Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Alternative approaches to predicting methane emissions from dairy cows

Previous attempts to apply statistical models, which correlate nutrient intake with methane production, have been of limited. value where predictions are obtained for nutrient intakes and diet types outside those. used in model construction. Dynamic mechanistic models have proved more suitable for extrapolation, but they remain computationally expensive and are not applied easily in practical situations. The first objective of this research focused on employing conventional techniques to generate statistical models of methane production appropriate to United Kingdom dairy systems. The second objective was to evaluate these models and a model published previously using both United Kingdom and North American data sets. Thirdly, nonlinear models were considered as alternatives to the conventional linear regressions. The United Kingdom calorimetry data used to construct the linear models also were used to develop the three. nonlinear alternatives that were ball of modified Mitscherlich (monomolecular) form. Of the linear models tested,, an equation from the literature proved most reliable across the full range of evaluation data (root mean square prediction error = 21.3%). However, the Mitscherlich models demonstrated the greatest degree of adaptability across diet types and intake level. The most successful model for simulating the independent data was a modified Mitscherlich equation with the steepness parameter set to represent dietary starch-to-ADF ratio (root mean square prediction error = 20.6%). However, when such data were unavailable, simpler Mitscherlich forms relating dry matter or metabolizable energy intake to methane production remained better alternatives relative to their linear counterparts.

Shrinking the posterior: A note on the Nerlovian model

Diebold and Lamb (1997) argue that since the long-run elasticity of supply derived from the Nerlovian model entails a ratio of random variables, it is without moments. They propose minimum expected loss estimation to correct this problem but in so-doing ignore the fact that a non white-noise-error is implicit in the model. We show that, as a consequence the estimator is biased and demonstrate that Bayesian estimation which fully accounts for the error structure is preferable.

Estimating numbers of infectious units from serial dilution assays

The paper concerns the design and analysis of serial dilution assays to estimate the infectivity of a sample of tissue when it is assumed that the sample contains a finite number of indivisible infectious units such that a subsample will be infectious if it contains one or more of these units. The aim of the study is to estimate the number of infectious units in the original sample. The standard approach to the analysis of data from such a study is based on the assumption of independence of aliquots both at the same dilution level and at different dilution levels, so that the numbers of infectious units in the aliquots follow independent Poisson distributions. An alternative approach is based on calculation of the expected value of the total number of samples tested that are not infectious. We derive the likelihood for the data on the basis of the discrete number of infectious units, enabling calculation of the maximum likelihood estimate and likelihood-based confidence intervals. We use the exact probabilities that are obtained to compare the maximum likelihood estimate with those given by the other methods in terms of bias and standard error and to compare the coverage of the confidence intervals. We show that the methods have very similar properties and conclude that for practical use the method that is based on the Poisson assumption is to be recommended, since it can be implemented by using standard statistical software. Finally we consider the design of serial dilution assays, concluding that it is important that neither the dilution factor nor the number of samples that remain untested should be too large.

Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference

We consider the case of a multicenter trial in which the center specific sample sizes are potentially small. Under homogeneity, the conventional procedure is to pool information using a weighted estimator where the weights used are inverse estimated center-specific variances. Whereas this procedure is efficient for conventional asymptotics (e. g. center-specific sample sizes become large, number of center fixed), it is commonly believed that the efficiency of this estimator holds true also for meta-analytic asymptotics (e.g. center-specific sample size bounded, potentially small, and number of centers large). In this contribution we demonstrate that this estimator fails to be efficient. In fact, it shows a persistent bias with increasing number of centers showing that it isnot meta-consistent. In addition, we show that the Cochran and Mantel-Haenszel weighted estimators are meta-consistent and, in more generality, provide conditions on the weights such that the associated weighted estimator is meta-consistent.

A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

On the question of proportionality of the count of observed Scrapie cases and the size of holding

Background: The present paper investigates the question of a suitable basic model for the number of scrapie cases in a holding and applications of this knowledge to the estimation of scrapie-ffected holding population sizes and adequacy of control measures within holding. Is the number of scrapie cases proportional to the size of the holding in which case it should be incorporated into the parameter of the error distribution for the scrapie counts? Or, is there a different - potentially more complex - relationship between case count and holding size in which case the information about the size of the holding should be better incorporated as a covariate in the modeling? Methods: We show that this question can be appropriately addressed via a simple zero-truncated Poisson model in which the hypothesis of proportionality enters as a special offset-model. Model comparisons can be achieved by means of likelihood ratio testing. The procedure is illustrated by means of surveillance data on classical scrapie in Great Britain. Furthermore, the model with the best fit is used to estimate the size of the scrapie-affected holding population in Great Britain by means of two capture-recapture estimators: the Poisson estimator and the generalized Zelterman estimator. Results: No evidence could be found for the hypothesis of proportionality. In fact, there is some evidence that this relationship follows a curved line which increases for small holdings up to a maximum after which it declines again. Furthermore, it is pointed out how crucial the correct model choice is when applied to capture-recapture estimation on the basis of zero-truncated Poisson models as well as on the basis of the generalized Zelterman estimator. Estimators based on the proportionality model return very different and unreasonable estimates for the population sizes. Conclusion: Our results stress the importance of an adequate modelling approach to the association between holding size and the number of cases of classical scrapie within holding. Reporting artefacts and speculative biological effects are hypothesized as the underlying causes of the observed curved relationship. The lack of adjustment for these artefacts might well render ineffective the current strategies for the control of the disease.

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio

This paper considers methods for testing for superiority or non-inferiority in active-control trials with binary data, when the relative treatment effect is expressed as an odds ratio. Three asymptotic tests for the log-odds ratio based on the unconditional binary likelihood are presented, namely the likelihood ratio, Wald and score tests. All three tests can be implemented straightforwardly in standard statistical software packages, as can the corresponding confidence intervals. Simulations indicate that the three alternatives are similar in terms of the Type I error, with values close to the nominal level. However, when the non-inferiority margin becomes large, the score test slightly exceeds the nominal level. In general, the highest power is obtained from the score test, although all three tests are similar and the observed differences in power are not of practical importance. Copyright (C) 2007 John Wiley & Sons, Ltd.

Adjusted jackknife for imputation under unequal probability sampling without replacement

Imputation is commonly used to compensate for item non-response in sample surveys. If we treat the imputed values as if they are true values, and then compute the variance estimates by using standard methods, such as the jackknife, we can seriously underestimate the true variances. We propose a modified jackknife variance estimator which is defined for any without-replacement unequal probability sampling design in the presence of imputation and non-negligible sampling fraction. Mean, ratio and random-imputation methods will be considered. The practical advantage of the method proposed is its breadth of applicability.