Quantile composite-based path modeling: algorithms, properties and applications

Composite-based path modeling aims to study the relationships among a set of constructs, that is a representation of theoretical concepts. Such constructs are operationalized as composites (i.e. linear combinations of observed or manifest variables). The traditional partial least squares approach to composite-based path modeling focuses on the conditional means of the response distributions, being based on ordinary least squares regressions. Several are the cases where limiting to the mean could not reveal interesting effects at other locations of the outcome variables. Among these: when response variables are highly skewed, distributions have heavy tails and the analysis is concerned also about the tail part, heteroscedastic variances of the errors is present, distributions are characterized by outliers and other extreme data. In such cases, the quantile approach to path modeling is a valuable tool to complement the traditional approach, analyzing the entire distribution of outcome variables. Previous research has already shown the benefits of Quantile Composite-based Path Modeling but the methodological properties of the method have never been investigated. This paper offers a complete description of Quantile Composite-based Path Modeling, illustrating in details the method, the algorithms, the partial optimization criteria along with the machinery for validating and assessing the models. The asymptotic properties of the method are investigated through a simulation study. Moreover, an application on chronic kidney disease in diabetic patients is used to provide guidelines for the interpretation of results and to show the potentialities of the method to detect heterogeneity in the variable relationships.

Relationship of Trace Metal Covariates and pH Distribution in Groundwater within Gold mining and Non-Gold mining Areas in Ghana

One of the most important defining characteristics of groundwater quality is pH as it fundamentally controls the amount and chemical form of many organic and inorganic solutes in groundwater. Groundwater data are frequently characterized by a wide degree of variability of the factors which possibly influence pH distribution. For this reason, it is challenging to link the spatio-temporal dynamics of pH to a single environmental factor by the ordinary least squares regression technique of the conditional mean. In this study, quantile regression was used to estimate the response of pH to nine environmental factors (As, Cd, Fe, Mn, Pb, turbidity, electrical conductivity, total dissolved solids and nitrates). Results of 25%, 50%, 75% quantile regression and ordinary least squares (OLS) regression were compared. The standard regression of the conditional means (OLS) underestimated the rates of change of pH due to the selected factors in comparison with the regression quantiles. The effect of arsenic increased for sampling locations with higher pH values (higher quantiles) likewise the influence of Pb and Mn. However, the effects of Cd and Fe decreased for sampling locations in higher quantiles. It can be concluded that these detected heterogeneities would be missed if this study had focused exclusively on the conditional means of the pH values. Consequently, quantile regression provides a more comprehensive account of possible spatio-temporal relationships between environmental covariates in groundwater. This study is one of the first to apply this technique on groundwater systems in sub-Saharan Africa. The approach is useful and interesting and has broad application for other mining environments especially tropical low-income countries where climatic conditions can drive rapid cycling or transformations of pollutants. It is also pertinent to geopolitical contexts where regulatory; monitoring and management capacities are weak and where mining pollution of groundwater largely occur.

Bond risk premia in consumption‐based models

Gaussian affine term structure models attribute time‐varying bond risk premia to changing risk prices driven by the conditional means of the risk factors, while structural models with recursive preferences credit it to stochastic volatility. We reconcile these competing channels by introducing a novel form of stochastic rate of time preference into an otherwise standard model with recursive preferences. Our model is affine and has analytical bond prices making it empirically tractable. We use particle Markov chain Monte Carlo to estimate the model, and find that time variation in bond term premia is predominantly driven by the risk price channel.

Glances That Matter: Applying Quantile Regression to Assess Driver Distraction from Off-Road Glances

This study assessed whether quantile regression can identify design specifications that lead to particularly long glances, which might go unnoticed with traditional analyses focusing on conditional means of off-road glances. Although substantial research indicates that long glances contribute disproportionately to crash risk, few studies have directly assessed the tails of the distribution. Failing to examine the distribution tails might underestimate the disproportionate risk on long glances imposed by secondary tasks. We applied quantile regression to assess the effects of secondary task type (reading or entry), system delay (delay or no delay), and text length (long or short) on off-road glance duration at 15th, 50th, and 85th quantiles. The results show that entry task, long text, and some combinations of variables led to longer glances than that would be expected given the central tendency of glance distributions. Quantile regression identifies secondary task features that produce long glances, which might be neglected by traditional analyses with conditional means.

Repeated responses in misclassification binary regression: A Bayesian approach

Binary regression models generally assume that the response variable is measured perfectly. However, in some situations, the outcome is subject to misclassification: a success may be erroneously classified as a failure or vice versa. Many methods, described in existing literature, have been developed to deal with misclassification, but we demonstrate that these methods may lead to serious inferential problems when only a single evaluation of the individual is taken. Thus, this study proposes to incorporate repeated and independent responses in misclassification binary regression models, considering the total number of successes obtained or even the simple majority classification. We use subjective prior distributions, as our conditional means prior, to evaluate and compare models. A data augmentation approach, Gibbs sampling, and Adaptive Rejection Metropolis Sampling are used for posterior inferences. Simulation studies suggested that repeated measures significantly improve the posterior estimates, in that these estimates are closer to those obtained in a case with no misclassifications with a lower standard deviation. Finally, we illustrate the usefulness of the new methodology with the analysis about defects in eyeglass lenses.

A probability based method for selecting the optimal personalized treatment from multiple treatments

In this work we propose a method for optimal treatment assignment based on individual covariate information for a patient. For the K treatment ([Formula: see text]) scenario, we compare quantities that are suitable surrogates to true conditional probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient specific scores constructed from patient-specific covariates. As opposed to methods based on conditional means, our method can be applied for a broad set of models and error structures. Furthermore, the proposed method has very desirable large sample properties. We suggest Single Index Models as appropriate models connecting outcome variables to covariates and our empirical investigations show that correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a Single Index Model structure. Furthermore, selection of a treatment using the proposed metric appears to incur no losses in terms of the average reward for cases when two treatments are close in terms of this metric. We also conduct a real data analysis to show the applicability of the proposed procedure. This analysis highlights possible gains both in terms of average response and survival time if one were to use the proposed method.

Robust functional regression model for marginal mean and subject-specific inferences

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well as interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals (PIs) for conditional mean curves. Numerical studies show that the proposed model provides a robust approach against data contamination or distribution misspecification, and the proposed PIs maintain the nominal confidence levels. A real data application is presented as an illustrative example.