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Below results based on the criteria 'Generalized Linear Model'
Total number of records returned: 5

What to do When Your Hessian is Not Invertible: Alternatives to Model Respecification in Nonlinear Estimation
Gill, Jeff
King, Gary

Uploaded 05-14-2002
Keywords Hessian
generalized inverse
maximum likelihood
statistical computing
importance sampling
generalized linear model
singular normal
Abstract What should a researcher do when statistical analysis software terminates before completion with a message that the Hessian is not invertable? The standard textbook advice is to respecify the model, but this is another way of saying that the researcher should change the question being asked. Obviously, however, computer programs should not be in the business of deciding what questions are worthy of study. Although noninvertable Hessians are sometimes signals of poorly posed questions, nonsensical models, or inappropriate estimators, they also frequently occur when information about the quantities of interest does exist in the data, through the likelihood function. We explain the problem in some detail and lay out two preliminary proposals for ways of dealing with noninvertable Hessians without changing the question asked.

Detection of Multinomial Voting Irregularities
Mebane, Walter R.
Sekhon, Jasjeet
Wand, Jonathan

Uploaded 07-17-2001
Keywords outlier detection
robust estimation
overdispersed multinomial
generalized linear model
2000 presidential election
voting irregularities
Abstract We develop a robust estimator for an overdispersed multinomial regression model that we use to detect vote count outliers in the 2000 presidential election. The count vector we model contains vote totals for five candidate categories: Buchanan, Bush, Gore, Nader and ``other.'' We estimate the multinomial model using county-level data from Florida. In Florida, the model produces results for Buchanan that are essentially the same as in a binomial model: Palm Beach County has the largest positive residual for Buchanan. The multinomial model shows additional large discrepancies that almost always hurt Gore or Nader and help Bush or Buchanan.

Learning in Campaigns: A Policy Moderating Model of Individual Contributions to House Candidates
Wand, Jonathan
Mebane, Walter R.

Uploaded 04-18-1999
Keywords FEC
campaign contributions
campaign finance
policy moderation
generalized linear model
negative binomial
time series
U.S. House of Representatives
1984 election
Abstract We propose a policy moderating model of individual campaign contributions to House campaigns. Based on a model that implies moderating behavior by voters, we hypothesize that individuals use expectations about the Presidential election outcome when deciding whether to donate money to a House candidate. Using daily campaign contributions data drawn from the FEC Itemized Contributions files for 1984, we estimate a generalized linear model for count data with serially correlated errors. We expand on previous empirical applications of this type of model by comparing standard errors derived from a sandwich estimator to confidence intervals produced by a nonparametric bootstrap.

A default prior distribution for logistic and other regression models
Gelman, Andrew
Jakulin, Aleks
Pittau, Maria Grazia
Su, Yu-Sung

Uploaded 08-03-2007
Keywords Bayesian inference
generalized linear model
least squares
hierarchical model
linear regression
logistic regression
multilevel model
noninformative prior distribution
Abstract We propose a new prior distribution for classical (non-hierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-$t$ prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. We implement a procedure to fit generalized linear models in R with this prior distribution by incorporating an approximate EM algorithm into the usual iteratively weighted least squares. We illustrate with several examples, including a series of logistic regressions predicting voting preferences, an imputation model for a public health data set, and a hierarchical logistic regression in epidemiology. We recommend this default prior distribution for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small) and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analysis as well as in automated procedures such as chained equations for missing-data imputation.

Spike and Slab Prior Distributions for Simultaneous Bayesian Hypothesis Testing, Model Selection, and Prediction, of Nonlinear Outcomes
Pang, Xun
Gill, Jeff

Uploaded 07-13-2009
Keywords Spike and Slab Prior
Hypothesis Testing
Bayesian Model Selection
Bayesian Model Averaging
Adaptive Rejection Sampling
Generalized Linear Model
Abstract A small body of literature has used the spike and slab prior specification for model selection with strictly linear outcomes. In this setup a two-component mixture distribution is stipulated for coefficients of interest with one part centered at zero with very high precision (the spike) and the other as a distribution diffusely centered at the research hypothesis (the slab). With the selective shrinkage, this setup incorporates the zero coefficient contingency directly into the modeling process to produce posterior probabilities for hypothesized outcomes. We extend the model to qualitative responses by designing a hierarchy of forms over both the parameter and model spaces to achieve variable selection, model averaging, and individual coefficient hypothesis testing. To overcome the technical challenges in estimating the marginal posterior distributions possibly with a dramatic ratio of density heights of the spike to the slab, we develop a hybrid Gibbs sampling algorithm using an adaptive rejection approach for various discrete outcome models, including dichotomous, polychotomous, and count responses. The performance of the models and methods are assessed with both Monte Carlo experiments and empirical applications in political science.

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