SOME STRATEGIES FOR SELECTING AND FITTING COVARIANCE STRUCTURES FOR REPEATED MEASURES

Since in longitudinal studies the covariance structure is often regarded as a nuisance parameter, the strategy has been to use a parsimonious covariance model that describes adequately the observed data and permits better inference on the parameters of interest. In this paper we present some diagnostic tools to choose an appropriate covariance structure and discuss some strategies for fitting it. The main diagnostic tool is the residual , computed as the standardized difference between the elements of the fitted covariance (concentration or correlation) matrix and the corresponding unstructured matrix. SAS Proc Calis is a very efficient procedure that fits many covariance structures in models with no fixed effects. Based on this procedure, we discuss some strategies to choose initial values and improve convergence problems in certain commonly used structures

MODEL SELECTION TECHNIQUES FOR REPEATED MEASURES COVARIANCE STRUCTURES

A parsimonious covariance structure of repeated measures is often sought for purposes of increased power for testing hypotheses about the means, and for insight into the stochastic processes governing the repeated measures. For normal data, model selection is often based upon likelihood ratio tests or information criteria derived from the likelihood, sometimes supplemented with graphical plots of correlations and partial correlations. We exploit the ordered nature of repeated measures to decompose the likelihood ratio goodness-of-fit test statistic, and display graphical fingerprints associated with the covariance structures to help detect covariance structure misspecification, in order to provide guidance in choosing an appropriate structure for the data. The proposed methodology is illustrated with simulated repeated measures data and then applied to an experiment to compare tillage methods of pasture establishment

ANALYSIS OF GENOTYPE-BY-ENVIRONMENT INTERACTION WITH AMMI MODELS USING SAS PROC MIXED

Genotype-by-environment (GE) interaction can be analyzed using different approaches. Among these, the additive main effects and multiplicative interaction model yields useful interpretations and can be applied successfully to plant breeding programs. In this paper we review fitting strategies for this model and show how to combine the capabilities of the Mixed and IML procedures in SAS to fit this model. This permits straightforward use of likelihood-based inference in standard and non standard situations like complex experimental designs. The proposed procedures were applied to data from red mottled bean variety trials conducted in the Dominican Republic and Puerto Rico in 9 environments with 30 lines (15 with indeterminate and 15 with determinate growth habit)

Response of groundwater levels to hydrologic conditions in karst aquifer system of northern Puerto Rico

Karst aquifers have unique characteristics that make them highly productive, but vulnerable to contamination. Groundwater flow in these highly heterogeneous aquifers range from diffuse to conduit flow modes, showing variable response to hydrologic events. The karst aquifer of northern Puerto Rico is characterized by a mixture of both diffuse and conduit flow modes. This work assesses the response of groundwater levels to different hydrologic events and conditions in various areas of the karst groundwater aquifer of northern Puerto Rico. Spatial and temporal data analytics methods were applied to precipitation and groundwater levels from multiple stations and sites along the study area. The analysis showed that there are sites with rapid response in groundwater levels after a rainfall event, whereas others have a slow response to rainfall events. The response is related to flow and recharge modes, antecedent moisture, and storage characteristics in the epikarst. This study will ultimately help in the prediction of flow and transport of contaminants in karst groundwater systems characterized by high primary and secondary porosity, such as those found in northern Puerto Rico

Estimating Preferential Flow in Karstic Aquifers Using Statistical Mixed Models

Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory‐scale Geo‐ HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow‐dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit‐like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108043/1/gwat12084.pd

VARIABILITY FOR ROOT FRESH WEIGHT AMONG TROPICAL TYPE VARIETIES OF SWEETPOTATO

Frequently, farmers in Puerto Rico complain that the tuberous roots from the recommended varieties differ in size, shape and weight, a situation that increases difficulties for marketing. Baseline information on the magnitude of losses related to inappropriate root size is not available. The objective was to assess roots' fresh weight distribution among varieties of sweetpotato of common use in Puerto Rico. Four varieties were grown in a location on the southern coastal valley. For this study roots harvested at 162 days were selected. Roots were weighed individually. Distribution of the individual root fresh weight for each variety was compared to theoretical distributions by using the Kolmogorov-Smimov Test. There was a high frequency of light-weighted roots. The Normal Distribution does not describe adequately the data for root fresh weight distribution from any of the varieties. Because of a high frequency of roots having lightweight, Lognormal and Weibull Distributions appear more adequate than the Normal Distribution to describe the actual root weight distribution. Roots end to be too small for the market, thus for commercial purposes, results stress that a relatively high percentage of photosynthates accumulated in the roots are lost. More emphasis on the selection for this characteristic is needed

High spin states in 93Sr

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