Bernoulli Regression Models: Re-examining Statistical Models with Binary Dependent Variables

The classical approach for specifying statistical models with binary dependent variables in econometrics using latent variables or threshold models can leave the model misspecified, resulting in biased and inconsistent estimates as well as erroneous inferences. Furthermore, methods for trying to alleviate such problems, such as univariate generalized linear models, have not provided an adequate alternative for ensuring the statistical adequacy of such models. The purpose of this paper is to re-examine the underlying probabilistic foundations of statistical models with binary dependent variables using the probabilistic reduction approach to provide an alternative approach for model specification. This re-examination leads to the development of the Bernoulli Regression Model. Simulated and empirical examples provide evidence that the Bernoulli Regression Model can provide a superior approach for specifying statistically adequate models for dichotomous choice processes.Bernoulli Regression Model, logistic regression, generalized linear models, discrete choice, probabilistic reduction approach, model specification, Research Methods/ Statistical Methods,

Multibody dynamics: Modeling component flexibility with fixed, free, loaded, constraint, and residual modes

The assumed-modes method in multibody dynamics allows the elastic deformation of each component in the system to be approximated by a sum of products of spatial and temporal functions commonly known as modes and modal coordinates respectively. The choice of component modes used to model articulating and non-articulating flexible multibody systems is examined. Attention is directed toward three classical Component Mode Synthesis (CMS) methods whereby component normal modes are generated by treating the component interface (I/F) as either fixed, free, or loaded with mass and stiffness contributions from the remaining components. The fixed and free I/F normal modes are augmented by static shape functions termed constraint and residual modes respectively. A mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed I/F plus constraint), MacNeal-Rubin (free I/F plus residual), or Benfield-Hruda (loaded I/F) mode sets in accordance with a modal ordering scheme derived from balance realization theory. The success of the approach is judged by comparing the actuator-to-sensor frequency response of the reduced order system with that of the full order system over the frequency range of interest. A finite element model of the Galileo spacecraft serves as an example in demonstrating the effectiveness of the proposed mode selection method

Social Game for Building Energy Efficiency: Utility Learning, Simulation, and Analysis

We describe a social game that we designed for encouraging energy efficient behavior amongst building occupants with the aim of reducing overall energy consumption in the building. Occupants vote for their desired lighting level and win points which are used in a lottery based on how far their vote is from the maximum setting. We assume that the occupants are utility maximizers and that their utility functions capture the tradeoff between winning points and their comfort level. We model the occupants as non-cooperative agents in a continuous game and we characterize their play using the Nash equilibrium concept. Using occupant voting data, we parameterize their utility functions and use a convex optimization problem to estimate the parameters. We simulate the game defined by the estimated utility functions and show that the estimated model for occupant behavior is a good predictor of their actual behavior. In addition, we show that due to the social game, there is a significant reduction in energy consumption

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice

Bernoulli Regression Models: Revisiting the Specification of Statistical Models with Binary Dependent Variables

The latent variable and generalized linear modelling approaches do not provide a systematic approach for modelling discrete choice observational data. Another alternative, the probabilistic reduction (PR) approach, provides a systematic way to specify such models that can yield reliable statistical and substantive inferences. The purpose of this paper is to re-examine the underlying probabilistic foundations of conditional statistical models with binary dependent variables using the PR approach. This leads to the development of the Bernoulli Regression Model, a family of statistical models, which includes the binary logistic regression model. The paper provides an explicit presentation of probabilistic model assumptions, guidance on model specification and estimation, and empirical application

Piloting a manualised weight management programme (Shape Up-LD) for overweight and obese persons with mild-moderate learning disabilities: study protocol for a pilot randomised controlled trial

National obesity rates have dramatically risen over the last decade. Being obese significantly reduces life expectancy, increases the risk of a range of diseases, and compromises quality of life. Costs to both the National Health Service and society are high. An increased prevalence of obesity in people with learning disabilities has been demonstrated. The consequences of obesity are particularly relevant to people with learning disabilities who are already confronted by health and social inequalities. In order to provide healthcare for all, and ensure equality of treatment for people with learning disabilities, services must be developed specifically with this population in mind. The aim of this project is to pilot the evaluation of a manualised weight management programme for overweight and obese persons with mild-moderate learning disabilities (Shape Up-LD)

PATTERNS OF DUCTILE DEFORMATION IN ATTICO-CYCLADIC MASSIF

The area of Lavrion constitutes the westernmost part of the Attico-Cycladic massif where the allochthonous Cycladic Greenschist-Blueschist unit overthrusts the para-authochthonous Basal unit. The tectonic contact of these units forms a crustal scale thrust zone which is the continuation of the Evia thrust. Our research was focused on quartz-rich schists of the overlying allochthonous unit. Combination of microstructural, finite strain data and quartz and calcite c-axis fabrics analysis was used to characterize the kinematics of rock flow within the thrust zone. The latter was formed under conditions of progressive exhumation and decompression of the high-pressure schists of the AtticoCycladic massif. A dominant top-to-the-ENE sense of shearing along the thrust zone is inferred by several shear sense criteria. The analysis of several specimens collected from various structural depths manifest that the deformation close to the thrust zone occurred under approximately plane strain conditions and was characterized by an Rxz strain ratio which fluctuates between 3 and 6.5

System Identification of a Nonlinear Mode for the Shuttle Radar Topography Mission

A study is presented to identify a nonlinear bending mode for a 60-m space structure. This study was done in support of the Shuttle Radar Topography Mission (SRTM) and postflight height reconstruction efforts. For this purpose, one linear model and three nonlinear models of the structural mode were considered and evaluated. The best model was determined based on in-flight data collected during the mission and was implemented as part of the final ground software that was used for reconstructing relative radar antenna motion for the SRTM interferometer payload. High accuracy estimates of the relative states were essential for supporting the motion compensation algorithm used in the radar interferometry processor for calculating the desired topographic maps. The improvement resulting fromidentifying nonlinear modal behavior contributed to meeting mission performance requirements

Non-linear dynamic response of a cable system with a tuned mass damper to stochastic base excitation via equivalent linearization technique

Abstract: Non-linear dynamic model of a cable–mass system with a transverse tuned mass damper is considered. The system is moving in a vertical host structure therefore the cable length varies slowly over time. Under the time-dependent external loads the sway of host structure with low frequencies and high amplitudes can be observed. That yields the base excitation which in turn results in the excitation of a cable system. The original model is governed by a system of non-linear partial differential equations with corresponding boundary conditions defined in a slowly time-variant space domain. To discretise the continuous model the Galerkin method is used. The assumption of the analysis is that the lateral displacements of the cable are coupled with its longitudinal elastic stretching. This brings the quadratic couplings between the longitudinal and transverse modes and cubic nonlinear terms due to the couplings between the transverse modes. To mitigate the dynamic response of the cable in the resonance region the tuned mass damper is applied. The stochastic base excitation, assumed as a narrow-band process mean-square equivalent to the harmonic process, is idealized with the aid of two linear filters: one second-order and one first-order. To determine the stochastic response the equivalent linearization technique is used. Mean values and variances of particular random state variable have been calculated numerically under various operational conditions. The stochastic results have been compared with the deterministic response to a harmonic process base excitation