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,

What do Bayesian methods offer population forecasters?

The Bayesian approach has a number of attractive properties for probabilistic forecasting. In this paper, we apply Bayesian time series models to obtain future population estimates with uncertainty for England and Wales. To account for heterogeneity found in the historical data, we add parameters to represent the stochastic volatility in the error terms. Uncertainty in model choice is incorporated through Bayesian model averaging techniques. The resulting predictive distributions from Bayesian forecasting models have two main advantages over those obtained using traditional stochastic models. Firstly, data and uncertainties in the parameters and model choice are explicitly included using probability distributions. As a result, more realistic probabilistic population forecasts can be obtained. Second, Bayesian models formally allow the incorporation of expert opinion, including uncertainty, into the forecast. Our results are discussed in relation to classical time series methods and existing cohort component projections. This paper demonstrates the flexibility of the Bayesian approach to simple population forecasting and provides insights into further developments of more complicated population models that include, for example, components of demographic change

Comparison of probabilistic choice models in humans

BACKGROUND: Probabilistic choice has been attracting attention in psychopharmacology and neuroeconomics. Several parametric models have been proposed for probabilistic choice; entropy model, Prelec's probability weight function, and hyperbola-like probability discounting functions. METHODS: In order to examine (i) fitness of the probabilistic models to behavioral data, (ii) relationships between the parameters and psychological processes, e.g., aversion to possible non-gain in each probabilistic choice and aversion to unpredictability, we estimated the parameters and AICc (Akaike Information Criterion with small sample correction) of the probabilistic choice models by assessing the points of subjective equality at seven probability values (95%–5%). We examined both fitness of the models parametrized by utilizing AICc, and the relationships between the model parameters and equation-free parameter of aversion to possible non-gain. RESULTS: Our results have shown that (i) the goodness of fitness for group data was [Entropy model>Prelec's function>General hyperbola>Simple hyperbola]; while Prelec's function best fitted individual data, (ii) aversion to possible non-gain and aversion to unpredictability are distinct psychological processes. CONCLUSION: Entropy and Prelec models can be utilized in psychopharmacological and neuroeconomic studies of risky decision-making

On propensity-frequentist models for stochastic phenomena; with applications to Bell's theorem

The paper develops models of statistical experiments that combine propensities with frequencies, the underlying theory being the branching space-times (BST) of Belnap (1992). The models are then applied to analyze Bell's theorem. We prove the so-called Bell-CH inequality via the assumptions of a BST version of Outcome Independence and of (non-probabilistic) No Conspiracy. Notably, neither the condition of probabilistic No Conspiracy nor the condition of Parameter Independence is needed in the proof. As the Bell-CH inequality is most likely experimentally falsified, the choice is this: contrary to the appearances, experimenters cannot choose some measurement settings, or some transitions, with spacelike related initial events, are correlated; or both

Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well

The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies

This paper considers a class of models in which rank-based payoffs are sensitive to small amounts of noise in decision making. Examples include auction, price-competition, coordination, and location games. Observed laboratory behavior in these games is often responsive to asymmetric costs associated with deviations from the Nash equilibrium. These payoff asymmetry effects are incorporated in an approach that introduces noisy behavior via probabilistic choice. In equilibrium, behavior is characterized by a probability distribution that satisfies a "rational expectations" consistency condition: the beliefs that determine player's expected payoffs match the decision distributions that arise from applying a logit probabilistic choice function to those expected payoffs. We prove existence of a unique, symmetric logit (quantal response) equilibrium and derive comparative statics results. The paper provides a unified perspective on many recent laboratory studies of games in which Nash equilibrium predictions are inconsistent with both intuition and experimental evidence.logit equilibrium, quantal response equilibrium, probabilistic choice, auctions.