(a) Using R, fit 3 binomial GLMs for these data corresponding to 3 link functions, logit, probit, and complementary log-log. Perform residual analysis for each model, using the deviance residuals. Obtain fitted values, π̂i, under each model and compare with observed proportions, yi/mi. Obtain the estimated dose-response curve under each model by evaluating π̂(x) = g(β̂1 + β̂2x) over a grid of value...

— Standard tools for the analysis of the (average) conditional association structure of the distribution on a multiway contingency table are log-linear models. A different association concept is that of marginal association and this paper demonstrates how marginal log-linear parameters can be used to measure this aspect of association. The paper gives a non-technical discussion of these two asp...

Standard tools for the analysis of the (average) conditional association structure of the distribution on a multiway contingency table are log-linear models. A different association concept is that of marginal association and this paper describes how marginal log-linear parameters can be used to measure this aspect of association. The paper gives a non-technical discussion of these two aspects ...

Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find the most likely configuration (MAP) of large-scale DPPs, which is NP-hard in general. Due to the submodular nature of the MAP objective, greedy algorithms h...

In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log–log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as fre...

We prove that for all algebraic number β > 1 the strings of zeros in the Rényi βexpansion dβ(1) of 1 exhibit a lacunarity bounded above by log(s(Pβ))/ log(β), where s(Pβ) is the size of the minimal polynomial of β. The conjecture about the specification of the β-shift, equivalently the uniform discreteness of the sets Zβ of β-integers, for β a Perron number is discussed. We propose a classifica...

On the positive half-line, there are two natural, and complementary, analogues of the single notion of symmetry of distributions on the real line. One is the R-symmetry recently proposed and investigated by Mudholkar and Wang (2007); the other is the ‘log-symmetry’ investigated here. Log-symmetry can be thought of either in terms of a random variable having the same distribution as its reciproc...