New Prediction Interval and Band in the Nonlinear Regression Model: Application to Predictive Modeling in Foods

This article is concerned with the proposal of a new prediction interval and band for the nonlinear regression model. The construction principle of this interval and band is based on an exact (the meaning of the term “exact” will be given later) confidence region for parameters of the nonlinear regression model. This region, fully described in Vila and Gauchi (2007 Vila , J.-P. , Gauchi , J.-P. ( 2007 ). Optimal designs based on exact confidence regions for parameter estimation of a nonlinear regression model . Journal of Statistical Planning and Inference 137 ( 9 ): 2935 – 2953 .[Crossref], [Web of Science ®] , [Google Scholar]), provides a rigorous justification for the new prediction interval and band that we propose. This new band is then compared to the classical bands (which are asymptotic and thus approximate for small n), and also to the band based on the bootstrap resampling method. The comparison of these bands is undertaken with simulated and real data from predictive modeling in food science.     

Efficient estimators for the good family

We consider the problem of estimating the two parameters of the discrete Good distribution. We first show that the sufficient statistics for the parameters are the arithmetic and the geometric means. The maximum likelihood estimators (MLE's) of the parameters are obtained by solving numerically a system of equations involving the Lerch zeta function and the sufficient statistics. We find an expression for the asymptotic variance-covariance matrix of the MLE's, which can be evaluated numerically. We show that the probability mass function satisfies a simple recurrence equation linear in the two parameters, and propose the quadratic distance estimator (QDE) which can be computed with an ineratively reweighted least-squares algorithm. the QDE is easy to calculate and admits a simple expression for its asymptotic variance-covariance matrix. We compute this matrix for the MLE's and the QDE for various values of the parameters and see that the QDE has very high asymptotic efficiency. Finally, we present a numerical example.     

More from Louis Baxter on doctors taking MAT

The question of whether or not doctors and other health care professionals on medication‐assisted treatment (MAT) are safe to practice medicine has been debated for the last few years since the advent of Food and Drug Administration (FDA)–approved MAT for opioid use disorder (OUD). The newly approved medications have been primarily buprenorphine formulations for OUD, naltrexone formulations for OUD and alcohol use disorder (AUD), and, most recently, an alpha 2‐adrenergic medication that specifically targets amelioration of opioid‐withdrawal symptoms from OUD (lofexidine). Quite frankly, the question of safety about medications to treat substance use disorder (SUD) has been asked since the development of methadone for OUD treatment more than 30 years ago.     

A more powerful unconditional exact test of homogeneity for 2 × c contingency table analysis

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the 5th percentiles of the distributions of the p-values of the exact test over a range of scenarios and implemented a regression model to predict the values for two-sample multinomial settings. Our results show that the new test is uniformly more powerful than Fisher's, Barnard's, and Boschloo's tests with gains in power as large as several hundred percent in certain scenarios. Lastly, we provide a real-life data example where the unadjusted unconditional exact test wrongly fails to reject the null hypothesis and the corrected unconditional exact test rejects the null appropriately.     

Institutional readiness for integrated watershed management: The case of the Maumee river

Is there such a thing as “institutional readiness” for integrated watershed management? One element of readiness is the ability of managers with watershed-related responsibilities to identify the policy and management objectives of potential partners. The geographic areas encompassed by large watersheds are under the overlapping jurisdictions of many agencies and organizations from each sector (public, non-profit, and private) as well as private landowners. Developing a watershed-based institutional atlas is a promising strategy for coping with this jurisdictional complexity. The authors examine the potential for developing such an atlas in the Maumee River watershed of Ohio, Indiana, and Michigan, and they assess other signals of readiness and partnerships in progress in the basin.     

Expressing Estimators of Expected Quality Adjusted Survival as Functions of Nelson-Aalen Estimators

Quality adjusted survival has been increasingly advocated in clinical trials to be assessed as a synthesis of survival and quality of life. We investigate nonparametric estimation of its expectation for a general multistate process with incomplete follow-up data. Upon establishing a representation of expected quality adjusted survival through marginal distributions of a set of defined events, we propose two estimators for expected quality adjusted survival. Expressed as functions of Nelson-Aalen estimators, the two estimators are strongly consistent and asymptotically normal. We derive their asymptotic variances and propose sample-based variance estimates, along with evaluation of asymptotic relative efficiency. Monte Carlo studies show that these estimation procedures perform well for practical sample sizes. We illustrate the methods using data from a national, multicenter AIDS clinical trial.     

Confidence biases and learning among intuitive Bayesians

We design a double-or-quits game to compare the speed of learning one’s specific ability with the speed of rising confidence as the task gets increasingly difficult. We find that people on average learn to be overconfident faster than they learn their true ability and we present an intuitive-Bayesian model of confidence which integrates confidence biases and learning. Uncertainty about one’s true ability to perform a task in isolation can be responsible for large and stable confidence biases, namely limited discrimination, the hard–easy effect, the Dunning–Kruger effect, conservative learning from experience and the overprecision phenomenon (without underprecision) if subjects act as Bayesian learners who rely only on sequentially perceived performance cues and contrarian illusory signals induced by doubt. Moreover, these biases are likely to persist since the Bayesian aggregation of past information consolidates the accumulation of errors and the perception of contrarian illusory signals generates conservatism and under-reaction to events. Taken together, these two features may explain why intuitive Bayesians make systematically wrong predictions of their own performance.     

Migration expectancy revisited: Results for the 1970s, 1980s and 1990s

Planners in a variety of situations require an improved understanding of migration trends if services and products that adequately meet constituent needs are to be provided. This note focuses on changes in migration expectancy over three decades in the context of the planning function. Using the CPS one-year migration question for the periods 1975–1976, 1980–1981, and 1987–1991, and the work of Wilber (1963) and Long (1973) as historical benchmarks, migration expectancy is found to have fallen since the earlier studies. Longer-distance migration (between counties and between states) has remained relatively constant over the same period so that these types of moves now account for a larger proportion of total residential mobility. The results are discussed in the context of their value to individuals and organizations who seek a better understanding of demographically-driven demand from services and products.This article is based on a paper presented at the Southern Demographic Association annual meeting, New Orleans, Louisiana, 22 October 1993.