Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method

The method of generalized estimating equations (GEEs) provides consistent estimates of the regression parameters in a marginal regression model for longitudinal data, even when the working correlation model is misspecified (Liang and Zeger, 1986). However, the efficiency of a GEE estimate can be seriously affected by the choice of the working correlation model. This study addresses this problem by proposing a hybrid method that combines multiple GEEs based on different working correlation models, using the empirical likelihood method (Qin and Lawless, 1994). Analyses show that this hybrid method is more efficient than a GEE using a misspecified working correlation model. Furthermore, if one of the working correlation structures correctly models the within-subject correlations, then this hybrid method provides the most efficient parameter estimates. In simulations, the hybrid method's finite-sample performance is superior to a GEE under any of the commonly used working correlation models and is almost fully efficient in all scenarios studied. The hybrid method is illustrated using data from a longitudinal study of the respiratory infection rates in 275 Indonesian children.

Estimation for the general sample selection models

Consider a general regression model with an arbitrary and unknown link function and a stochastic selection variable that determines whether the outcome variable is observable or missing. The paper proposes U-statistics that are based on kernel functions as estimators for the directions of the parameter vectors in the link function and the selection equation, and shows that these estimators are consistent and asymptotically normal.

A quasi-likelihood method for fractal-dimension estimation

We propose a simple method of constructing quasi-likelihood functions for dependent data based on conditional-mean-variance relationships, and apply the method to estimating the fractal dimension from box-counting data. Simulation studies were carried out to compare this method with the traditional methods. We also applied this technique to real data from fishing grounds in the Gulf of Carpentaria, Australia

Robust estimation using the Huber function with a data-dependent tuning constant

Robust estimation often relies on a dispersion function that is more slowly varying at large values than the square function. However, the choice of tuning constant in dispersion functions may impact the estimation efficiency to a great extent. For a given family of dispersion functions such as the Huber family, we suggest obtaining the "best" tuning constant from the data so that the asymptotic efficiency is maximized. This data-driven approach can automatically adjust the value of the tuning constant to provide the necessary resistance against outliers. Simulation studies show that substantial efficiency can be gained by this data-dependent approach compared with the traditional approach in which the tuning constant is fixed. We briefly illustrate the proposed method using two datasets.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Effect of individual variability on estimation of population parameters from length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock when there is individual variability in the von Bertalanffy growth parameter L-infinity and investigate the possible bias in the estimates when the individual variability is ignored. Three methods are examined: (i) the regression method based on the Beverton and Holt's (1956, Rapp. P.V. Reun. Cons. Int. Explor. Mer, 140: 67-83) equation; (ii) the moment method of Powell (1979, Rapp. PV. Reun. Int. Explor. Mer, 175: 167-169); and (iii) a generalization of Powell's method that estimates the individual variability to be incorporated into the estimation. It is found that the biases in the estimates from the existing methods are, in general, substantial, even when individual variability in growth is small and recruitment is uniform, and the generalized method performs better in terms of bias but is subject to a larger variation. There is a need to develop robust and flexible methods to deal with individual variability in the analysis of length-frequency data.

An improved Fabens method for estimation of growth parameters in the vonBertalanffy model with individual asymptotes

In the analysis of tagging data, it has been found that the least-squares method, based on the increment function known as the Fabens method, produces biased estimates because individual variability in growth is not allowed for. This paper modifies the Fabens method to account for individual variability in the length asymptote. Significance tests using t-statistics or log-likelihood ratio statistics may be applied to show the level of individual variability. Simulation results indicate that the modified method reduces the biases in the estimates to negligible proportions. Tagging data from tiger prawns (Penaeus esculentus and Penaeus semisulcatus) and rock lobster (Panulirus ornatus) are analysed as an illustration.

Growth curves with explanatory variables and estimation of the effect of tagging

The von Bertalanffy growth model is extended to incorporate explanatory variables. The generalized model includes the switched growth model and the seasonal growth model as special cases, and can also be used to assess the tagging effect on growth. Distribution-free and consistent estimating functions are constructed for estimation of growth parameters from tag-recapture data in which age at release is unknown. This generalizes the work of James (1991, Biometrics 47 1519-1530) who considered the classical model and allowed for individual variability in growth. A real dataset from barramundi (Lates calcarifer) is analysed to estimate the growth parameters and possible effect of tagging on growth.

Traffic and nucleation events as main sources of ultrafine particles in high-insolation developed world cities

Road traffic emissions are often considered the main source of ultrafine particles (UFP, diameter smaller than 100 nm) in urban environments. However, recent studies worldwide have shown that - in high-insolation urban regions at least - new particle formation events can also contribute to UFP. In order to quantify such events we systematically studied three cities located in predominantly sunny environments: Barcelona (Spain), Madrid (Spain) and Brisbane (Australia). Three long term datasets (1-2 years) of fine and ultrafine particle number size distributions (measured by SMPS, Scanning Mobility Particle Sizer) were analysed. Compared to total particle number concentrations, aerosol size distributions offer far more information on the type, origin and atmospheric evolution of the particles. By applying k-Means clustering analysis, we categorized the collected aerosol size distributions in three main categories: “Traffic” (prevailing 44-63% of the time), “Nucleation” (14-19%) and “Background pollution and Specific cases” (7-22%). Measurements from Rome (Italy) and Los Angeles (California) were also included to complement the study. The daily variation of the average UFP concentrations for a typical nucleation day at each site revealed a similar pattern for all cities, with three distinct particle bursts. A morning and an evening spike reflected traffic rush hours, whereas a third one at midday showed nucleation events. The photochemically nucleated particles burst lasted 1-4 hours, reaching sizes of 30-40 nm. On average, the occurrence of particle size spectra dominated by nucleation events was 16% of the time, showing the importance of this process as a source of UFP in urban environments exposed to high solar radiation. On average, nucleation events lasting for 2 hours or more occurred on 55% of the days, this extending to >4hrs in 28% of the days, demonstrating that atmospheric conditions in urban environments are not favourable to the growth of photochemically nucleated particles. In summary, although traffic remains the main source of UFP in urban areas, in developed countries with high insolation urban nucleation events are also a main source of UFP. If traffic-related particle concentrations are reduced in the future, nucleation events will likely increase in urban areas, due to the reduced urban condensation sinks.

The influence of pre-processing on the estimation of readability of web documents

This paper investigates the effect that text pre-processing approaches have on the estimation of the readability of web pages. Readability has been highlighted as an important aspect of web search result personalisation in previous work. The most widely used text readability measures rely on surface level characteristics of text, such as the length of words and sentences. We demonstrate that different tools for extracting text from web pages lead to very different estimations of readability. This has an important implication for search engines because search result personalisation strategies that consider users reading ability may fail if incorrect text readability estimations are computed.

Traffic safety at road–rail level crossings using a driving simulator and traffic simulation

Several intelligent transportation systems (ITS) were used with an advanced driving simulator to assess its influence on driving behavior. Three types of ITS interventions were tested: video in vehicle, audio in vehicle, and on-road flashing marker. The results from the driving simulator were inputs for a developed model that used traffic microsimulation (VISSIM 5.4) to assess the safety interventions. Using a driving simulator, 58 participants were required to drive through active and passive crossings with and without an ITS device and in the presence or absence of an approaching train. The effect of changes in driver speed and compliance rate was greater at passive crossings than at active crossings. The slight difference in speed of drivers approaching ITS devices indicated that ITS helped drivers encounter crossings in a safer way. Since the traffic simulation was not able to replicate a dynamic speed change or a probability of stopping that varied depending on ITS safety devices, some modifications were made to the traffic simulation. The results showed that exposure to ITS devices at active crossings did not influence drivers’ behavior significantly according to the traffic performance indicator, such as delay time, number of stops, speed, and stopped delay. However, the results of traffic simulation for passive crossings, where low traffic volumes and low train headway normally occur, showed that ITS devices improved overall traffic performance.

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.