Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Efficiency of research performance of Australian universities : a reappraisal using a bootstrap truncated regression approach

The motivation of the study stems from the results reported in the Excellence in Research for Australia (ERA) 2010 report. The report showed that only 12 universities performed research at or above international standards, of which, the Group of Eight (G8) universities filled the top eight spots. While performance of universities was based on number of research outputs, total amount of research income and other quantitative indicators, the measure of efficiency or productivity was not considered. The objectives of this paper are twofold. First, to provide a review of the research performance of 37 Australian universities using the data envelopment analysis (DEA) bootstrap approach of Simar and Wilson (2007). Second, to determine sources of productivity drivers by regressing the efficiency scores against a set of environmental variables.

A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

An extended regression approach to estimating loads and their uncertainties in Great Barrier Reef catchments

There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates by minimizing the biases and making use of possible predictive variables. The load estimation procedure can be summarized by the following four steps: - (i) output the flow rates at regular time intervals (e.g. 10 minutes) using a time series model that captures all the peak flows; - (ii) output the predicted flow rates as in (i) at the concentration sampling times, if the corresponding flow rates are not collected; - (iii) establish a predictive model for the concentration data, which incorporates all possible predictor variables and output the predicted concentrations at the regular time intervals as in (i), and; - (iv) obtain the sum of all the products of the predicted flow and the predicted concentration over the regular time intervals to represent an estimate of the load. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized regression (rating-curve) approach with additional predictors that capture unique features in the flow data, namely the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and cumulative discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. The model also has the capacity to accommodate autocorrelation in model errors which are the result of intensive sampling during floods. Incorporating this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach using the concentrations of total suspended sediment (TSS) and nitrogen oxide (NOx) and gauged flow data from the Burdekin River, a catchment delivering to the Great Barrier Reef. The sampling biases for NOx concentrations range from 2 to 10 times indicating severe biases. As we expect, the traditional average and extrapolation methods produce much higher estimates than those when bias in sampling is taken into account.

Beta-binomial/Poisson regression models for repeated bivariate counts

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

pK determination. A mean field, Poisson-Boltzmann approach

A model describing dissociation of monoprotonic acid and a method for the determination of its pK value are presented. The model is based on a mean field approximation. The Poisson-Boltzmann equation, adopting spherical symmetry, is numerically solved, and the solution of its linearized form is written. By use of the pH values of a dilution experiment of galacturonic acid as the entry data, the proposed method allowed estimation of the value of pK = 3.25 at a temperature of 25 degrees C. Values for the complex dimensions and dissociation degree are calculated using experimental pH values for solution concentration values ranging from 0.1 to 60 mM. The present analysis leads to the conclusion that the Poisson-Boltzmann equation or its linear form is equally suited for the description of such systems.

Modeling absolute differences in life expectancy with a censored skew-normal regression approach.

Parameter estimates from commonly used multivariable parametric survival regression models do not directly quantify differences in years of life expectancy. Gaussian linear regression models give results in terms of absolute mean differences, but are not appropriate in modeling life expectancy, because in many situations time to death has a negative skewed distribution. A regression approach using a skew-normal distribution would be an alternative to parametric survival models in the modeling of life expectancy, because parameter estimates can be interpreted in terms of survival time differences while allowing for skewness of the distribution. In this paper we show how to use the skew-normal regression so that censored and left-truncated observations are accounted for. With this we model differences in life expectancy using data from the Swiss National Cohort Study and from official life expectancy estimates and compare the results with those derived from commonly used survival regression models. We conclude that a censored skew-normal survival regression approach for left-truncated observations can be used to model differences in life expectancy across covariates of interest.

Measuring fixed costs for firms' use of a free trade agreement : threshold regression approach

In this paper, by employing the threshold regression method, we estimate the average tariff equivalent of fixed costs for the use of a free trade agreement (FTA) among all existing FTAs in the world. It is estimated to be 3.2%. This global estimate serves as a reference rate in the evaluation of each FTA’s fixed costs.

Economic crises and tourism competitiveness: A Markov swtiching regression approach

Authors discuss the effects that economic crises generate on the global market shares of tourism destinations, through a series of potential transmission mechanisms based on the main economic competitiveness determinants identified in the previous literature using a non-linear approach. Specifically a Markov Switching Regression approach is used to estimate the effect of two basic transmission mechanisms: reductions of internal and external tourism demands and falling investment.