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,

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)

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

Neutrino Fluxes from CMSSM LSP Annihilations in the Sun

We evaluate the neutrino fluxes to be expected from neutralino LSP annihilations inside the Sun, within the minimal supersymmetric extension of the Standard Model with supersymmetry-breaking scalar and gaugino masses constrained to be universal at the GUT scale (the CMSSM). We find that there are large regions of typical CMSSM $(m_{1/2}, m_0)$ planes where the LSP density inside the Sun is not in equilibrium, so that the annihilation rate may be far below the capture rate. We show that neutrino fluxes are dependent on the solar model at the 20% level, and adopt the AGSS09 model of Serenelli et al. for our detailed studies. We find that there are large regions of the CMSSM $(m_{1/2}, m_0)$ planes where the capture rate is not dominated by spin-dependent LSP-proton scattering, e.g., at large $m_{1/2}$ along the CMSSM coannihilation strip. We calculate neutrino fluxes above various threshold energies for points along the coannihilation/rapid-annihilation and focus-point strips where the CMSSM yields the correct cosmological relic density for tan(beta) = 10 and 55 for $\mu$ > 0, exploring their sensitivities to uncertainties in the spin-dependent and -independent scattering matrix elements. We also present detailed neutrino spectra for four benchmark models that illustrate generic possibilities within the CMSSM. Scanning the cosmologically-favored parts of the parameter space of the CMSSM, we find that the IceCube/DeepCore detector can probe at best only parts of this parameter space, notably the focus-point region and possibly also at the low-mass tip of the coannihilation strip.Comment: 32 pages, 13 figures. v2: updated/expanded discussion of IceCube/DeepCor