures are old enough to verify that overgrazing is a factor on seeded pastures as well as on native tallgrass prairies. This results in invasion and dominance by smooth brome (Bromus inermis Leyss.) and Kentucky bluegrass (Pea pratensis L.). Recently Samson and Moser (1982) demonstrated the effectiveness of a spring application of atrazine [2chloro+(ethylamino)-6(isopropyl amino)-s-triazine] in shifting the composition of native rangeland dominated by Kentucky bluegrass to warm-season remnant big bluestem and sod-seeded switchgrass in a single growing season. Waller and Schmidt (1983) also shifted species composition in native rangeland from a Kentucky bluegrass and smooth brome dominated mixture to one dominated by remnant warmseason grasses, primarily big bluestem, by a single spring applicaAuthors are county extension agent, Cooperative Extension Service, Stapleton, Neb.; professor, Dep. of Agronomy; supervisory research geneticist, USDA-AR% graduate research assistant, Dep. of Agronomy; and associate professor, Biometrics and Information Systems Center, Univ. of Nebraska, Lincoln, 68583. Gates is currently assistant professor Iberia Research Station, Louisiana State University Agricultural Center, Jeanerette 70544. Research is based on a thesis presented by T.O. Dill to the faculty of the Graduate College of the Univ. of Nebraska in partial fulfillment of the requirements of the M.S. degree. This paper is published as Journal #7680 of the Nebraska Agricultural Experiment Station. The authors express appreciation to Mr. LaMoine Brownlee, (retired) supervisory agronomis!, Roman L. Hruska, U.S. Meat Animal Research Center, Clay Center, Neb., for his assistance in this research. Manuscript accepted 14 May 1985. 72 tion of atrazine. The purpose of this study was to determine if the seeded warmseason pastures could be renovated by using atrazine to suppress cool-season competition. A second objective was to evaluate the use of atrazine in stands dominated by smooth brome rather than Kentucky bluegrass. Materials and Methods Study Area This study was conducted in south central Nebraska 6.5 km west of Clay Center, on the Roman L. Hruska U.S. Meat Animal Research Center (MARC). The area is located within the True Prairie region of North America (Weaver 1965). The topography is gently rolling to nearly level. Soils are formed in deep windblown Peorian loess, with a subsoil of glacial outwash and till. The study site is mapped as Crete silt loam (fine, montmorillonitic, mesic, Pachic Arguistoll) thick solum, with 0 to 1% slope. Average annual precipitation is 69 cm with 80% occurring from April through September. Average growing season is 148 days and the normal grazing period on range is from 1 May to 3 1 October (Hammer et al. 1981). Pasture History There are 4,450 ha of seeded, warm-season grasses at MARC. The study areas were formerly cultivated areas with grasses seeded into milo [Sorghum bicolor (L.) Moench.] stubble in the spring of 1967. Seed mix species were ‘Pawnee’ big bluestem, ‘Nebraska 54’ indiangrass, ‘Trailway’ sideoats grama, ‘Nebraska 27’ sand lovegrass, [Eragrostis trichodes(Nutt.) Wood]; and a legume, ‘Empire’ birdsfoot trefoil (Lotus corniculatus L.). Annual spring and summer grazing was initiated in the spring of 1969 (L. Brownlee 198 1, personal communication). Spring applications of 73 kg/ ha ammonium nitrate (NHdNOs) were made in alternating years. The overgrazing required to maintain herd size in beef cattle genetic studies allowed smooth brome to dominate the pastures. Kentucky bluegrass and annual brome (Bromus spp.) also appeared. The study area had been in smooth brome for many years and buried seed and rhizomes may have contributed to its occurrence. Additionally, roadside vegetation at MARC is a mixture of smooth brome and Kentucky bluegrass, providing a potential seed source. These cool-season grasses could exploit the wet springs when the seeded warm-season grasses were dormant. A grazing exclosure in one pasture was used to statistically define treatment effects over a 2-year period following a single herbicide application, The grazed portion of the pasture was used to determine the magnitude of treatment response. Additional pastures were sprayed in 3 different years to qualitatively evaluate the year effect and provide evidence of repeatability of treatment response. Grazing Exclosure Treatments, an unsprayed control and 1.1 2.2, or 3.3 kg (ai)/ ha atrazine (AAtrex 4L), were applied on 2 April 1981 within the exclosure using a conventional pressurized boom (3 m) sprayer. The herbicide solution was mixed for the low rate using a carrier volume of 200 1 /ha. Multiple passes were used to achieve the 2 higher treatments. Prior to growth initiation and before treatment application, the dormant standing crop was removed by mowing and raking. This is a common practice when dormant vegetation restricts the ease and efficiency of herbicide application. For easier data collection and to reduce the effect of shading from previous JOURNAL OF RANGE MANAGEMENT 39(l), January 1966 year’s growth, standing crop was also removed prior to the 1982 growing season. The experimental design was a randomized complete block with 4 replications. Plots (experimental unit) were 3 X 6 m and separated by 3-m alleys. Species composition data were obtained in May and October 198 1 and 1982. Warm-season species were at the 2 to 5 leaf stage and easily distinguishable in May of both years. Stand density and potential production eliminated the use of more conventional line transects or ten-point frames. Ten l-m rods used as line transects were randomly placed at right angles on either side of a line running lengthwise through the center of each plot. Relative species composition was estimated by counting basal culms of each species that intercepted the line (sampling rod). At the end of the second growing season, species composition was also determined in a similar manner outside the exclosure in the grazed portion of the pasture. Five randomly located transects (100 m) radiated away from the grazing exclosure and ten l-m rods were randomly located perpendicular to each transect. The area immediately adjacent to the fencing was excluded. Yield (above-ground biomass) was estimated by hand clipping individual species within 3 quadrats at ground level on 3 harvest date in 1981 and 1982. Quadrats (0.2 m*) were randomly located in each plot on each harvest date. Quadrats clipped in a previous sampling were not resampled. Samples were ovendried in a forced air oven for 48 hours at 68O C and weighed. Preplanned, orthogonal contrasts were used to compare treatment responses (Steel and Torrie 1980). Analyses were on plot means of above-ground biomass for warm-season grasses, coolseason grasses, and total herbage. Warm-season herbage was the sum of individual yields of the key species: big bluestem and indiangrass. Cool-season herbage was the sum of the individual yields of the prominent species: smooth brome, annual bromes, and Kentucky bluegrass. Total herbage was the sum of yields for warm-season grasses, cool-season grasses, and all other aboveground vegetation. Regression analysis was used to evaluate consistency of response. A multivariate analysis was used to determine significant treatment by time interactions for shifts in relative species composition (Stroup and Stubbendieck 1983). Pasture Demonstration During the 3 years following treatment of the grazing exclosure, I1 entire pastures (approximately 65 ha each) received a single spring application of atrazine. Each pasture selected was characteristic of the grazing exclosure. In 1982,3 pastures were sprayed 10 April with 2.2 kg/ ha atrazine. Five pastures were similarly treated in 1983. Three pastures were sprayed in 1984 with 2.8 kg/ha. Pas

On the shelf life of pharmaceutical products.

This article proposes new terminology that distinguishes between different concepts involved in the discussion of the shelf life of pharmaceutical products. Such comprehensive and common language is currently lacking from various guidelines, which confuses implementation and impedes comparisons of different methodologies. The five new terms that are necessary for a coherent discussion of shelf life are: true shelf life, estimated shelf life, supported shelf life, maximum shelf life, and labeled shelf life. These concepts are already in use, but not named as such. The article discusses various levels of “product” on which different stakeholders tend to focus (e.g., a single-dosage unit, a batch, a production process, etc.). The article also highlights a key missing element in the discussion of shelf life—a Quality Statement, which defines the quality standard for all key stakeholders. Arguments are presented that for regulatory and statistical reasons the true product shelf life should be defined in terms of a suitably small quantile (e.g., fifth) of the distribution of batch shelf lives. The choice of quantile translates to an upper bound on the probability that a randomly selected batch will be nonconforming when tested at the storage time defined by the labeled shelf life. For this strategy, a random-batch model is required. This approach, unlike a fixed-batch model, allows estimation of both within- and between-batch variability, and allows inferences to be made about the entire production process. This work was conducted by the Stability Shelf Life Working Group of the Product Quality Research Institute.

EFFECT OF NITROGEN AND SULFUR APPLICATIONS ON POT CHRYSANTHEMUM PRODUCTION AND POSTHARVEST PERFORMANCE. I. LEAF NITROGEN AND SULFUR CONCENTRATIONS

Chrysanthemums are one of the most important flowering plants produced internationally year round. The objectives of this research were to evaluate the effects of reducing nitrogen (N) applications by adding sulfur (S) and to determine if N* S interactions occur during the production and postharvest longevity of pot chrysanthemums. Pot chrysanthemum ‘White Diamond’ was grown in a peat-based medium following a typical production schedule except for fertilization. Plants received N at 50, 100, 150, or 200 mg L−1 in combination with S at 0, 5, 10, 20, or 80 mg L−1. Variablesevaluated were leaf N and S concentrations, plant height, leaf area, days to bud set, and first flower color and inflorescence anthesis as well as size and longevity under simulated interior conditions. In this article, leaf N and S concentrations are the variables discussed. In general, N* S interactions were significant for leaf S, but not leaf N concentration. Applications of 50 mg N L−1 resulted in poor leaf N and S concentration and plants of questionable quality. Nitrogen applied at 100, 150, or 200 mg L−1 in combination with at least 10 mg S L−1 had acceptable leaf N concentrations and produced plants of commercial quality. Thus, N applications can be reduced by half when S is applied during commercial production.