David B. Hitchcock

A Comparison of Hierarchical Methods for Clustering Functional Data

Functional data analysis (FDA)—the analysis of data that can be considered a set of observed continuous functions—is an increasingly common class of statistical analysis. One of the most widely used FDA methods is the cluster analysis of functional data; however, little work has been done to compare the performance of clustering methods on functional data. In this article, a simulation study compares the performance of four major hierarchical methods for clustering functional data. The simulated data varied in three ways: the nature of the signal functions (periodic, non periodic, or mixed), the amount of noise added to the signal functions, and the pattern of the true cluster sizes. The Rand index was used to compare the performance of each clustering method. As a secondary goal, clustering methods were also compared when the number of clusters has been misspecified. To illustrate the results, a real set of functional data was clustered where the true clustering structure is believed to be known. Comparing the clustering methods for the real data set confirmed the findings of the simulation. This study yields concrete suggestions to future researchers to determine the best method for clustering their functional data.

Resveratrol prevents embryonic oxidative stress and apoptosis associated with diabetic embryopathy, and improves glucose and lipid profile of diabetic dam

SCOPE Diabetic embryopathy, a consequence of diabetic pregnancy, is associated with increase in embryonic oxidative stress and apoptosis, which lead to severe embryonic damage at early stage of organogenesis. METHODS AND RESULTS This study investigated if resveratrol, found in red grapes and blue-berries, may prevent diabetes-induced oxidative stress and apoptosis in embryos and have beneficial effects in diabetic dams. A rodent model of diabetic embryopathy was used. Diabetes was associated with lowered reduced glutathione levels (26.98%), increased total thiol (100.47%) and lipid peroxidation (124.73%) in embryos, and increased blood sugar (384.03%), cholesterol (98.39%) and triglyceride (1025.35%) in diabetic dams. Increased apoptosis (272.20%) was also observed in the embryos of diabetic dams. Administration of resveratrol (100 mg/kg body weight (b.w.)) during pregnancy prevented both oxidative stress and apoptosis in embryos. Resveratrol reduced embryonic maldevelopment by improving embryo weight (41.23%), crown rump length (16.50%) and somite number (11.22%). It further improved the glucose (33.32%) and lipid (cholesterol 41.74%, triglyceride 60.64%) profile of the diabetic dams, which also represents the protective role of resveratrol in diabetes. CONCLUSION Resveratrol was found to prevent embryonic oxidative stress and apoptosis. It also improved glucose and lipid profile of diabetic dams, indicating the beneficial effects in diabetic pregnancy.

A History of the Metropolis-Hastings Algorithm

The Metropolis–Hastings algorithm is an extremely popular Markov chain Monte Carlo technique among statisticians. This article explores the history of the algorithm, highlighting key personalities and events in its development. We relate reasons for the delay in the acceptance of the algorithm and reasons for its recent popularity.

James-Stein shrinkage to improve k-means cluster analysis

We study a general algorithm to improve the accuracy in cluster analysis that employs the James-Stein shrinkage effect in k-means clustering. We shrink the centroids of clusters toward the overall mean of all data using a James-Stein-type adjustment, and then the James-Stein shrinkage estimators act as the new centroids in the next clustering iteration until convergence. We compare the shrinkage results to the traditional k-means method. A Monte Carlo simulation shows that the magnitude of the improvement depends on the within-cluster variance and especially on the effective dimension of the covariance matrix. Using the Rand index, we demonstrate that accuracy increases significantly in simulated data and in a real data example.

Integrating Ranch Forage Production, Cattle Performance, and Economics in Ranch Management Systems for Southern Florida

Abstract The presence of grazing cattle near open waterways has created environmental concerns related to the potential for water contamination. In Florida the removal of cattle from grazing landscapes or decreasing stocking density is being investigated as one option to improve the quality of surface water runoff draining into Lake Okeechobee, Florida. The objective of this study was to determine the effects of stocking rate on cow-calf performance, forage availability and quality, and ranch economic performance. Experimental pastures were established on a southern Florida cow-calf operation with stocking rates of 0.58, 1.01, and 1.35 ha·cow−1 on summer pastures and 0.93, 1.62, and 2.16 ha·cow−1 on winter pastures, corresponding to high, medium, and low rates, respectively. The study was conducted over 4 consecutive production years. Cow body condition scores (BCS), pregnancy rate, and calf average daily gain were used as measures of animal performance. Forage utilization was estimated by measuring the difference between forage yield inside and outside grazing exclusion cages and forage quality by crude protein and in vitro organic matter digestibility. Forage yield, utilization, and quality were not significantly affected by stocking rate. Although statistically not significant (P = 0.17), cattle in the high stocking rate experienced a numerically greater loss of BCS following the winter grazing period, but stocking rate did not affect pregnancy rate or calf gains. Production (kg weaned calves·ha−1) was increased (P < 0.01) for a high stocking rate compared with medium and low stocking rates. Overall ranch profitability will decrease as stocking rates decline. Ranch revenues decrease one-for-one as stocking rates decrease. At the same time, unit cow costs increase at an increasing rate as fewer brood cows are left to support the ranchs fixed cost structure.

A Validation Study Concerning the Effects of Interview Content, Retention Interval, and Grade on Children's Recall Accuracy for Dietary Intake and/or Physical Activity

BACKGROUND Practitioners and researchers are interested in assessing childrens dietary intake and physical activity together to maximize resources and minimize subject burden. OBJECTIVE Our aim was to investigate differences in dietary and/or physical activity recall accuracy by content (diet only; physical activity only; diet and physical activity), retention interval (same-day recalls in the afternoon; previous-day recalls in the morning), and grade (third; fifth). DESIGN Children (n=144; 66% African American, 13% white, 12% Hispanic, 9% other; 50% girls) from four schools were randomly selected for interviews about one of three contents. Each content group was equally divided by retention interval, each equally divided by grade, each equally divided by sex. Information concerning diet and physical activity at school was validated with school-provided breakfast and lunch observations, and accelerometry, respectively. Dietary accuracy measures were food-item omission and intrusion rates, and kilocalorie correspondence rate and inflation ratio. Physical activity accuracy measures were absolute and arithmetic differences for moderate to vigorous physical activity minutes. STATISTICAL ANALYSES PERFORMED For each accuracy measure, linear models determined effects of content, retention interval, grade, and their two-way and three-way interactions; ethnicity and sex were control variables. RESULTS Content was significant within four interactions: intrusion rate (content×retention-interval×grade; P=0.0004), correspondence rate (content×grade; P=0.0004), inflation ratio (content×grade; P=0.0104), and arithmetic difference (content×retention-interval×grade; P=0.0070). Retention interval was significant for correspondence rate (P=0.0004), inflation ratio (P=0.0014), and three interactions: omission rate (retention-interval×grade; P=0.0095), intrusion rate, and arithmetic difference (both already mentioned). Grade was significant for absolute difference (P=0.0233) and five interactions mentioned. Content effects depended on other factors. Grade effects were mixed. Dietary accuracy was better with same-day than previous-day retention interval. CONCLUSIONS Results do not support integrating dietary intake and physical activity in childrens recalls, but do support using shorter rather than longer retention intervals to yield more accurate dietary recalls. Additional validation studies need to clarify age effects and identify evidence-based practices to improve childrens accuracy for recalling dietary intake and/or physical activity.

A Pilot Study of the Effects of Interview Content, Retention Interval, and Grade on Accuracy of Dietary Information From Children

OBJECTIVE Investigate differences in dietary recall accuracy by interview content (diet only or diet and physical activity), retention interval (same day or previous day), and grade (third or fifth). METHODS Thirty-two children observed eating school-provided meals and interviewed once each; interview content and retention interval randomly assigned. Multivariate analysis of variance on rates for omissions (foods observed but unreported) and intrusions (foods reported but unobserved); independent variables: interview content, retention interval, grade. RESULTS Accuracy differed by retention interval (P = .05; better for same day [omission rate, intrusion rate: 28%, 20%] than previous day [54%, 45%]) but not interview content (P > .48; diet only: 41%, 33%; diet and physical activity: 41%, 33%) or grade (P > .27; third: 48%, 42%; fifth: 34%, 24%). CONCLUSIONS AND IMPLICATIONS Although the small sample limits firm conclusions, results provide evidence-based direction to enhance accuracy: specifically, to shorten the retention interval. Larger validation studies need to investigate the combined effect of interview content, retention interval, and grade on accuracy.

The effect of pre-smoothing functional data on cluster analysis

We investigate the possible benefits of pre-smoothing functional data before performing a cluster analysis. A simulation study compares the accuracy of clustering results on the basis of the use of unsmoothed functional data—and two smoothed versions of the data—as the inputs in a clustering algorithm. Smoothing is usually found to produce a more accurate clustering, with the best results arising from a novel James–Stein-type shrinkage adjustment to the standard linear smoother. Two real functional data sets are clustered using the competing methods to illustrate the procedure.

Improved Estimation of Dissimilarities by Presmoothing Functional Data

We examine the effect of presmoothing functional data on estimating the dissimilarities among objects in a dataset, with applications to cluster analysis and other distance methods, such as multidimensional scaling and statistical matching. We prove that a shrinkage method of smoothing results in a better estimator of the dissimilarities among a set of noisy curves. For a model with independent noise structure, the smoothed-data dissimilarity estimator dominates the observed-data estimator. For a dependent-error model—often applicable when the functional data are measured nearly continuously over some domain—an asymptotic domination result is given for the smoothed-data estimator. A simulation study indicates the magnitude of improvement provided by the shrinkage estimator and examines its behavior for heavy-tailed noise structure. The shrinkage estimator presented here combines Stein estimation and basis function-based linear smoothers in a novel manner. Statisticians increasingly analyze sizable sets of functional data, and the results in this article are a useful contribution to the theory of the effect of presmoothing on functional data analysis.

Effectiveness of Prompts on Fourth-Grade Children's Dietary Recall Accuracy Depends on Retention Interval and Varies by Gender

BACKGROUND Dietary recall accuracy is related to retention interval (RI) (i.e., time between to-be-reported meals and the interview), and possibly to prompts. To the best of our knowledge, no study has evaluated their combined effect. OBJECTIVE The combined influence of RI and prompts on childrens recall accuracy was investigated in this study. Two RIs [short (prior-24-h recall obtained in afternoon) and long (previous-day recall obtained in morning)] were crossed with 4 prompts [forward (distant-to-recent), meal-name (breakfast, lunch, etc.), open (no instructions), and reverse (recent-to-distant)], creating 8 conditions. METHODS Fourth-grade children (n = 480; 50% girls) were randomly selected from consenting children at 10 schools in 4 districts in a southern state during 3 school years (2011-2012, 2012-2013, and 2013-2014). Each child was observed eating school-provided breakfast and lunch, and interviewed one time under 1 of the 8 conditions. Condition assignment was constrained so that each had 60 children (30 girls). Accuracy measures were food-item omission and intrusion rates, and energy correspondence rate and inflation ratio. For each measure, linear models determined effects of RI, prompt, gender, and interactions (2-way, 3-way); race/ethnicity, school year, and district were control variables. RESULTS RI (P values < 0.015) and prompt (P values < 0.005) were significant for all 4 accuracy measures. RI × prompt (P values < 0.001) was significant for 3 accuracy measures (not intrusion rate). Prompt × gender (P = 0.005) was significant for omission rate. RI × prompt × gender was significant for intrusion rate and inflation ratio (P values < 0.001). For the short vs. long RI across prompts and genders, accuracy was better by 33-50% for each accuracy measure. CONCLUSIONS To obtain the most accurate recalls possible from children, studies should be designed to use a short rather than long RI. Prompts affect childrens recall accuracy, although the effectiveness of different prompts depends on RI and varies by gender: at a short RI, the choice of prompts has little systematic effect on accuracy, whereas at a long RI, reverse prompts may elicit the most accurate recalls.