Iteratively specified tree-based regression : theory and trip generation example

Focuses on a study which introduced an iterative modeling method that combines properties of ordinary least squares (OLS) with hierarchical tree-based regression (HTBR) in transportation engineering. Information on OLS and HTBR; Comparison and contrasts of OLS and HTBR; Conclusions.

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros

Identification of factors contributing to recurrence of venous leg ulcers

Background and Significance Venous leg ulcers are a significant cause of chronic ill-health for 1–3% of those aged over 60 years, increasing in incidence with age. The condition is difficult and costly to heal, consuming 1–2.5% of total health budgets in developed countries and up to 50% of community nursing time. Unfortunately after healing, there is a recurrence rate of 60 to 70%, frequently within the first 12 months after heaing. Although some risk factors associated with higher recurrence rates have been identified (e.g. prolonged ulcer duration, deep vein thrombosis), in general there is limited evidence on treatments to effectively prevent recurrence. Patients are generally advised to undertake activities which aim to improve the impaired venous return (e.g. compression therapy, leg elevation, exercise). However, only compression therapy has some evidence to support its effectiveness in prevention and problems with adherence to this strategy are well documented. Aim The aim of this research was to identify factors associated with recurrence by determining relationships between recurrence and demographic factors, health, physical activity, psychosocial factors and self-care activities to prevent recurrence. Methods Two studies were undertaken: a retrospective study of participants diagnosed with a venous leg ulcer which healed 12 to 36 months prior to the study (n=122); and a prospective longitudinal study of participants recruited as their ulcer healed and data collected for 12 months following healing (n=80). Data were collected from medical records on demographics, medical history and ulcer history and treatments; and from self-report questionnaires on physical activity, nutrition, psychosocial measures, ulcer history, compression and other self-care activities. Follow-up data for the prospective study were collected every three months for 12 months after healing. For the retrospective study, a logistic regression model determined the independent influences of variables on recurrence. For the prospective study, median time to recurrence was calculated using the Kaplan-Meier method and a Cox proportional-hazards regression model was used to adjust for potential confounders and determine effects of preventive strategies and psychosocial factors on recurrence. Results In total, 68% of participants in the retrospective study and 44% of participants in the prospective study suffered a recurrence. After mutual adjustment for all variables in multivariable regression models, leg elevation, compression therapy, self efficacy and physical activity were found to be consistently related to recurrence in both studies. In the retrospective study, leg elevation, wearing Class 2 or 3 compression hosiery, the level of physical activity, cardiac disease and self efficacy scores remained significantly associated (p<0.05) with recurrence. The model was significant (p <0.001); with a R2 equivalent of 0.62. Examination of relationships between psychosocial factors and adherence to wearing compression hosiery found wearing compression hosiery was significantly positively associated with participants’ knowledge of the cause of their condition (p=0.002), higher self-efficacy scores (p=0.026) and lower depression scores (p=0.009). Analysis of data from the prospective study found there were 35 recurrences (44%) in the 12 months following healing and median time to recurrence was 27 weeks. After adjustment for potential confounders, a Cox proportional hazards regression model found that at least an hour/day of leg elevation, six or more days/week in Class 2 (20–25mmHg) or 3 (30–40mmHg) compression hosiery, higher social support scale scores and higher General Self-Efficacy scores remained significantly associated (p<0.05) with a lower risk of recurrence, while male gender and a history of DVT remained significant risk factors for recurrence. Overall the model was significant (p <0.001); with an R2 equivalent 0.72. Conclusions The high rates of recurrence found in the studies highlight the urgent need for further information in this area to support development of effective strategies for prevention. Overall, results indicate leg elevation, physical activity, compression hosiery and strategies to improve self-efficacy are likely to prevent recurrence. In addition, optimal management of depression and strategies to improve patient knowledge and self-efficacy may positively influence adherence to compression therapy. This research provides important information for development of strategies to prevent recurrence of venous leg ulcers, with the potential to improve health and decrease health care costs in this population.

Relationships between preventive activities, psychosocial factors and recurrence of venous leg ulcers : a prospective study

Aim To identify relationships between preventive activities, psychosocial factors and leg ulcer recurrence in patients with chronic venous leg ulcers. Background Chronic venous leg ulcers are slow to heal and frequently recur, resulting in years of suffering and intensive use of health care resources. Methods A prospective longitudinal study was undertaken with a sample of 80 patients with a venous leg ulcer recruited when their ulcer healed. Data were collected from 2006–2009 from medical records on demographics, medical history and ulcer history; and from self-report questionnaires on physical activity, nutrition, preventive activities and psychosocial measures. Follow-up data were collected via questionnaires every three months for 12 months after healing. Median time to recurrence was calculated using the Kaplan-Meier method. A Cox proportional-hazards regression model was used to adjust for potential confounders and determine effects of preventive strategies and psychosocial factors on recurrence. Results: There were 35 recurrences in a sample of 80 participants. Median time to recurrence was 27 weeks. After adjustment for potential confounders, a Cox proportional hazards regression model found that at least an hour/day of leg elevation, six or more days/week in Class 2 (20–25mmHg) or 3 (30–40mmHg) compression hosiery, higher social support scale scores and higher General Self-Efficacy scores remained significantly associated (p<0.05) with a lower risk of recurrence, while male gender and a history of DVT remained significant risk factors for recurrence. Conclusion Results indicate that leg elevation, compression hosiery, high levels of self-efficacy and strong social support will help prevent recurrence.

Multi-step ahead direct prediction for the machine condition prognosis using regression trees and neuro-fuzzy systems

This paper presents an approach to predict the operating conditions of machine based on classification and regression trees (CART) and adaptive neuro-fuzzy inference system (ANFIS) in association with direct prediction strategy for multi-step ahead prediction of time series techniques. In this study, the number of available observations and the number of predicted steps are initially determined by using false nearest neighbor method and auto mutual information technique, respectively. These values are subsequently utilized as inputs for prediction models to forecast the future values of the machines’ operating conditions. The performance of the proposed approach is then evaluated by using real trending data of low methane compressor. A comparative study of the predicted results obtained from CART and ANFIS models is also carried out to appraise the prediction capability of these models. The results show that the ANFIS prediction model can track the change in machine conditions and has the potential for using as a tool to machine fault prognosis.

Adding a receding horizon to Locally Weighted Regression for learning robot control

There have been notable advances in learning to control complex robotic systems using methods such as Locally Weighted Regression (LWR). In this paper we explore some potential limits of LWR for robotic applications, particularly investigating its application to systems with a long horizon of temporal dependence. We define the horizon of temporal dependence as the delay from a control input to a desired change in output. LWR alone cannot be used in a temporally dependent system to find meaningful control values from only the current state variables and output, as the relationship between the input and the current state is under-constrained. By introducing a receding horizon of the future output states of the system, we show that sufficient constraint is applied to learn good solutions through LWR. The new method, Receding Horizon Locally Weighted Regression (RH-LWR), is demonstrated through one-shot learning on a real Series Elastic Actuator controlling a pendulum.

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.

Predicting residue-wise contact orders in proteins by support vector regression

Background The residue-wise contact order (RWCO) describes the sequence separations between the residues of interest and its contacting residues in a protein sequence. It is a new kind of one-dimensional protein structure that represents the extent of long-range contacts and is considered as a generalization of contact order. Together with secondary structure, accessible surface area, the B factor, and contact number, RWCO provides comprehensive and indispensable important information to reconstructing the protein three-dimensional structure from a set of one-dimensional structural properties. Accurately predicting RWCO values could have many important applications in protein three-dimensional structure prediction and protein folding rate prediction, and give deep insights into protein sequence-structure relationships. Results We developed a novel approach to predict residue-wise contact order values in proteins based on support vector regression (SVR), starting from primary amino acid sequences. We explored seven different sequence encoding schemes to examine their effects on the prediction performance, including local sequence in the form of PSI-BLAST profiles, local sequence plus amino acid composition, local sequence plus molecular weight, local sequence plus secondary structure predicted by PSIPRED, local sequence plus molecular weight and amino acid composition, local sequence plus molecular weight and predicted secondary structure, and local sequence plus molecular weight, amino acid composition and predicted secondary structure. When using local sequences with multiple sequence alignments in the form of PSI-BLAST profiles, we could predict the RWCO distribution with a Pearson correlation coefficient (CC) between the predicted and observed RWCO values of 0.55, and root mean square error (RMSE) of 0.82, based on a well-defined dataset with 680 protein sequences. Moreover, by incorporating global features such as molecular weight and amino acid composition we could further improve the prediction performance with the CC to 0.57 and an RMSE of 0.79. In addition, combining the predicted secondary structure by PSIPRED was found to significantly improve the prediction performance and could yield the best prediction accuracy with a CC of 0.60 and RMSE of 0.78, which provided at least comparable performance compared with the other existing methods. Conclusion The SVR method shows a prediction performance competitive with or at least comparable to the previously developed linear regression-based methods for predicting RWCO values. In contrast to support vector classification (SVC), SVR is very good at estimating the raw value profiles of the samples. The successful application of the SVR approach in this study reinforces the fact that support vector regression is a powerful tool in extracting the protein sequence-structure relationship and in estimating the protein structural profiles from amino acid sequences.

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.

Operational performance of low-cost carriers and international airlines : New evidence using a bootstrap truncated regression

Between 2001 and 2005, the US airline industry faced financial turmoil. At the same time, the European airline industry entered a period of substantive deregulation. This period witnessed opportunities for low-cost carriers to become more competitive in the market as a result of these combined events. To help assess airline performance in the aftermath of these events, this paper provides new evidence of technical efficiency for 42 national and international airlines in 2006 using the data envelopment analysis (DEA) bootstrap approach first proposed by Simar and Wilson (J Econ, 136:31-64, 2007). In the first stage, technical efficiency scores are estimated using a bootstrap DEA model. In the second stage, a truncated regression is employed to quantify the economic drivers underlying measured technical efficiency. The results highlight the key role played by non-discretionary inputs in measures of airline technical efficiency.