@article{redpath_gumpertz_ballington_bassil_ashrafi_2021, title={Genotype, Environment, Year, and Harvest Effects on Fruit Quality Traits of Five Blueberry (Vaccinium corymbosum L.) Cultivars}, volume={11}, ISSN={["2073-4395"]}, url={https://doi.org/10.3390/agronomy11091788}, DOI={10.3390/agronomy11091788}, abstractNote={Blueberries (Vaccinium spp.) comprise a broad range of perennial woody species. Introgression of native species into cultivated germplasm has adapted Vaccinium germplasm to a range of climates and growing conditions for cultivated blueberry. Genetic differences signify phenotypic variance that is observed among blueberry accessions. In addition, variability in geographic and climatic growing conditions between environments or within the same environment across different years may further affect fruit and plant phenotypic expression. As a result, a phenotype is a function of genetic background (G), environment (E), and their interaction (G × E). In addition, other temporally regulated factors such as year (Y) and harvest time (H) impact plant and fruit quality phenotypic variation. Our research aimed to assess the genotypic performance of five blueberry cultivars, including ‘Echota’, ‘O’Neal’, ‘Reveille’, ‘Summit’, and ‘Sunrise’. The selected cultivars were phenotyped for various fruit quality-related traits over two sequential harvests in two years and two locations. Our results indicated that genotype was a significant source of variation for most phenotypic characteristics. Further, the effect of Y × H and G × Y × H significantly affected the majority of studied phenotypic traits. Within the studied genotypes, ‘Reveille’ and ‘O’Neal’ phenotypic stability were consistent across locations and years; additionally, ‘Summit’ phenotypic characteristics were stable across years, environments, and harvests. Clonal plant replicates within a genotype, harvest, and environment, in addition to individual fruit measures, were the most significant sources of variability.}, number={9}, journal={AGRONOMY-BASEL}, author={Redpath, Lauren E. and Gumpertz, Marcia and Ballington, James R. and Bassil, Nahla and Ashrafi, Hamid}, year={2021}, month={Sep} }
 @article{trussell_gumpertz_2020, title={Comparison of the Effectiveness of Online Homework With Handwritten Homework in Electrical and Computer Engineering Classes}, volume={63}, ISSN={["1557-9638"]}, DOI={10.1109/TE.2020.2971198}, abstractNote={Contribution: This article compares the predictive performance of the scores on WeBWorK homework (online) with those of standard handwritten homework. The comparison is done across six undergraduate electrical engineering classes where each of the nine instructors have used both homework modalities. Background: Online homework systems have been used for many years, but analysis of their effectiveness is mixed. Previous work has been limited to a small number of classes in a wide variety of disciplines. This article has a larger number of classes and instructors than previous studies. The classes cover many basic topic areas in electrical and computer engineering, so is directly applicable to the audience of these transactions. Research Question: What is the effect of online homework compared to traditional handwritten homework on the performance of the students on the final exams in selected ECE classes? Methodology: Mixed-effects analysis of variance models are used to determine the predictive ability of performance on homework of the two modalities on the performance on the final exams. The data are limited to classes where the instructors have taught the class using both modalities. These models incorporate the effect of modalities for each instructor and the effect of the modalities across all classes. Findings: The result is that there is no significant statistical difference in the two modalities to predict final exam scores. This indicates that the advantages of using the automated online system can be obtained with no detrimental effect on the students’ learning.}, number={3}, journal={IEEE TRANSACTIONS ON EDUCATION}, author={Trussell, H. Joel and Gumpertz, Marcia L.}, year={2020}, month={Aug}, pages={209–215} }
 @article{durodoye_gumpertz_wilson_griffith_ahmad_2020, title={Tenure and Promotion Outcomes at Four Large Land Grant Universities: Examining the Role of Gender, Race, and Academic Discipline}, volume={61}, ISSN={["1573-188X"]}, DOI={10.1007/s11162-019-09573-9}, number={5}, journal={RESEARCH IN HIGHER EDUCATION}, author={Durodoye, Raifu, Jr. and Gumpertz, Marcia and Wilson, Alyson and Griffith, Emily and Ahmad, Seher}, year={2020}, month={Aug}, pages={628–651} }
 @article{gumpertz_durodoye_griffith_wilson_2017, title={Retention and promotion of women and underrepresented minority faculty in science and engineering at four large land grant institutions}, volume={12}, number={11}, journal={PLoS One}, author={Gumpertz, M. and Durodoye, R. and Griffith, E. and Wilson, A.}, year={2017} }
 @article{aspinwall_li_mckeand_isik_gumpertz_2010, title={Prediction of whole-stem alpha-cellulose yield, lignin content, and wood density in juvenile and mature loblolly pine}, volume={34}, number={2}, journal={Southern Journal of Applied Forestry}, author={Aspinwall, M. J. and Li, B. L. and McKeand, S. E. and Isik, F. and Gumpertz, M. L.}, year={2010}, pages={84–90} }
 @article{eckard_isik_bullock_li_gumpertz_2010, title={Selection efficiency for solid wood traits in pinus taeda using time-of-flight acoustic and micro-drill resistance methods}, volume={56}, number={3}, journal={Forest Science}, author={Eckard, J. T. and Isik, F. and Bullock, B. and Li, B. L. and Gumpertz, M.}, year={2010}, pages={233–241} }
 @article{champlin_kilgo_gumpertz_moorman_2009, title={Avian Response to Microclimate in Canopy Gaps in a Bottomland Hardwood Forest}, volume={8}, ISSN={["1938-5412"]}, DOI={10.1656/058.008.0110}, abstractNote={Abstract Microclimate may influence use of early successional habitat by birds. We assessed the relationships between avian habitat use and microclimate (temperature, light intensity, and relative humidity) in experimentally created canopy gaps in a bottomland hardwood forest on the Savannah River Site, SC. Gaps were 2- to 3-year-old group-selection timber harvest openings of three sizes (0.13, 0.26, 0.50 ha). Our study was conducted from spring through fall, encompassing four bird-use periods (spring migration, breeding, post-breeding, and fall migration), in 2002 and 2003. We used mist netting and simultaneously recorded microclimate variables to determine the influence of microclimate on bird habitat use. Microclimate was strongly affected by net location within canopy gaps in both years. Temperature generally was higher on the west side of gaps, light intensity was greater in gap centers, and relative humidity was higher on the east side of gaps. However, we found few relationships between bird captures and the microclimate variables. Bird captures were inversely correlated with temperature during the breeding and post-breeding periods in 2002 and positively correlated with temperature during spring 2003. Captures were high where humidity was high during post-breeding 2002, and captures were low where humidity was high during spring 2003. We conclude that variations in the local microclimate had minor influence on avian habitat use within gaps. Instead, habitat selection in relatively mild regions like the southeastern US is based primarily on vegetation structure, while other factors, including microclimate, are less important.}, number={1}, journal={SOUTHEASTERN NATURALIST}, author={Champlin, Tracey B. and Kilgo, John C. and Gumpertz, Marcia L. and Moorman, Christopher E.}, year={2009}, pages={107–120} }
 @article{gumpertz_2009, title={Introduction to this special issue on statistics for wildfire processes}, volume={16}, ISSN={["1352-8505"]}, DOI={10.1007/s10651-007-0081-5}, abstractNote={This special issue on statistics for wildfire processes brings together foresters, wildfire ecologists, statisticians,mathematicians, and economists. All of these disciplines bring different interests, approaches and expertise to the modeling of wildfire processes. It is not necessarily easy, however, to communicate across disciplines or follow the developments in a variety of fields. Hence, the papers in this issue are primarily expository in nature, with the goal of facilitating and cross-fertilizing cross-disciplinary research on wildfire modeling. The papers in this issue were first presented in two conferences that brought wildfire modelers together. The first seed of the idea for the special issue was planted in a theme session of the 2005 annual meeting of the Eastern North American Region (ENAR) of the Biometric Society in Austin, TX, titled “Statistical Analysis of Wildfire Data.” The project was fertilized and grew in May of that year at a 5-day “Workshop on Forest Fires and Point Processes” at the Fields Institute in Toronto. This issue begins with a paper by B. M. Wotton explaining the Canadian forest fire danger rating system, which is used by Canadian fire management agencies. Fire managers usemodels to help predict forest fire growth and intensity andmakedecisions each day about where to position fire fighting resources. This paper gives statistical modelers a view of these uses of fire models, the current types of models employed by fire managers, and the need for understanding how the relationship between the Canadian Fire Weather Index System outputs and fuel moisture and the probability of fire occurrence vary among regions of the country and forest types. The next two papers describe ideas for stochastic wildfire models that could potentially be used for forecasting the spread of fires that have already started. The first of these, by Boychuk et al., describes a model in which fire spreads from cell to}, number={2}, journal={ENVIRONMENTAL AND ECOLOGICAL STATISTICS}, author={Gumpertz, Marcia}, year={2009}, month={Jun}, pages={105–106} }
 @article{sherrill_mullin_bullock_mckeand_purnell_gumpertz_isik_2008, title={An evaluation of selection for volume growth in loblolly pine}, volume={57}, ISSN={["2509-8934"]}, DOI={10.1515/sg-2008-0004}, abstractNote={Abstract}, number={1}, journal={SILVAE GENETICA}, author={Sherrill, J. R. and Mullin, T. J. and Bullock, B. P. and McKeand, S. E. and Purnell, R. C. and Gumpertz, M. L. and Isik, F.}, year={2008}, pages={22–28} }
 @article{isik_gumpertz_li_goldfarb_sun_2008, title={Analysis of cellulose microfibril angle using a linear mixed model in Pinus taeda clones}, volume={38}, ISSN={["1208-6037"]}, DOI={10.1139/X08-010}, abstractNote={ Variation in microfibril angle (MFA) (degrees) among loblolly pine ( Pinus taeda L.) full-sib families and clones was investigated using 43 clones from nine full-sib crosses tested at two locations. When the experiments were 12 years old, a total of 316 trees were drilled and 12 mm thick wood increment cores were collected. MFA for each growth ring in the wood core was measured using the SilviScan-2 tool. A quadratic mixed model was fitted to evaluate the MFA variation over different rings. Among the error covariance structures tested in the model, autoregressive order 1 was the best model for producing MFA estimates with the smallest errors. Estimated MFA was about 33° in the pith (ring 1) of the trees and decreased to 18° in the outer wood (ring 11). Full-sib crosses and clones within crosses explained about 12.5% of the total phenotypic variation. Repeatability of full-sib family means (H2f = 0.46) was moderate but repeatability of clone means was high (H2c = 0.79). Although it is possible to improve (decrease) MFA with recurrent selection in tree improvement programs to improve lumber quality, cost efficient and rapid methods for measuring MFA are needed. }, number={6}, journal={CANADIAN JOURNAL OF FOREST RESEARCH}, publisher={Canadian Science Publishing}, author={Isik, Fikret and Gumpertz, Marcia and Li, Bailian and Goldfarb, Barry and Sun, Xuan}, year={2008}, month={Jun}, pages={1676–1689} }
 @article{liu_gumpertz_hu_ristaino_2008, title={Effect of prior tillage and soil fertility amendments on dispersal of Phytophthora capsici and infection of pepper}, volume={120}, ISSN={["1573-8469"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-38649084121&partnerID=MN8TOARS}, DOI={10.1007/s10658-007-9216-7}, number={3}, journal={EUROPEAN JOURNAL OF PLANT PATHOLOGY}, author={Liu, Bo and Gumpertz, Marcia L. and Hu, Shuijin and Ristaino, Jean Beagle}, year={2008}, month={Mar}, pages={273–287} }
 @article{pradhan_hoover_clark_gumpertz_wollum_cobb_strock_2008, title={Septic tank additive impacts on microbial populations}, volume={70}, number={6}, journal={Journal of Environmental Health}, author={Pradhan, S. and Hoover, M. T. and Clark, G. H. and Gumpertz, M. and Wollum, A. G. and Cobb, C. and Strock, J.}, year={2008}, pages={22–27} }
 @article{liu_tu_hu_gumpertz_ristaino_2007, title={Effect of organnic, sustainable, and conventional management strategies in grower fields on soil physical, chemical, and biological factors and the incidence of Southern blight}, volume={37}, ISSN={["1873-0272"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34748831003&partnerID=MN8TOARS}, DOI={10.1016/j.apsoil.2007.06.007}, abstractNote={The objectives of our research were to evaluate the impact of organic, sustainable, and conventional management strategies in grower fields on soil physical, chemical, and biological factors including soil microbial species and functional diversity and their effect on the Basidiomycete plant pathogen Sclerotium rolfsii, causal agent of Southern blight. Soils from 10 field locations including conventional, organic and sustainable farms were sampled and assayed for disease suppressiveness in greenhouse assays, and soil quality indicators. Soils from organic and sustainable farms were more suppressive to Southern blight than soils from conventional farms. Soils from organic farms had improved soil chemical factors and higher levels of extractable C and N, higher microbial biomass carbon and nitrogen, and net mineralizable N. In addition, soil microbial respiration was higher in soils from organic than sustainable or conventional farms, indicating that microbial activity was greater in these soils. Populations of fungi and thermophiles were significantly higher in soils from organic and sustainable than conventional fields. The diversity of bacterial functional communities was also greater in soils from organic farms, while species diversity was similar. Soils from organic and sustainable farms had improved soil health as indicated by a number of soil physical, chemical and biological factors and reduced disease.}, number={3}, journal={APPLIED SOIL ECOLOGY}, author={Liu, Bo and Tu, Cong and Hu, Shuijin and Gumpertz, Marcia and Ristaino, Jean Beagle}, year={2007}, month={Nov}, pages={202–214} }
 @article{hong_white_weisz_gumpertz_duffera_cassel_2007, title={Groundwater nitrate spatial and temporal patterns and correlations: Influence of natural controls and nitrogen management}, volume={6}, ISSN={["1539-1663"]}, DOI={10.2136/vzj2006.0065}, abstractNote={To use shallow groundwater NO3–N concentration as an indicator of groundwater quality requires understanding its patterns, correlations, and controls across space and time. Within a study comparing variable‐rate and uniform N management, our objectives were to determine groundwater NO3–N patterns and correlations at various spatial and temporal scales and their association with natural controls and N management. Experiments in a random, complete block design were conducted in a 2‐yr crop rotation in North Carolina that included one variable‐rate and two uniform N management treatments to wheat (Triticum aestivumL.) and corn (Zea maysL.). We measured groundwater NO3–N and depth every 2 wk at 60 well nests, sampling the 0.9‐ to 3.7‐m depth. Field‐mean NO3–N varied with time from 5.5 to 15.3 mg NO3–N L−1These variations were correlated primarily with concurrent changes in water table elevation and depth. Mean NO3–N exhibited two preferred states: high when the water table was shallow and low when the water table was deep. Temporal NO3–N fluctuations greatly exceeded treatment effects. Treatments appeared to affect NO3–N temporal covariance structure. Groundwater NO3–N spatial patterns and correlations were associated mostly with saturated hydraulic conductivity and water table fluctuations and appeared influenced by subsurface lateral flow. When treatment effects became consistently significant later in the study, they overrode natural controls, and NO3–N was spatially uncorrelated or exhibited shorter spatial correlation ranges and patterns associated predominantly with treatments.}, number={1}, journal={VADOSE ZONE JOURNAL}, publisher={Soil Science Society of America}, author={Hong, Nan and White, Jeffrey G. and Weisz, Randy and Gumpertz, Marcia L. and Duffera, Miressa G. and Cassel, D. Keith}, year={2007}, month={Feb}, pages={53–66} }
 @article{liu_gumpertz_hu_ristaino_2007, title={Long-term effects of organic and synthetic soil fertility amendments on soil microbial communities and the development of southern blight}, volume={39}, ISSN={["1879-3428"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34250215285&partnerID=MN8TOARS}, DOI={10.1016/j.soilbio.2007.04.001}, abstractNote={The effects of tillage and soil fertility amendments on the relationship between the suppressiveness of soils to southern blight and soil physical, chemical and biological factors were examined in experimental station plots in North Carolina. Main plots were either tilled frequently or surface-mulched after one initial tillage. Organic soil amendments including composted cotton gin trash, composted poultry manure, an incorporated rye–vetch green manure, or synthetic fertilizer were applied to subplots in a split-plot design experiment. Incidence of southern blight was lower in surfaced-mulched than tilled soils. Incidence of southern blight was also lower in soils amended with cotton gin trash than those amended with poultry manure, rye–vetch green manure or synthetic fertilizer. Soil water content was negatively correlated with the incidence of disease in both years. Disease incidence was negatively correlated with the level of potassium, calcium, cation exchange capacity (CEC), base saturation (BS) and humic matter in 2002, and net mineralizable nitrogen in 2001. Although, populations of thermophilic organisms were significantly higher in soils amended with cotton gin trash than the other three fertility amendments in each year, there was no significant correlation between the populations of thermophiles and incidence of the disease. Bacterial community diversity indices based on community-level physiological profiling (CLPP) and denaturing gradient gel electrophoresis (DGGE) were significantly higher in soils amended with cotton gin trash than those amended with poultry manure, green manure or synthetic fertilizer. There was a significant negative correlation between the incidence of southern blight, and CLPP and DGGE diversity indices. Greater differences in the richness of bacterial functional groups than genotypes were observed. These results demonstrate that organic soil fertility amendments and cotton gin trash in particular, reduced the development of the disease and affected soil physical, chemical and biological parameters.}, number={9}, journal={SOIL BIOLOGY & BIOCHEMISTRY}, author={Liu, Bo and Gumpertz, Marcia L. and Hu, Shuijin and Ristaino, Jean Beagle}, year={2007}, month={Sep}, pages={2302–2316} }
 @article{mitchell_genton_gumpertz_2006, title={A likelihood ratio test for separability of covariances}, volume={97}, ISSN={["0047-259X"]}, DOI={10.1016/j.jmva.2005.07.005}, abstractNote={We propose a formal test of separability of covariance models based on a likelihood ratio statistic. The test is developed in the context of multivariate repeated measures (for example, several variables measured at multiple times on many subjects), but can also apply to a replicated spatio-temporal process and to problems in meteorology, where horizontal and vertical covariances are often assumed to be separable. Separable models are a common way to model spatio-temporal covariances because of the computational benefits resulting from the joint space–time covariance being factored into the product of a covariance function that depends only on space and a covariance function that depends only on time. We show that when the null hypothesis of separability holds, the distribution of the test statistic does not depend on the type of separable model. Thus, it is possible to develop reference distributions of the test statistic under the null hypothesis. These distributions are used to evaluate the power of the test for certain nonseparable models. The test does not require second-order stationarity, isotropy, or specification of a covariance model. We apply the test to a multivariate repeated measures problem.}, number={5}, journal={JOURNAL OF MULTIVARIATE ANALYSIS}, author={Mitchell, MW and Genton, MG and Gumpertz, ML}, year={2006}, month={May}, pages={1025–1043} }
 @article{gumpertz_pickle_miller_bell_2006, title={Geographic patterns of advanced breast cancer in Los Angeles: Associations with biological and sociodemographic factors (United States)}, volume={17}, ISSN={["0957-5243"]}, DOI={10.1007/s10552-005-0513-1}, abstractNote={{"Label"=>"OBJECTIVE", "NlmCategory"=>"OBJECTIVE"} Examination of patterns of advanced breast cancer may provide evidence needed to direct health care resources to those communities or population groups in greatest need. We assessed to what degree biologic, ethnic, and sociodemographic factors could explain such patterns within Los Angeles County. {"Label"=>"METHODS", "NlmCategory"=>"METHODS"} The proportion of cases of advanced disease among all breast cancer cases identified during 1992-1996 were analyzed using generalized linear mixed models with random census tract effects. Models included characteristics of the individual and her tumor, census tract of residence, and aggregated health districts. {"Label"=>"RESULTS", "NlmCategory"=>"RESULTS"} Approximately 6% of cases, ranging from 4% for Asian to 10% for Black women, were diagnosed as advanced, exhibiting striking geographic patterns. Tumor histology and hormone receptor status were most predictive of advanced disease. Sociodemographic variables such as marital status, median income, and distance to nearest mammography unit showed additional association with risk. {"Label"=>"CONCLUSIONS", "NlmCategory"=>"CONCLUSIONS"} These models explain most of the geographical patterns and eliminate differences between White and Hispanic but not Asian or Black women, identify subpopulations at high risk of advanced disease, and suggest cancer control opportunities.}, number={3}, journal={CANCER CAUSES & CONTROL}, author={Gumpertz, ML and Pickle, LW and Miller, BA and Bell, BS}, year={2006}, month={Apr}, pages={325–339} }
 @inproceedings{aspinwall_li_mckeand_isik_gumpertz_2006, title={Predicting whole-stem wood properties in loblolly pine}, volume={40}, booktitle={Information Exchange Group 40 Conference, Incorporating Genetic Advances into Forest Productivity Systems: Value for All Landowners.
Exchange Group 40 Conference, Incorporating Genetic Advances into Forest
Productivity Systems: Value for All Landowners.}, author={Aspinwall, M. and Li, B. and McKeand, S. and Isik, F. and Gumpertz, M.}, year={2006} }
 @article{hong_white_weisz_crozier_gumpertz_cassel_2006, title={Remote Sensing-Informed Variable-Rate Nitrogen Management of Wheat and Corn}, volume={98}, ISSN={["1435-0645"]}, DOI={10.2134/agronj2005.0154}, abstractNote={In‐season, site‐specific, variable‐rate (SS) N management based on remote sensing (RS) may reduce N losses to groundwater while maintaining or increasing yield and N fertilizer‐use efficiency. We compared in‐season, RS‐informed N management applied on a uniform, field‐average (FA) or SS basis with the current uniform best management practice (BMP) based on “Realistic Yield Expectations” (RYE) in a typical 2‐yr southeastern U.S. coastal plain rotation: winter wheat (Triticum aestivum L.)–double‐crop soybean [Glycine max (L.) Merr.]–corn (Zea mays L.). Compared with the RYE‐based BMP, RS‐informed SS management achieved: (i) a maximum of 2.3 mg L−1 less groundwater NO3–N after 2001 wheat due to 39 kg ha−1 less fertilizer N and a 25% greater harvest N ratio (N in grain or forage/total N applied); (ii) 370 kg ha−1 more 2002 corn grain with 32 kg ha−1 greater N applied, similar harvest N ratio, and 37 kg ha−1 greater surplus N; (iii) 670 kg ha−1 more 2003 wheat grain associated with 14 kg ha−1 greater fertilizer N, 27% greater harvest N ratio, and 9 kg ha−1 less surplus N. Excepting one corn FA treatment that received excessive N, RS‐informed management produced equal or greater economic returns to N than RYE, and less surplus N for wheat. Treatments produced enduring effects on groundwater [NO3–N] consistent with agronomic results, but small relative to temporal [NO3–N] fluctuations that were positively correlated with water table elevation. To assess N management in leaching‐prone soils, frequent, periodic groundwater monitoring during and after the cropping season appears essential.}, number={2}, journal={Agronomy Journal}, publisher={American Society of Agronomy}, author={Hong, N. and White, J.G. and Weisz, R. and Crozier, C.R. and Gumpertz, M.L. and Cassel, D.K.}, year={2006}, pages={327–338} }
 @article{genton_butry_gumpertz_prestemon_2006, title={Spatio-temporal analysis of wildfire ignitions in the St Johns River Water Management District, Florida}, volume={15}, ISSN={["1448-5516"]}, DOI={10.1071/WF04034}, abstractNote={

We analyse the spatio-temporal structure of wildfire ignitions in the St Johns River Water Management District in north-eastern Florida. We show, using tools to analyse point patterns (e.g. the L-function), that wildfire events occur in clusters. Clustering of these events correlates with irregular distribution of fire ignitions, including lightning and human sources, and fuels on the landscape. In addition, we define a relative clustering index that summarizes the amount of clustering over various spatial scales. We carry our analysis in three steps: purely temporal, purely spatial, and spatio-temporal. Our results show that arson and lightning are the leading causes of wildfires in this region and that ignitions by railroad, lightning, and arson are spatially more clustered than ignitions by other accidental causes.
}, number={1}, journal={INTERNATIONAL JOURNAL OF WILDLAND FIRE}, author={Genton, MG and Butry, DT and Gumpertz, ML and Prestemon, JP}, year={2006}, pages={87–97} }
 @article{hong_white_gumpertz_weisz_2005, title={Spatial analysis of precision agriculture treatments in randomized complete blocks: Guidelines for covariance model selection}, volume={97}, ISSN={["1435-0645"]}, DOI={10.2134/agronj2004.0130}, abstractNote={Failure to account for spatially correlated errors when present in the classical randomized complete block (RCB) analysis may cause inefficient estimation of treatment significance. Covariance model selection is a necessary component for spatial adjustment to estimate treatment significance. We discuss methods for selecting a covariance model in RCB analyses in the presence of spatial correlation and demonstrate one procedure in detail. The procedure uses three models: the randomized complete block with independent and identically distributed errors (RCBiid), RCB with correlated errors, and models with correlated errors but no block effects. The semivariogram of the residuals from fitting a model with just fixed effects, the likelihood ratio test, and Akaike Information Criterion are used for model selection. To illustrate the procedure, we analyzed winter wheat (Triticum aestivum L.) forage and corn (Zea mays L.) grain yield in the presence of spatial heterogeneity within blocks from a site‐specific N management study. We compared the selected covariance models to the RCBiid models and to other spatial models with respect to the estimation of treatment significance. The procedure can be extended to any experiment with fixed effects, or with both fixed and random effects, and which may potentially have spatially correlated errors. The procedure is systematic and readily implemented; however, it remains difficult to evaluate whether an adequate covariance model has been selected.}, number={4}, journal={AGRONOMY JOURNAL}, publisher={American Society of Agronomy}, author={Hong, N and White, JG and Gumpertz, ML and Weisz, R}, year={2005}, pages={1082–1096} }
 @article{qiao_gumpertz_van kempen_2005, title={Stability of a pancreatic enzyme cocktail during in vitro protein digestibility assays}, volume={29}, ISSN={["0145-8884"]}, DOI={10.1111/j.1745-4514.2005.00003.x}, abstractNote={To maximize the efficiency of utilization of a pancreatic enzyme cocktail and estimate the contamination for in vitro protein digestibility assays, the specific activity losses of trypsin and chymotrypsin and the digestion of the enzyme proteins were studied. In the absence of protein substrate, increase of enzyme concentration augmented the half-lives of trypsin and chymotrypsin and decreased the digestion of enzymatic proteins. In contrast, in the presence of substrate, increase of enzyme concentration decreased trypsin's half-life. Increase of pH augmented the digestion of enzymatic proteins. The results indicated the optimum time for utilization of the enzymes depended on pH, enzyme concentration and presence of substrate. At the time when digestion of the proteins ceased, the average size of the hydroly sates was calculated between 3.1 and 5.4 amino acid residues, suggesting most proteins in the enzyme cocktail would be detected as digestible proteins.}, number={2}, journal={JOURNAL OF FOOD BIOCHEMISTRY}, author={Qiao, YR and Gumpertz, M and Van Kempen, T}, year={2005}, month={Apr}, pages={205–220} }
 @article{mitchell_genton_gumpertz_2005, title={Testing for separability of space-time covariances}, volume={16}, ISSN={["1099-095X"]}, DOI={10.1002/env.737}, abstractNote={Abstract}, number={8}, journal={ENVIRONMETRICS}, author={Mitchell, MW and Genton, MG and Gumpertz, ML}, year={2005}, month={Dec}, pages={819–831} }
 @inproceedings{sherrill_mullin_bullock_mckeand_purnell_gumpertz_2005, title={Total inside-bark volume estimation for loblolly pine (Pinus taeda L.) in genetic trials}, booktitle={Proceedings of the 28th Southern Forest Tree Improvement Conference}, author={Sherrill, J. R. and Mullin, T. J. and Bullock, B. P. and McKeand, S. E. and Purnell, R. C. and Gumpertz, M. L.}, year={2005}, pages={123–125} }
 @article{eun_fellner_gumpertz_2004, title={Methane production by mixed ruminal cultures incubated in dual-flow fermentors}, volume={87}, ISSN={["1525-3198"]}, DOI={10.3168/jds.S0022-0302(04)73148-3}, abstractNote={This study evaluated the effects of dilution rate and forage-to-concentrate ratio on gas production by rumen microbes. Continuous cultures were used to monitor methane production at three liquid dilution rates (3.2, 6.3, or 12.5%/h) and three forage-to-concentrate ratios (70:30, 50:50, or 30:70). Filtered ruminal contents were allowed 6 d of adaptation to diets followed by 7 d of data collection. Forage consisted of pelleted alfalfa and the concentrate mix included ground corn, soybean meal, and a mineral and vitamin premix. The experiment was replicated in a split-plot design. Total volatile fatty acid production averaged 58.0 mmol/d and was not affected by treatment. Molar proportion of acetate increased with increasing forage-to-concentrate ratio. Molar proportion of propionate tended to decrease at dilution rate of 12.5%/h and increased with the medium and low forage-to-concentrate ratio. Culture pH tended to be greater at a dilution rate of 12.5%/h. Methane production that was calculated from stoichiometric equations was not affected by treatments. However, methane production based on methane concentration in fermentor headspace resulted in an interaction effect of treatments. Stoichiometric equations underestimated methane output at higher dilution rates and with high forage diets. Total diet fermentability was lowest at dilution rate of 3.2%/h. Increasing dilution rates increased microbial yield; increasing the proportion of concentrate improved microbial efficiency. Dilution rate and forage-to-concentrate ratio altered the partition of substrate by microbes. Methane production based on actual concentrations differed from values estimated using stoichiometry of end-product appearance.}, number={1}, journal={JOURNAL OF DAIRY SCIENCE}, author={Eun, JS and Fellner, V and Gumpertz, ML}, year={2004}, month={Jan}, pages={112–121} }
 @book{giesbrecht_gumpertz_2004, title={Planning, construction, and statistical analysis of comparative experiments}, ISBN={0471213950}, DOI={10.1002/0471476471}, publisher={Hoboken, NJ: Wiley}, author={Giesbrecht, F. G. and Gumpertz, M. L..}, year={2004} }
 @article{pollen_daubert_prabhasankar_drake_gumpertz_2004, title={Quantifying fluid food texture}, volume={35}, ISSN={["1745-4603"]}, DOI={10.1111/j.1745-4603.2004.35515.x}, abstractNote={ABSTRACT}, number={6}, journal={JOURNAL OF TEXTURE STUDIES}, author={Pollen, NR and Daubert, CR and Prabhasankar, R and Drake, MA and Gumpertz, ML}, year={2004}, pages={643–657} }
 @article{eun_fellner_burns_gumpertz_2003, title={Eastern gamagrass evaluated as hay or silage for lactating dairy cows}, volume={19}, ISBN={1080-7446}, DOI={10.15232/s1080-7446(15)31442-x}, abstractNote={Twenty lactating Holstein cows were used to determine the nutritional value of eastern gamagrass. Dietary treatments consisted of 1) gamagrass hay and no corn (HNC), 2) gamagrass silage (S) and no corn (SNC), 3) S and low corn (SLC), 4) S and medium corn (SMC), and 5) S and high corn (SHC). Gamagrass fed as hay or silage did not change (P>0.10) milk yield, but corn inclusion tended to increase (P<0.08) milk yield. Yields of milk protein (0.69 vs 0.80 kg/d), lactose (1.23 vs 1.44 kg/d), and solids-not-fat (2.12 vs 2.48 kg/d) tended to be greater for SNC than for HNC (P<0.08). Corn inclusion increased milk yields compared with SNC. Gamagrass fed as silage resulted in a greater feed conversion efficiency than did gamagrass fed as hay (2.16 vs 1.88; P<0.01). Adding corn to S reduced feed efficiency. Conversion of feed N to milk N was greater (P<0.01) for gamagrass fed as silage than for hay. Milk urea N (MUN) concentration was greater (P<0.01) for cows fed HNC than for cows on all other treatments. Feeding S significantly lessened MUN concentration. Including corn at the medium and high levels further reduced MUN concentration (P<0.05). Increased energy from corn at the high level increased milk yield and tended to increase conversion of feed N into milk protein. Gamagrass fed as silage without or with corn improved the N status of the cows, as indicated by lesser MUN concentrations.}, number={5}, journal={Professional Animal Scientists}, author={Eun, J. S. and Fellner, Vivek and Burns, J. C. and Gumpertz, M. L.}, year={2003}, pages={362} }
 @article{kim_lieffering_kobayashi_okada_mitchell_gumpertz_2003, title={Effects of free-air CO2 enrichment and nitrogen supply on the yield of temperate paddy rice crops}, volume={83}, ISSN={["1872-6852"]}, DOI={10.1016/S0378-4290(03)00076-5}, abstractNote={Increasing atmospheric CO2 concentrations [CO2] are generally expected to enhance photosynthesis and growth of agricultural C3 cereal crops and as a result substantially increase yields. However, little is known about the combined effect of elevated [CO2] and nitrogen (N) supply on grain yield. To better understand the interactive effects of these factors on the yield of rice (Oryza sativa L.), we conducted a free-air CO2 enrichment (FACE) experiment at Shizukuishi, Iwate, Japan, in 1998–2000, using the japonica cultivar Akitakomachi. The target [CO2] of the elevated [CO2] plots was 200 ppmV above that in the ambient air. Three levels of N were supplied: low (LN, 4 g N m−2), medium (MN, 8 (1998) and 9 g N m−2 (1999, 2000)) and high N (HN, 12 (1998) and 15 g N m−2 (1999, 2000)). The MN level was similar to that recommended to local farmers. Across the 3 years, there was a positive [CO2]×N interaction for grain yield, with yields increasing only 7% with LN but about 15% with MN and HN. A similar interaction was found for fertile spikelet number per square meter. Across N levels and years, the [CO2]-induced increases in yield were closely related but less than the increases in total dry matter production: as a result harvest index (HI) decreased slightly with elevated [CO2]. This decrease in HI was due in part to a reduction in the number of productive (panicle bearing) tillers relative to total tiller number with elevated [CO2]. Yield increases were related most strongly to greater spikelet number per unit ground area, which in turn were due to increases in both panicle number per square meter and spikelet number per panicle. Small increases in individual grain mass with elevated [CO2] had only a minor effect on the overall yield increases. The spikelet number response to elevated [CO2] was limited with LN, but we found no evidence that N supply at levels greater than that recommended (i.e. above the MN level of N supply) resulted in further increases in spikelet number with elevated [CO2]. This suggests that for the cultivars and conditions of this experiment, the [CO2]-induced increases in yield will approach a ceiling at the recommended rates of N supply.}, number={3}, journal={FIELD CROPS RESEARCH}, author={Kim, HY and Lieffering, M and Kobayashi, K and Okada, M and Mitchell, MW and Gumpertz, M}, year={2003}, month={Sep}, pages={261–270} }
 @article{brown_foegeding_daubert_drake_gumpertz_2003, title={Relationships among rheological and sensorial properties of young cheeses}, volume={86}, ISSN={["0022-0302"]}, DOI={10.3168/jds.S0022-0302(03)73905-8}, abstractNote={This study investigated the sensory and rheological properties of young cheeses in order to better understand perceived cheese texture. Mozzarella and Monterey Jacks were tested at 4, 10, 17, and 38 d of age; process cheese was tested at 4 d. Rheological methods were used to determine the linear and nonlinear viscoelastic and fracture properties. A trained sensory panel developed a descriptive language and reference scales to evaluate cheese texture. All methods differentiated the cheeses by variety. Principal component analysis of sensory texture revealed that three principal components explained 96.1% of the total variation in the cheeses. The perception of firmness decreased as the cheeses aged, whereas the perception of springiness increased. Principal component analysis of the rheological parameters (three principal components: 87.9% of the variance) showed that the cheeses' solid-like response (storage modulus and fracture modulus) decreased during aging, while phase angle, maximum compliance, and retardation time increased. Analysis of the instrumental and sensory parameters (three principal components: 82.1% of the variance) revealed groupings of parameters according to cheese rigidity, resiliency, and chewdown texture. Rheological properties were highly associated with rigidity and resiliency, but less so with chewdown texture.}, number={10}, journal={JOURNAL OF DAIRY SCIENCE}, author={Brown, JA and Foegeding, EA and Daubert, CR and Drake, MA and Gumpertz, M}, year={2003}, month={Oct}, pages={3054–3067} }
 @article{mitchell_gumpertz_2003, title={Spatio-temporal prediction inside a free-air CO2 enrichment system}, volume={8}, ISSN={["1085-7117"]}, DOI={10.1198/1085711032183}, abstractNote={The Japanese RiceFACE (Free-Air CO2 Enrichment) project was a three-year investigation into the effect of elevated CO2 on rice. Four rings were built to emit elevated levels of CO2. The aim of the FACE system is to provide a level of CO2 enrichment 200 ppm above tmbient throughout the plot, without changing any other aspect of the microclimate within the plot. However, there can be substantial spatial variation in the CO2 level from the center to the edges of the plots. One of our main objectives was to predict the seasonal mean levels of CO2 for multiple subregions within the plots. However, the dataset was very large and followed a nonnormal distribution. Furthermore, the mean and variance were nonstationary. To overcome these difficulties daily means were used rather than individual measurements, the mean was modeled with multiple covariates that varied over both time and space, and the variance was modeled as an increasing function of the square of the distance from the center of the plot. A separable space-time covariance structure was used, and estimation was performed using nonlinear methods, REML, and EGLS. Finally, cross-validation was used to assess the validity of the model.}, number={3}, journal={JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS}, author={Mitchell, MW and Gumpertz, ML}, year={2003}, month={Sep}, pages={310–327} }
 @article{qiao_gumpertz_van kempen_2002, title={Stability of pepsin (EC 3.4.23.1) during in vitro protein digestibility assay}, volume={26}, ISSN={["0145-8884"]}, DOI={10.1111/j.1745-4514.2002.tb00759.x}, abstractNote={To maximize the efficiency of utilization of pepsin and estimate the contamination of pepsin for in vitro protein digestibility assays, the specific activity decay and peptide bond hydrolysis of pepsin incubated at different pH and concentration were studied with the bovine hemoglobin method and the o-phthaldialdehyde method, respectively. It was found that increase of pH and concentration of pepsin increased pepsin's half-life for both specific activity decay and peptide bond hydrolysis. The half-life for specific activity decay was not extended by the presence of a substrate protein. The results indicated the time needed to maximize pepsin utilization depended on pH and the concentration of pepsin. At the time when all specific activity of pepsin was lost, the average size of pepsin autolysates was between 6.9 and 12.1 amino acid residues, suggesting most peptic protein would be fractionated as digestible protein.}, number={4}, journal={JOURNAL OF FOOD BIOCHEMISTRY}, author={Qiao, YR and Gumpertz, M and Van Kempen, T}, year={2002}, month={Sep}, pages={355–375} }
 @article{wu_gumpertz_boos_2001, title={Comparison of GEE, MINQUE, ML, and REML estimating equations for normally distributed data}, volume={55}, ISSN={["0003-1305"]}, DOI={10.1198/000313001750358608}, abstractNote={Generalized estimating equations (GEE) provide a regression framework for analyzing correlated data that are not necessarily assumed to be normal. For linear mixed models assuming normality, maximum likelihood (ML) and restricted maximum likelihood (REML) are commonly used for estimating variance and covariance parameters. In the analysis of variance tradition, minimum norm quadratic unbiased estimation (MINQUE) has been developed to estimate variance and covariance components without relying on distributional assumptions. This article rewrites the ML, REML, and MINQUE estimating equations in a form similar to GEE. This form is not particularly useful for computations, but it provides a very clear picture of the similarities and differences of the four methods. The derivations are straightforward and suitable for a linear models course.}, number={2}, journal={AMERICAN STATISTICIAN}, author={Wu, CT and Gumpertz, ML and Boos, DD}, year={2001}, month={May}, pages={125–130} }
 @article{strock_cassel_gumpertz_2001, title={Spatial variability of water and bromide transport through variably saturated soil blocks}, volume={65}, ISSN={["1435-0661"]}, DOI={10.2136/sssaj2001.1607}, abstractNote={Water and solute transport pathways through soil are very complex. Soil properties affecting solute transport vary spatially and temporally within a soil profile and across landscape positions. The objective of this laboratory study was to evaluate water and bromide (Br) transport through 38‐ by 38‐ by 60‐cm‐deep undisturbed blocks of Cecil soil (Clayey, kaolinitic, thermic Typic Kanhapludults) collected from three contrasting landscape positions (interfluve, linear slope, and foot slope) in the Piedmont region of North Carolina. Two replicate soil blocks from each position were placed on a grid lysimeter‐plate effluent collection system which facilitated collection of the effluent from 81 discrete cells under −2.5 kPa pressure. Each block was equilibrated for 5 d with a once daily application of 3.5 L of 0.005 M CaSO4 solution by a water drop applicator at a rate of 14 mm h−1 Four‐hundred mL of KBr solution (4000 g Br m−2) was uniformly sprayed onto the soil surface. Thereafter, 3.5 L of 0.005 M CaSO4 solution was applied daily for the duration of each experiment (19–33 d). Effluent volume and Br concentration in the effluent were measured daily for each of the 81 4 by 4‐cm cells. Cumulative water outflow and Br distribution plots, spatial distribution of cumulative effluent percent, frequency plots, and Br breakthrough curves (BTCs) showed that differences in preferential flow of water and Br occurred for soil blocks from different landscape positions. Differences in preferential flow of water and Br were attributed to soil horizon thickness, soil texture and structure, macroporosity, and slope gradient. Preferential flow of water and Br under variably saturated conditions was found to be highly variable within a given soil profile and that differences in the distribution and magnitude of preferential flow occurred across topographic positions.}, number={6}, journal={SOIL SCIENCE SOCIETY OF AMERICA JOURNAL}, author={Strock, JS and Cassel, DK and Gumpertz, ML}, year={2001}, pages={1607–1617} }
 @article{gumpertz_wu_pye_2000, title={Logistic regression for southern pine beetle outbreaks with spatial and temporal autocorrelation}, volume={46}, number={1}, journal={Forest Science}, author={Gumpertz, M. L. and Wu, C. and Pye, J. M.}, year={2000}, pages={95–107} }
 @misc{ristaino_gumpertz_2000, title={New frontiers in the study of dispersal and spatial analysis of epidemics caused by species in the genus Phytophthora}, volume={38}, ISSN={["1545-2107"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0033748429&partnerID=MN8TOARS}, DOI={10.1146/annurev.phyto.38.1.541}, abstractNote={ Diseases caused by species in the genus Phytophthora are responsible for significant economic losses on a wide range of host plants. Spatial pattern is one of the most characteristic ecological properties of a species, and reflects environmental and genetic heterogeneity and reproductive population growth acting on the processes of reproduction, dispersal, and mortality. Species of Phytophthora can be dispersed either in soil, via surface water movement down rows, from rain splash dispersal, by air, or via movement by humans or invertebrate activity. Dispersal results in patchiness in patterns of disease or inoculum in soil. In this chapter we discuss the mechanisms of dispersal of members of this important genus and describe several methods that can be used to statistically analyze data for which spatial coordinates are known. The methods include testing spatial autocorrelation for binary data or continuous data, semivariograms, and regression models for spatial data. The goal of spatial pattern analysis is to gain an understanding of the mechanisms of dispersal of propagules and to sort out the physical and biological factors that are important for spread of plant pathogens and ultimately, for disease management. }, number={2000}, journal={ANNUAL REVIEW OF PHYTOPATHOLOGY}, author={Ristaino, JB and Gumpertz, ML}, year={2000}, pages={541-+} }
 @article{sujkowski_parra_gumpertz_ristaino_2000, title={Temporal dynamics of Phytophthora blight on bell pepper in relation to the mechanisms of dispersal of primary inoculum of Phytophthora capsici in soil}, volume={90}, ISSN={["0031-949X"]}, DOI={10.1094/phyto.2000.90.2.148}, abstractNote={ The effect of components of primary inoculum dispersal in soil on the temporal dynamics of Phytophthora blight epidemics in bell pepper was evaluated in field and growth-chamber experiments. Phytophthora capsici may potentially be dispersed by one of several mechanisms in the soil, including inoculum movement to roots, root growth to inoculum, and root-to-root spread. Individual components of primary inoculum dispersal were manipulated in field plots by introducing (i) sporangia and mycelia directly in soil so that all three mechanisms of dispersal were possible, (ii) a plant with sporulating lesions on the soil surface in a plastic polyvinyl chloride (PVC) tube so inoculum movement to roots was possible, (iii) a wax-encased peat pot containing sporangia and mycelia in soil so root growth to inoculum was possible, (iv) a wax-encased peat pot containing infected roots in soil so root-to-root spread was possible, (v) noninfested V8 vermiculite media into soil directly as a control, or (vi) wax-encased noninfested soil as a control. In 1995 and 1996, final incidence of disease was highest in plots where sporangia and mycelia were buried directly in soil and all mechanisms of dispersal were operative (60 and 32%) and where infected plants were placed in PVC tubes on the soil surface and inoculum movement to roots occurred with rainfall (89 and 23%). Disease onset was delayed in 1995 and 1996, and final incidence was lower in plants in plots where wax-encased sporangia (6 and 22%) or wax-encased infected roots (22%) were buried in soil and root growth to inoculum or root-to-root spread occurred. Incidence of root infections was higher over time in plots where inoculum moved to roots or all mechanisms of dispersal were possible. In growth-chamber studies, ultimately all plants became diseased regardless of the dispersal mechanism of primary inoculum, but disease onset was delayed when plant roots had to grow through a wax layer to inoculum or infected roots in tension funnels that contained small volumes of soil. Our data from both field and growth-chamber studies demonstrate that the mechanism of dispersal of the primary inoculum in soil can have large effects on the temporal dynamics of disease. }, number={2}, journal={PHYTOPATHOLOGY}, author={Sujkowski, LS and Parra, GR and Gumpertz, ML and Ristaino, JB}, year={2000}, month={Feb}, pages={148–156} }
 @article{bayesian analysis of agricultural field experiments - discussion_1999, volume={61}, number={1999}, journal={Journal of the Royal Statistical Society. Series B, Methodological}, year={1999}, pages={717–7464} }
 @inbook{gumpertz_pantula_1998, title={Random coefficient regression}, booktitle={Samuel Kotz (Editor-in-chief), Encyclopedia of statistical sciences}, publisher={New York: Wiley}, author={Gumpertz, M. L. and Pantula, S. G.}, year={1998}, pages={581–588} }
 @article{gumpertz_graham_ristaino_1997, title={Autologistic model of spatial pattern of Phytophythora epidemic in bell pepper: effects of soil variables on disease presence}, volume={2}, number={2}, journal={Journal of Agricultural, Biological, and Environmental Statistics}, author={Gumpertz, M. L. and Graham, J. M. and Ristaino, J. B.}, year={1997}, pages={131–156} }
 @inbook{gumpertz_larkin_ristaino_1997, title={Geostatistical applications in epidemiology}, booktitle={Exercises in plant disease epidemiology}, publisher={St. Paul, Minn.: APS Press}, author={Gumpertz, M. L. and Larkin, R. P. and Ristaino, J. B.}, editor={L. J. Francl and Neher, D. A.Editors}, year={1997}, pages={94–99} }
 @inbook{gumpertz_ristaino_1997, title={Spatial autocorrelation: Methods for continuous variables}, booktitle={Exercises in plant disease epidemiology}, publisher={St. Paul, Minn.: APS Press}, author={Gumpertz, M. L. and Ristaino, J. B.}, editor={L. J. Francl and Neher, D. A.Editors}, year={1997}, pages={72–77} }
 @inbook{gumpertz_1997, title={Testing spatial autocorrelation for binary or categorical response variables}, booktitle={Exercises in plant disease epidemiology}, publisher={St. Paul, Minn.: APS Press}, author={Gumpertz, M. L.}, editor={L. J. Francl and Neher, D. A.Editors}, year={1997}, pages={78–84} }
 @article{brownie_gumpertz_1997, title={Validity of spatial analyses for large field trials}, volume={2}, number={1}, journal={Journal of Agricultural, Biological, and Environmental Statistics}, author={Brownie, C. and Gumpertz, M. L.}, year={1997}, pages={1–23} }
 @inbook{gumpertz_1997, title={Visualizing spatial patterns}, booktitle={Exercises in plant disease epidemiology}, publisher={St. Paul, Minn.: APS Press}, author={Gumpertz, M. L.}, editor={L. J. Francl and Neher, D. A.Editors}, year={1997}, pages={59–63} }
 @article{gumpertz_brownie_1993, title={REPEATED-MEASURES IN RANDOMIZED BLOCK AND SPLIT-PLOT EXPERIMENTS}, volume={23}, ISSN={["0045-5067"]}, DOI={10.1139/x93-083}, abstractNote={ Randomized block and split-plot designs are among the most commonly used experimental designs in forest research. Measurements for plots in a block (or subplots in a whole plot) are correlated with each other, and these correlations must be taken into account when analyzing repeated-measures data from blocked designs. The analysis is similar to repeated-measures analysis for a completely randomized design, but test statistics must allow for random block × time effects, and standard errors for treatment means must also incorporate block to block variation and variation among plots within a block. Two types of statistical analysis are often recommended for repeated-measures data: analysis of contrasts of the repeated factor and multivariate analysis of variance. A complete analysis of repeated measures should usually contain both of these components, just as in univariate analysis of variance it is often necessary to decompose the main effects into single degree of freedom contrasts to answer the research objectives. We demonstrate the multivariate analysis of variance and the analysis of contrasts in detail for two experiments. In addition, estimation of coefficients assuming a polynomial growth curve is discussed in detail for one of these experiments. The first experiment, a randomized complete block design, is a forest nutrition study of the long-term effects of midrotation nitrogen and phosphorus fertilization on loblolly pine (Pinustaeda L.); the second experiment, a split-plot design, is an air-pollution study of the effects of ozone and acid precipitation on loblolly pine growth. }, number={4}, journal={CANADIAN JOURNAL OF FOREST RESEARCH-REVUE CANADIENNE DE RECHERCHE FORESTIERE}, author={GUMPERTZ, ML and BROWNIE, C}, year={1993}, month={Apr}, pages={625–639} }
 @article{gumpertz_rawlings_1992, title={NONLINEAR-REGRESSION WITH VARIANCE-COMPONENTS - MODELING EFFECTS OF OZONE ON CROP YIELD}, volume={32}, ISSN={["0011-183X"]}, DOI={10.2135/cropsci1992.0011183X003200010045x}, abstractNote={Split‐plot experimental designs are common in studies of the effects of air pollutants on crop yields. Nonlinear functions such as the Weibull function have been used extensively to model the effect of ozone (O3) exposure on yield of several crop species. The usual nonlinear regression model, which assumes independent errors, is not appropriate for data from nested or split‐plot designs in which there is more than one source of random variation. The nonlinear model with variance components combines a nonlinear model for the mean with additive random effects to describe the covariance structure. We propose an estimated generalized least squares (EGLS) method of estimating the parameters for this model. This method is demonstrated and compared with results from ordinary nonlinear least squares for data from the National Crop Loss Assessment Network (NCLAN) program regarding the effects of O3 on soybean [Glycine max (L.) Merr.]. In this example, all methods give similar point estimates of the parameters of the Weibull function. The advantage of estimated generalized least squares is that it produces proper estimates of the variances of the parameters, estimated yields, and relative yield losses, which take the covariance structure into account. Model selection, hypothesis testing, and construction of confidence intervals are also demonstrated. A computer program that fits the nonlinear model with variance components by the EGLS method is available from the authors.}, number={1}, journal={CROP SCIENCE}, author={GUMPERTZ, ML and RAWLINGS, JO}, year={1992}, pages={219–224} }