Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

The place of philosophy of law between justice and efficiency

A discussion regarding the complex relationship that exists between the concepts of efficiency and justice goes a long way back and raises several relevant arguments. One of them, and it must be rejected in advance, is that justice is in the realm of public law, while efficiency in that of private law. Is it unacceptable that the balance between public and private law leads to the belief of a divided legal system; one system, one set of laws, one legal system. Legislators and judges are responsible for determining a balance and no theory can postulate that the balance will always be found with a simple cut between public and private law to distinguish when the criterion should be justice or when it should be efficiency. It is reductionist to confine the discussion to single goals of efficiency and justice, when human dignity and human rights should also be considered when one is discussing law. Moreover, a discussion limited to only the concepts of justice and efficiency, relies on a belief that the terms are mutually exclusive. Posner has said that the economic analysis of law has limits and philosophy of law plays an extremely important role in this discourse, which must be interdisciplinary. There can be no goal other than the realization of human rights and there can be no justice if not shared by all of mankind

Nonlinear Parameterization in Bi-Criteria Sample Balancing

Sample balancing is widely used in applied research to adjust a sample data to achieve better correspondence to Census statistics. The classic Deming-Stephan iterative proportional approach finds the weights of observations by fitting the cross-tables of sample counts to known margins. This work considers a bi-criteria objective for finding weights with maximum possible effective base size. This approach is presented as a ridge regression with the exponential nonlinear parameterization that produces nonnegative weights for sample balancing

Regression Split by Levels of the Dependent Variable

Multiple regression coefficients split by the levels of the dependent variable are examined. The decomposition of the coefficients can be defined by points on the ordinal scale or by levels in the numerical response using the Gifi system of binary variables. This approach permits consideration of specific values of the coefficients at each layer of the response variable. Numerical results illustrate how to identify levels of interpretable regression coefficients

La postmodernidad a debate

Lipovetsky summarizes an interpretation of postmodernity in this lecture. Its keywords are neoindividualism and the empire of fashion. From this point of view, the most important aspect of the issue consists of the advancement of individual autonomy in the context of a new social logic which is “presentist”, multiformal and indeterminate

Entropy Criterion In Logistic Regression And Shapley Value Of Predictors

Entropy criterion is used for constructing a binary response regression model with a logistic link. This approach yields a logistic model with coefficients proportional to the coefficients of linear regression. Based on this property, the Shapley value estimation of predictors’ contribution is applied for obtaining robust coefficients of the linear aggregate adjusted to the logistic model. This procedure produces a logistic regression with interpretable coefficients robust to multicollinearity. Numerical results demonstrate theoretical and practical advantages of the entropy-logistic regression

Priorities in Thurstone Scaling and Steady-State Probabilities in Markov Stochastic Modeling

Thurstone scaling is widely used in marketing and advertising research where various methods of applied psychology are utilized. This article considers several analytical tools useful for positioning a set of items on a Thurstone scale via regression modeling and Markov stochastic processing in the form of Chapman-Kolmogorov equations. These approaches produce interval and ratio scales of preferences and enrich the possibilities of paired comparison estimation applied for solving practical problems of prioritization and probability of choice modeling

Optimal Lp-Metric for Minimizing Powered Deviations in Regression

Minimizations by least squares or by least absolute deviations are well known criteria in regression modeling. In this work the criterion of generalized mean by powered deviations is suggested. If the parameter of the generalized mean equals one or two, the fitting corresponds to the least absolute or the least squared deviations, respectively. Varying the power parameter yields an optimum value for the objective with a minimum possible residual error. Estimation of a most favorable value of the generalized mean parameter shows that it almost does not depend on data. The optimal power always occurs to be close to 1.7, so these powered deviations should be used for a better regression fit