Choosing the proper link function for binary data

textSince generalized linear model (GLM) with binary response variable is widely used in many disciplines, many efforts have been made to construct a fit model. However, little attention is paid to the link functions, which play a critical role in GLM model. In this article, we compared three link functions and evaluated different model selection methods based on these three link functions. Also, we provided some suggestions on how to choose the proper link function for binary data.Statistic

Symmetric and Asymmetric Rounding

If rounded data are used in estimating moments and regression coefficients, the estimates are typically more or less biased. The purpose of the paper is to study the bias inducing effect of rounding, which is also seen when population moments instead of their estimates are considered. Under appropriate conditions this effect can be approximately specified by versions of Sheppard's correction formula. We discuss the conditions under which these approximations are valid. We also investigate the efficiency loss that comes along with rounding. The rounding error, which corresponds to the measurement error of a measurement error model, has a marginal distribution which can be approximated by the uniform distribution. We generalize the concept of simple rounding to that of asymmetric rounding and study its effect on the mean and variance of a distribution under similar circumstances as with simple rounding

Testing and Learning on Distributions with Symmetric Noise Invariance

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered differences can be due to different types of measurement noise, data collection artefacts or other irrelevant sources of variability. We propose distances between distributions which encode invariance to additive symmetric noise, aimed at testing whether the assumed true underlying processes differ. Moreover, we construct invariant features of distributions, leading to learning algorithms robust to the impairment of the input distributions with symmetric additive noise.Comment: 22 page

On the Independence Jeffreys prior for skew--symmetric models with applications

We study the Jeffreys prior of the skewness parameter of a general class of scalar skew--symmetric models. It is shown that this prior is symmetric about 0, proper, and with tails $O(\lambda^{-3/2})$ under mild regularity conditions. We also calculate the independence Jeffreys prior for the case with unknown location and scale parameters. Sufficient conditions for the existence of the corresponding posterior distribution are investigated for the case when the sampling model belongs to the family of skew--symmetric scale mixtures of normal distributions. The usefulness of these results is illustrated using the skew--logistic model and two applications with real data

The Incidence of the Mortgage Interest Deduction: Evidence from the Market for Home Purchase Loans

This article examines the incidence of the largest housing-related subsidy in the federal budget, the home mortgage interest deduction (MID). The author uses the difference in interest rates for loans made around the MID limit to identify the incidence of the subsidy. Using data on individual mortgages originated in 2004, the author estimates that for every $1,000 borrowed without the MID, the interest rate on the entire loan decreases by between 3.3 and 4.4 percent. Results suggest that lenders capture between 9 and 17 percent of the subsidy created by the home MID through higher mortgage interest rates