Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.

Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

On Time Series Analysis of Public Health and Biomedical Data

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

Experimental and modeling study of the filtration and oxidation characteristics of a diesel oxidation catalyst and a catalyzed particulate filter

A diesel oxidation catalyst (DOC) with a catalyzed diesel particulate filter (CPF) is an effective exhaust aftertreatment device that reduces particulate emissions from diesel engines, and properly designed DOC-CPF systems provide passive regeneration of the filter by the oxidation of PM via thermal and NO2/temperature-assisted means under various vehicle duty cycles. However, controlling the backpressure on engines caused by the addition of the CPF to the exhaust system requires a good understanding of the filtration and oxidation processes taking place inside the filter as the deposition and oxidation of solid particulate matter (PM) change as functions of loading time. In order to understand the solid PM loading characteristics in the CPF, an experimental and modeling study was conducted using emissions data measured from the exhaust of a John Deere 6.8 liter, turbocharged and after-cooled engine with a low-pressure loop EGR system and a DOC-CPF system (or a CCRT® - Catalyzed Continuously Regenerating Trap®, as named by Johnson Matthey) in the exhaust system. A series of experiments were conducted to evaluate the performance of the DOC-only, CPF-only and DOC-CPF configurations at two engine speeds (2200 and 1650 rpm) and various loads on the engine ranging from 5 to 100% of maximum torque at both speeds. Pressure drop across the DOC and CPF, mass deposited in the CPF at the end of loading, upstream and downstream gaseous and particulate emissions, and particle size distributions were measured at different times during the experiments to characterize the pressure drop and filtration efficiency of the DOCCPF system as functions of loading time. Pressure drop characteristics measured experimentally across the DOC-CPF system showed a distinct deep-bed filtration region characterized by a non-linear pressure drop rise, followed by a transition region, and then by a cake-filtration region with steadily increasing pressure drop with loading time at engine load cases with CPF inlet temperatures less than 325 °C. At the engine load cases with CPF inlet temperatures greater than 360 °C, the deep-bed filtration region had a steep rise in pressure drop followed by a decrease in pressure drop (due to wall PM oxidation) in the cake filtration region. Filtration efficiencies observed during PM cake filtration were greater than 90% in all engine load cases. Two computer models, i.e., the MTU 1-D DOC model and the MTU 1-D 2-layer CPF model were developed and/or improved from existing models as part of this research and calibrated using the data obtained from these experiments. The 1-D DOC model employs a three-way catalytic reaction scheme for CO, HC and NO oxidation, and is used to predict CO, HC, NO and NO2 concentrations downstream of the DOC. Calibration results from the 1-D DOC model to experimental data at 2200 and 1650 rpm are presented. The 1-D 2-layer CPF model uses a ‘2-filters in series approach’ for filtration, PM deposition and oxidation in the PM cake and substrate wall via thermal (O2) and NO2/temperature-assisted mechanisms, and production of NO2 as the exhaust gas mixture passes through the CPF catalyst washcoat. Calibration results from the 1-D 2-layer CPF model to experimental data at 2200 rpm are presented. Comparisons of filtration and oxidation behavior of the CPF at sample load-cases in both configurations are also presented. The input parameters and selected results are also compared with a similar research work with an earlier version of the CCRT®, to compare and explain differences in the fundamental behavior of the CCRT® used in these two research studies. An analysis of the results from the calibrated CPF model suggests that pressure drop across the CPF depends mainly on PM loading and oxidation in the substrate wall, and also that the substrate wall initiates PM filtration and helps in forming a PM cake layer on the wall. After formation of the PM cake layer of about 1-2 µm on the wall, the PM cake becomes the primary filter and performs 98-99% of PM filtration. In all load cases, most of PM mass deposited was in the PM cake layer, and PM oxidation in the PM cake layer accounted for 95-99% of total PM mass oxidized during loading. Overall PM oxidation efficiency of the DOC-CPF device increased with increasing CPF inlet temperatures and NO2 flow rates, and was higher in the CCRT® configuration compared to the CPF-only configuration due to higher CPF inlet NO2 concentrations. Filtration efficiencies greater than 90% were observed within 90-100 minutes of loading time (starting with a clean filter) in all load cases, due to the fact that the PM cake on the substrate wall forms a very efficient filter. A good strategy for maintaining high filtration efficiency and low pressure drop of the device while performing active regeneration would be to clean the PM cake filter partially (i.e., by retaining a cake layer of 1-2 µm thickness on the substrate wall) and to completely oxidize the PM deposited in the substrate wall. The data presented support this strategy.

Model to describe the mode I fracture of steel fiber reinforced ultra-high performance concrete

Ultra-high performance fiber reinforced concrete (UHPFRC) has arisen from the implementation of a variety of concrete engineering and materials science concepts developed over the last century. This material offers superior strength, serviceability, and durability over its conventional counterparts. One of the most important differences for UHPFRC over other concrete materials is its ability to resist fracture through the use of randomly dispersed discontinuous fibers and improvements to the fiber-matrix bond. Of particular interest is the materials ability to achieve higher loads after first crack, as well as its high fracture toughness. In this research, a study of the fracture behavior of UHPFRC with steel fibers was conducted to look at the effect of several parameters related to the fracture behavior and to develop a fracture model based on a non-linear curve fit of the data. To determine this, a series of three-point bending tests were performed on various single edge notched prisms (SENPs). Compression tests were also performed for quality assurance. Testing was conducted on specimens of different cross-sections, span/depth (S/D) ratios, curing regimes, ages, and fiber contents. By comparing the results from prisms of different sizes this study examines the weakening mechanism due to the size effect. Furthermore, by employing the concept of fracture energy it was possible to obtain a comparison of the fracture toughness and ductility. The model was determined based on a fit to P-w fracture curves, which was cross referenced for comparability to the results. Once obtained the model was then compared to the models proposed by the AFGC in the 2003 and to the ACI 544 model for conventional fiber reinforced concretes.

Sampling-Design Effects on Properties of Species-Area Relationships - A Case Study from Estonian Dry Grassland Communities

Despite widespread use of species-area relationships (SARs), dispute remains over the most representative SAR model. Using data of small-scale SARs of Estonian dry grassland communities, we address three questions: (1) Which model describes these SARs best when known artifacts are excluded? (2) How do deviating sampling procedures (marginal instead of central position of the smaller plots in relation to the largest plot; single values instead of average values; randomly located subplots instead of nested subplots) influence the properties of the SARs? (3) Are those effects likely to bias the selection of the best model? Our general dataset consisted of 16 series of nested-plots (1 cm(2)-100 m(2), any-part system), each of which comprised five series of subplots located in the four corners and the centre of the 100-m(2) plot. Data for the three pairs of compared sampling designs were generated from this dataset by subsampling. Five function types (power, quadratic power, logarithmic, Michaelis-Menten, Lomolino) were fitted with non-linear regression. In some of the communities, we found extremely high species densities (including bryophytes and lichens), namely up to eight species in 1 cm(2) and up to 140 species in 100 m(2), which appear to be the highest documented values on these scales. For SARs constructed from nested-plot average-value data, the regular power function generally was the best model, closely followed by the quadratic power function, while the logarithmic and Michaelis-Menten functions performed poorly throughout. However, the relative fit of the latter two models increased significantly relative to the respective best model when the single-value or random-sampling method was applied, however, the power function normally remained far superior. These results confirm the hypothesis that both single-value and random-sampling approaches cause artifacts by increasing stochasticity in the data, which can lead to the selection of inappropriate models.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

Ein neues psychoendokrin-validiertes Verfahren zur Erfassung von Stressbewältigungsfertigkeiten (ISBF)

Background: We previously found good psychometric properties of the Inventory for assessment of stress management skills (German translation: Inventar zur Erfassung von Stressbewältigungsfertigkeiten), ISBF, a short questionnaire for combined assessment of different perceived stress management skills in the general population. Here, we investigate whether stress management skills as measured by ISBF relate to cortisol stress reactivity in two independent studies, a laboratory study (study 1) and a field study (study 2). Methods: 35 healthy non-smoking and medication-free men in study 1 (age mean±SEM:38.0±1.6) and 35 male and female employees in study 2 (age mean±SEM:32.9±1.2) underwent an acute standardized psychosocial stress task combining public speaking and mental arithmetic in front of an audience. We assessed stress management skills (ISBF) and measured salivary cortisol before and after stress and several times up to 60 min (study 2) and 120 min (study 1) thereafter. Potential confounders were controlled. Results:. General linear models controlling for potential confounders revealed that in both studies, higher stress management skills (ISBF total score) were independently associated with lower cortisol levels before and after stress (main effects ISBF: p’s<.055) and lower cortisol stress reactivity (interaction ISBF-by-stress: p’s<.029). Post-hoc-testing of ISBF subscales suggest lower cortisol stress reactivity with higher “relaxation abilities” (both studies) and higher scores in the scale “cognitive strategies and problem solving” (study 2). Conclusions: Our findings suggest blunted increases in cortisol following stress with increasing stress management skills as measured by ISBF. This suggests that the ISBF not only relates to subjective psychological but also objective physiological stress indicators which may further underscore the validity of the questionnaire.

Ar diffusion in K-feldspar: present and absent

The mechanisms of Ar release from K-feldspar samples in laboratory experiments and during their geological history are assessed here. Modern petrology clearly established that the chemical and isotopic record of minerals is normally dominated by aqueous recrystallization. The laboratory critique is trickier, which explains why so many conflicting approaches have been able to survive long past their expiration date. Current models are evaluated for self-consistency; especially Arrhenian non-linearity leads to paradoxes. The models’ testable geological predictions suggest that temperature-based downslope extrapolations often overestimate observed geological Ar mobility substantially. An updated interpretation is based on the unrelatedness of geological behaviour to laboratory experiments. The isotopic record of K-feldspar in geological samples is not a unique function of temperature, as recrystallisation promoted by aqueous fluids is the predominant mechanism controlling isotope transport. K-feldspar should therefore be viewed as a hygrochronometer. Laboratory degassing proceeds from structural rearrangements and phase transitions such as are observed in situ at high temperature in Na and Pb feldspars. These effects violate the mathematics of an inert Fick’s Law matrix and preclude downslope extrapolation. The similar upward-concave, non-linear shapes of Arrhenius trajectories of many silicates, hydrous and anhydrous, are likely common manifestations of structural rearrangements in silicate structures.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Present state of global wetland extent and wetland methane modelling: conclusions from a model inter-comparison project (WETCHIMP)

Global wetlands are believed to be climate sensitive, and are the largest natural emitters of methane (CH4). Increased wetland CH4 emissions could act as a positive feedback to future warming. The Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) investigated our present ability to simulate large-scale wetland characteristics and corresponding CH4 emissions. To ensure inter-comparability, we used a common experimental protocol driving all models with the same climate and carbon dioxide (CO2) forcing datasets. The WETCHIMP experiments were conducted for model equilibrium states as well as transient simulations covering the last century. Sensitivity experiments investigated model response to changes in selected forcing inputs (precipitation, temperature, and atmospheric CO2 concentration). Ten models participated, covering the spectrum from simple to relatively complex, including models tailored either for regional or global simulations. The models also varied in methods to calculate wetland size and location, with some models simulating wetland area prognostically, while other models relied on remotely sensed inundation datasets, or an approach intermediate between the two. Four major conclusions emerged from the project. First, the suite of models demonstrate extensive disagreement in their simulations of wetland areal extent and CH4 emissions, in both space and time. Simple metrics of wetland area, such as the latitudinal gradient, show large variability, principally between models that use inundation dataset information and those that independently determine wetland area. Agreement between the models improves for zonally summed CH4 emissions, but large variation between the models remains. For annual global CH4 emissions, the models vary by ±40% of the all-model mean (190 Tg CH4 yr−1). Second, all models show a strong positive response to increased atmospheric CO2 concentrations (857 ppm) in both CH4 emissions and wetland area. In response to increasing global temperatures (+3.4 °C globally spatially uniform), on average, the models decreased wetland area and CH4 fluxes, primarily in the tropics, but the magnitude and sign of the response varied greatly. Models were least sensitive to increased global precipitation (+3.9 % globally spatially uniform) with a consistent small positive response in CH4 fluxes and wetland area. Results from the 20th century transient simulation show that interactions between climate forcings could have strong non-linear effects. Third, we presently do not have sufficient wetland methane observation datasets adequate to evaluate model fluxes at a spatial scale comparable to model grid cells (commonly 0.5°). This limitation severely restricts our ability to model global wetland CH4 emissions with confidence. Our simulated wetland extents are also difficult to evaluate due to extensive disagreements between wetland mapping and remotely sensed inundation datasets. Fourth, the large range in predicted CH4 emission rates leads to the conclusion that there is both substantial parameter and structural uncertainty in large-scale CH4 emission models, even after uncertainties in wetland areas are accounted for.

Towards a taxonomy of common factors in psychotherapy-results of an expert survey

BACKGROUND: How change comes about is hotly debated in psychotherapy research. One camp considers 'non-specific' or 'common factors', shared by different therapy approaches, as essential, whereas researchers of the other camp consider specific techniques as the essential ingredients of change. This controversy, however, suffers from unclear terminology and logical inconsistencies. The Taxonomy Project therefore aims at contributing to the definition and conceptualization of common factors of psychotherapy by analyzing their differential associations to standard techniques. METHODS: A review identified 22 common factors discussed in psychotherapy research literature. We conducted a survey, in which 68 psychotherapy experts assessed how common factors are implemented by specific techniques. Using hierarchical linear models, we predicted each common factor by techniques and by experts' age, gender and allegiance to a therapy orientation. RESULTS: Common factors differed largely in their relevance for technique implementation. Patient engagement, Affective experiencing and Therapeutic alliance were judged most relevant. Common factors also differed with respect to how well they could be explained by the set of techniques. We present detailed profiles of all common factors by the (positively or negatively) associated techniques. There were indications of a biased taxonomy not covering the embodiment of psychotherapy (expressed by body-centred techniques such as progressive muscle relaxation, biofeedback training and hypnosis). Likewise, common factors did not adequately represent effective psychodynamic and systemic techniques. CONCLUSION: This taxonomic endeavour is a step towards a clarification of important core constructs of psychotherapy. KEY PRACTITIONER MESSAGE: This article relates standard techniques of psychotherapy (well known to practising therapists) to the change factors/change mechanisms discussed in psychotherapy theory. It gives a short review of the current debate on the mechanisms by which psychotherapy works. We provide detailed profiles of change mechanisms and how they may be generated by practice techniques.

ATMOSPHERIC RETRIEVAL ANALYSIS OF THE DIRECTLY IMAGED EXOPLANET HR 8799b

Directly imaged exoplanets are unexplored laboratories for the application of the spectral and temperature retrieval method, where the chemistry and composition of their atmospheres are inferred from inverse modeling of the available data. As a pilot study, we focus on the extrasolar gas giant HR 8799b, for which more than 50 data points are available. We upgrade our non-linear optimal estimation retrieval method to include a phenomenological model of clouds that requires the cloud optical depth and monodisperse particle size to be specified. Previous studies have focused on forward models with assumed values of the exoplanetary properties; there is no consensus on the best-fit values of the radius, mass, surface gravity, and effective temperature of HR 8799b. We show that cloud-free models produce reasonable fits to the data if the atmosphere is of super-solar metallicity and non-solar elemental abundances. Intermediate cloudy models with moderate values of the cloud optical depth and micron-sized particles provide an equally reasonable fit to the data and require a lower mean molecular weight. We report our best-fit values for the radius, mass, surface gravity, and effective temperature of HR 8799b. The mean molecular weight is about 3.8, while the carbon-to-oxygen ratio is about unity due to the prevalence of carbon monoxide. Our study emphasizes the need for robust claims about the nature of an exoplanetary atmosphere to be based on analyses involving both photometry and spectroscopy and inferred from beyond a few photometric data points, such as are typically reported for hot Jupiters.