Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection

A modeling paradigm is proposed for covariate, variance and working correlation structure selection for longitudinal data analysis. Appropriate selection of covariates is pertinent to correct variance modeling and selecting the appropriate covariates and variance function is vital to correlation structure selection. This leads to a stepwise model selection procedure that deploys a combination of different model selection criteria. Although these criteria find a common theoretical root based on approximating the Kullback-Leibler distance, they are designed to address different aspects of model selection and have different merits and limitations. For example, the extended quasi-likelihood information criterion (EQIC) with a covariance penalty performs well for covariate selection even when the working variance function is misspecified, but EQIC contains little information on correlation structures. The proposed model selection strategies are outlined and a Monte Carlo assessment of their finite sample properties is reported. Two longitudinal studies are used for illustration.

Early stopping by using stochastic curtailment in a three-arm sequential trial

Summary. Interim analysis is important in a large clinical trial for ethical and cost considerations. Sometimes, an interim analysis needs to be performed at an earlier than planned time point. In that case, methods using stochastic curtailment are useful in examining the data for early stopping while controlling the inflation of type I and type II errors. We consider a three-arm randomized study of treatments to reduce perioperative blood loss following major surgery. Owing to slow accrual, an unplanned interim analysis was required by the study team to determine whether the study should be continued. We distinguish two different cases: when all treatments are under direct comparison and when one of the treatments is a control. We used simulations to study the operating characteristics of five different stochastic curtailment methods. We also considered the influence of timing of the interim analyses on the type I error and power of the test. We found that the type I error and power between the different methods can be quite different. The analysis for the perioperative blood loss trial was carried out at approximately a quarter of the planned sample size. We found that there is little evidence that the active treatments are better than a placebo and recommended closure of the trial.

Modeling of a pressure modulated desalination system using bond graph methodology

A desalination system is a complex multi energy domain system comprising power/energy flow across several domains such as electrical, thermal, and hydraulic. The dynamic modeling of a desalination system that comprehensively addresses all these multi energy domains is not adequately addressed in the literature. This paper proposes to address the issue of modeling the various energy domains for the case of a single stage flash evaporation desalination system. This paper presents a detailed bond graph modeling of a desalination unit with seamless integration of the power flow across electrical, thermal, and hydraulic domains. The paper further proposes a performance index function that leads to the tracking of the optimal chamber pressure giving the optimal flow rate for a given unit of energy expended. The model has been validated in steady state conditions by simulation and experimentation.

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

Bias reduction using stochastic approximation

The paper studies stochastic approximation as a technique for bias reduction. The proposed method does not require approximating the bias explicitly, nor does it rely on having independent identically distributed (i.i.d.) data. The method always removes the leading bias term, under very mild conditions, as long as auxiliary samples from distributions with given parameters are available. Expectation and variance of the bias-corrected estimate are given. Examples in sequential clinical trials (non-i.i.d. case), curved exponential models (i.i.d. case) and length-biased sampling (where the estimates are inconsistent) are used to illustrate the applications of the proposed method and its small sample properties.

Modeling the role of competition and cooperation in the evolution of katydid acoustic synchrony

The precise timing of individual signals in response to those of signaling neighbors is seen in many animal species. Synchrony is the most striking of the resultant timing patterns. One of the best examples of acoustic synchrony is in katydid choruses where males produce chirps with a high degree of temporal overlap. Cooperative hypotheses that speculate on the evolutionary origins of acousti synchrony include the preservation of the species-specific call pattern, reduced predation risks, and increased call intensity. An alternative suggestion is that synchrony evolved as an epiphenomenon of competition between males in response to a female preference for chirps that lead other chirps. Previous models investigating the evolutionary origins of synchrony focused only on intrasexual competitive interactions. We investigated both competitive and cooperative hypotheses for the evolution of synchrony in the katydid Mecopoda ``Chirper'' using physiologically and ecologically realistic simulation models incorporating the natural variation in call features, ecology, female preferences, and spacing patterns, specifically aggregation. We found that although a female preference for leading chirps enables synchronous males to have some selective advantage, it is the female preference for the increased intensity of aggregations of synchronous males that enables synchrony to evolve as an evolutionarily stable strategy.

Risk management strategies using seasonal climate forecasting in irrigated cotton production: a tale of stochastic dominance.

Decision-making in agriculture is carried out in an uncertain environment with farmers often seeking information to reduce risk. As a result of the extreme variability of rainfall and stream-flows in north-eastern Australia, water supplies for irrigated agriculture are a limiting factor and a source of risk. The present study examined the use of seasonal climate forecasting (SCF) when calculating planting areas for irrigated cotton in the northern Murray Darling Basin. Results show that minimising risk by adjusting plant areas in response to SCF can lead to significant gains in gross margin returns. However, how farmers respond to SCF is dependent on several other factors including irrigators’ attitude towards risk.

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ ε ⋅dσ from the constitutive equation relating the strain rate (ε) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

Modeling chickpea growth and development: Nitrogen accumulation and use

Quantitative information regarding nitrogen (N) accumulation and its distribution to leaves, stems and grains under varying environmental and growth conditions are limited for chickpea (Cicer arietinum L.). The information is required for the development of crop growth models and also for assessment of the contribution of chickpea to N balances in cropping systems. Accordingly, these processes were quantified in chickpea under different environmental and growth conditions (still without water or N deficit) using four field experiments and 1325 N measurements. N concentration ([N]) in green leaves was 50 mg g-1 up to beginning of seed growth, and then it declined linearly to 30 mg g-1 at the end of seed growth phase. [N] in senesced leaves was 12 mg g-1. Stem [N] decreased from 30 mg g-1 early in the season to 8 mg g-1 in senesced stems at maturity. Pod [N] was constant (35 mg g-1), but grain [N] decreased from 60 mg g-1 early in seed growth to 43 mg g-1 at maturity. Total N accumulation ranged between 9 and 30 g m-2. N accumulation was closely linked to biomass accumulation until maturity. N accumulation efficiency (N accumulation relative to biomass accumulation) was 0.033 g g-1 where total biomass was -2 and during early growth period, but it decreased to 0.0176 g g-1 during the later growth period when total biomass was >218 g m-2. During vegetative growth (up to first-pod), 58% of N was partitioned to leaves and 42% to stems. Depending on growth conditions, 37-72% of leaf N and 12-56% of stem N was remobilized to the grains. The parameter estimates and functions obtained in this study can be used in chickpea simulation models to simulate N accumulation and distribution.

Modeling growth of hydrogen bubbles in aluminum castings using the level-set method

A new approach is proposed to solve for the growth as well as the movement of hydrogen bubbles during solidification in aluminum castings. A level-set methodology has been adopted to handle this multiphase phenomenon. A microscale domain is considered and the growth and movement of hydrogen bubbles in this domain has been studied. The growth characteristics of hydrogen bubbles have been evaluated under free growth conditions in a melt having a hydrogen input caused b solidification occurring around the microdomain.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Optimal Parameter Trajectory Estimation in Parameterized SDEs: An Algorithmic Procedure

We consider the problem of estimating the optimal parameter trajectory over a finite time interval in a parameterized stochastic differential equation (SDE), and propose a simulation-based algorithm for this purpose. Towards this end, we consider a discretization of the SDE over finite time instants and reformulate the problem as one of finding an optimal parameter at each of these instants. A stochastic approximation algorithm based on the smoothed functional technique is adapted to this setting for finding the optimal parameter trajectory. A proof of convergence of the algorithm is presented and results of numerical experiments over two different settings are shown. The algorithm is seen to exhibit good performance. We also present extensions of our framework to the case of finding optimal parameterized feedback policies for controlled SDE and present numerical results in this scenario as well.

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1. Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity. 2. We analyse a stochastic environment model of the red kangaroo (Macropus rufus), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates. 3. Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate. 4. Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates. 5. Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c. 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c. 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

PMU measurement based dynamic load modeling using SVC devices in online environment

Online dynamic load modeling has become possible with the availability of Static Voltage Compensator (SVC) and Phasor Measurement Unit (PMU) devices. The power of the load response to the small random bounded voltage fluctuations caused from SVC can be measured by PMU for modelling purposes. The aim of this paper is to illustrate the capability of identifying an aggregated load model from high voltage substation level in the online environment. The induction motor is used as the main test subject since it contributes the majority of the dynamic loads. A test system representing simple electromechanical generator model serving dynamic loads through the transmission network is used to verify the proposed method. Also, dynamic load with multiple induction motors are modeled to achieve a better realistic load representation.