NEAREST NEIGHBOR ADJUSTED BEST LINEAR UNBIASED PREDICTION IN FIELD EXPERIMENTS

In field experiments with large numbers of treatments, inference can be affected by 1) local variation, and 2) method of analysis . The standard approach to local, or spatial, variation in the design of experiments is blocking. While the randomized complete block design is obviously unsuitable for experiments with large numbers of treatments, incomplete block designs - even apparently well-chosen ones - may be only partial solutions. Various nearest neighbor adjustment procedures are an alternative approach to spatial variation . Treatment effects are usually estimated using standard linear model methods. That is, linear unbiased estimates are obtained using ordinary least squares or, for example when nearest neighbor adjustments are used, generalized least squares. This follows from regarding treatment as a fixed effect. However, when there are large numbers of treatments, regarding treatment as a random effect and obtaining best linear unbiased predictors (BLUP) can improve precision . Nearest neighbor methods and BLUP have had largely parallel development. The purpose of this paper is to put them together

ON USING PROC MIXED FOR LONGITUDINAL DATA

PROC MIXED has become a standard tool for analyzing repeated measures data. Its popularity results from a wide choice of correlated error models compared to other software, e.g. PROC GLM. However, PROC MIXED\u27s versatility comes at a price. Users must take care. Problems may result from MIXED defaults. These include: questionable criteria for selecting correlated error models; starting values that may impede REML estimation of covariance components; and biased standard errors and test statistics. Problems may be induced by inadequate design. This paper is a survey of current knowledge about mixed model methods for repeated measures. Examples are presented using PROC MIXED to demonstrate these problems and ways to address them

SOME FACTORS LIMITING THE USE OF GENERALIZED LINEAR MODELS IN AGRICULTURAL RESEARCH

The generalized linear model (GLM) is a hot topic in statistics. Numerous research articles on GLM\u27s appear in each edition of all major journals in statistics. GLM\u27s are the subject of substantial numbers of presentations at most statistics conferences. Despite the high level of interest and research activity within the statistics community, GLM\u27s are not widely used, with some exceptions, by biological scientists in the statistical analysis of their research data. Why? Reasons include 1) many statisticians are not comfortable with GLM\u27s, 2) the biological research community is not familiar with GLM\u27s, and 3) there is little in introductory statistics courses as currently taught to change (1) or (2). Whether or not this is a real problem is unclear. This paper looks at some of the factors underlying the current state of GLM\u27s in statistical practice in biology

A SIMULATION STUDY TO EVALUATE PROC MIXED ANALYSIS OF REPEATED MEASURES DATA

Experiments with repeated measurements are common in pharmaceutical trials, agricultural research, and other biological disciplines. Many aspects of the analysis of such experiments remain controversial. With increasingly sophisticated software becoming available, e.g. PROC MIXED, data analysts have more options from which to choose, and hence more questions about the value and impact of these options. These dilemmas include the following. MIXED offers a number of different correlated error models and several criteria for choosing among competing models. How do the model selection criteria behave? How is inference affected if the correlated error model is misspecified? Some texts use random between subject error effects in the model in addition to correlated errors. Others use only the correlated error structure. How does this affect inference? MIXED has several ways to determine degrees of freedom, including a new option to use Kenward and Roger\u27s procedure. The Kenward-Roger procedure also corrects test statistics and standard errors for bias. How do the various degree-of-freedom options compare? When is the bias serious enough to worry about and how well does the Kenward-Roger option work? Some models are prone to convergence problems. When are these most likely to occur and how should they be addressed? We present the results of several simulation studies conducted to help understand the impact of various decisions on the small sample behavior of typical situations that arise in animal health and agricultural settings

A COMPARISON OF SOME METHODS TO ANALYZE REPEATED MEASURES ORDINAL CATEGORICAL DATA

Recent advances in statistical software made possible by the rapid development of computer technology in the past decade have made many new procedures available to data analysts. We focus in this paper on methods for ordinal categorical data with repeated measures that can be implemented using SAS. These procedures are illustrated using data from an animal health experiment. The responses, measured as severity of symptoms on an ordinal scale, are recorded for test animals over time. The experiment was designed to estimate treatment and time effects on the severity of symptoms. The data were analyzed with various approaches using PROC MIXED, PROC NLMIXED, PROC GENMOD, and the GLIMMIX macro. In this paper, we compare the strengths and weaknesses of these different methods

SMALL SAMPLE POWER CHARACTERISTICS OF GENERALIZED MIXED MODEL PROCEDURES FOR BINARY REPEATED MEASURES DATA USING SAS

Researchers in the agricultural and biological sciences often conduct experiments with repeated measures and categorical response variables. Recent advances in statisticalcomputing have made several options available to analyze data from these experiments. For example, SAS has several procedures based on generalized mixed model theory. These include PROC GENMOD, MIXED, NLMIXED, and the GLIMMIX macro. Inference for these procedures depends on asymptotic theory. While statistics literature contains some information about the small-sample behavior, there is much that remains unknown. This presentation will focus on Bernoulli response variables. Power characteristics are compared via simulation for several scenarios involving relatively small repeated measures experiments

GENERALIZED LINEAR MIXED MODELS: AN APPLICATION

The purpose of this paper is to present a specific application of the generalized linear mixed model. Often of interest to animal-breeders is the estimation of genetic parameters associated with certain traits. When the trait is measured in terms of a normally distributed response variable, standard variance-component estimation and mixed-model procedures can be used. Increasingly, breeders are interested in categorical traits (degree of calving difficulty, number born, etc.). An application of the generalized linear mixed to an animal breeding study of the number of lambs born alive will be presented. We will show how the model is determined, how the estimation equations are formed, and the resulting inference

ANALYSIS OF SPATIAL VARIABILITY USING PROC MIXED

Many data sets in agricultural research have spatially correlated observations. Examples include field trials conducted on heterogeneous plots for which blocking is inadequate, soil fertility surveys, ground water resource research, etc. Such data sets may be intended for treatment comparisons or for characterization. In either case, linear models with correlated errors are typically used. Geostatistical models such as those used in kriging are often used to estimate the error structure . SAS PROC MIXED allows the estimation of the parameters of mixed linear models with correlated errors. Fixed and random effects are estimated by generalized least squares. Variance and covariance components are estimated by restricted maximum likelihood (REML) . The purpose of this presentation is to show how PROC MIXED can be used to work with spatial data. Several examples will be presented to illustrate how various analyses could be approached and some of the pitfalls users may encounter

HOW GOOD ARE SPATIAL GLM\u27S? A SIMULATION STUDY

An area of increasing interest to agricultural and ecological researchers is the analysis of spatially correlated non-normal data. A generalized linear model(GLM) accounting for spatial covariance was presented by Gotway and Stroup (1997). Their method included approximate inference based on asymptotic distributions. A simulation study was conducted to assess the small sample behavior of their proposed estimates and test statistics. This study suggests that the spatial GLM yields unbiased estimates of treatment means and differences for binomial data, that the spatial GLM improves precision, as measured by MSE, and that the approximate F-statistic is acceptable for hypothesis testing

Improving Root Health and Yield of Dry Beans in the Nebraska Panhandle with a New Technique for Reducing Soil Compaction

A field study conducted during the 2001 and 2002 growing seasons investigated the integration of fungicide applications and tillage methods for reducing root health problems in dry bean (Phaseolus vulgaris) plants by alleviating soil compaction and its potential exacerbation of root disease. Several cultural practices were combined with applications of the strobilurin fungicide azoxystrobin. Soil compaction was created artificially throughout the entire plot area. Six treatments, consisting of four tillage treatments and two combinations of tillage or applications of azoxystrobin, were tested to alleviate the compaction and enhance root health. Tillage treatments included a compacted control with no additional tillage, formation of beds approximately 10 cm above soil surface, zone tillage with an implement using in-row shanks, and both zone tillage and bedding combined. Fungicide treatments utilized the combination of both zone tillage and bedding with fungicide applications, and a fungicide treatment singly. Effects of compaction on plant vigor and disease development and severity were evaluated 67 and 83 days after planting in 2001 and 2002, respectively, by a visual estimation of plot vigor and by destructively sampling and making root and hypocotyl disease ratings on dry bean plants from nonharvest rows. Soil resistance and moisture were measured in plots 80 and 104 days after planting in 2001 and 2002, respectively, to estimate degree of compaction. In both years, Fusarium root rot, caused by Fusarium solani f. sp. phaseoli, was determined to be the main root disease impacting plant health in studies. All measured variables (root disease index, plant vigor ratings, total seed yield, seed size, and soil resistance) were significantly improved by any treatment that included zone tillage prior to planting. No added advantages were observed for decreasing disease or improving root health and plant performance with the use of azoxystrobin or by planting on raised beds. This is the first study to evaluate zone tillage as a method of reducing plant stress and root disease in dry bean plants