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Below results based on the criteria 'Bayesian inference.'
Total number of records returned: 20

Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models
Gelman, Andrew
Pardoe, Iain

Uploaded 04-16-2004
Keywords adjusted R-squared
Bayesian inference
hierarchical model
multilevel regression
partial pooling
Abstract Explained variance (R2) is a familiar summary of the fit of a linear regression and has been generalized in various ways to multilevel (hierarchical) models. The multilevel models we consider in this paper are characterized by hierarchical data structures in which individuals are grouped into units (which themselves might be further grouped into larger units), and there are variables measured on individuals and each grouping unit. The models are based on regression relationships at different levels, with the first level corresponding to the individual data, and subsequent levels corresponding to between-group regressions of individual predictor effects on grouping unit variables. We present an approach to defining R2 at each level of the multilevel model, rather than attempting to create a single summary measure of fit. Our method is based on comparing variances in a single fitted model rather than comparing to a null model. In simple regression, our measure generalizes the classical adjusted R2. We also discuss a related variance comparison to summarize the degree to which estimates at each level of the model are pooled together based on the level-specific regression relationship, rather than estimated separately. This pooling factor is related to the concept of shrinkage in simple hierarchical models. We illustrate the methods on a dataset of radon in houses within counties using a series of models ranging from a simple linear regression model to a multilevel varying-intercept, varying-slope model.

Prior distributions for Bayesian data analysis in political science
Gelman, Andrew

Uploaded 02-25-2009
Keywords Bayesian inference
hierarchical models
mixture models
prior information
Abstract Prior information is often what makes Bayesian inference work. In the political science examples of which we are aware aware, information needs to come in, whether as regression predictors or regularization (that is, prior distributions) on parameters. We illustrate with a few examples from our own research.

Estimating incumbency advantage and its variation, as an example of a before/after study
Gelman, Andrew
Huang, Zaiying

Uploaded 02-07-2003
Keywords Bayesian inference
before-after study
Congressional elections
Abstract Incumbency advantage is one of the most studied features in American legislative elections. In this paper, we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth century: our estimate of the overall pattern of incumbency advantage over time is similar to previous estimates (although slightly lower), and we also find a pattern of increasing variation. In addition to the application to incumbency advantage, our approach represents a new method, using multilevel modeling, for estimating effects in before/after studies.

Bayesian Methods: A Social and Behavioral Sciences Approach, ANSWER KEY TO THE SECOND EDITION. Odd Numbers.
Park, Hong Min
Gill, Jeff

Uploaded 09-14-2010
Keywords Bayes
Bayesian inference
Bayes Factor
Markov chain
Monte Carlo
hierarchical models
Abstract This is the odd-numbered exercise answers to the second edition of Bayesian Methods: A Social and Behavioral Sciences Approach (minus Chapter 13). Course Instructors can get the full set from Chapman & Hall/CRC upon request.

State-Level Opinions from National Surveys: Poststratification using Hierarchical Logistic Regression
Park, David K.
Gelman, Andrew
Bafumi, Joseph

Uploaded 07-12-2002
Keywords Bayesian Inference
Public Opinion
Abstract Previous researchers have pooled national surveys in order to construct state-level opinions. However, in order to overcome the small n problem for less populous states, they have aggregated a decade or more of national surveys to construct their measures. For example, Erikson, Wright and McIver (1993) pooled 122 national surveys conducted over 13 years to produce state-level partisan and ideology estimates. Brace, Sims-Butler, Arceneaux, and Johnson (2002) pooled 22 surveys over a 25-year period to produce state-level opinions on a number of specific issues. We construct a hierarchical logistic regression model for the mean of a binary response variable conditional on poststratification cells. This approach combines the modeling approach often used in small-area estimation with the population information used in poststratification (see Gelman and Little 1997). We produce state-level estimates pooling seven national surveys conducted over a nine-day period. We first apply the method to a set of U.S pre-election polls, poststratified by state, region, as well as the usual demographic variables and evaluate the model by comparing it to state-level election outcomes. We then produce state-level partisan and ideology estimates by comparing it to Erikson, Wright and McIver's estimates.

Detecting Changes in Network Time Series using Bayesian Inference: Applications to Historical Voting and Text Datasets
Park, Jong Hee
Sohn, Yunkyu

Uploaded 07-23-2015
Keywords network dynamics
stochastic block model
hidden Markov model
Bayesian inference
voting data
text data
Abstract Studying network dynamics is receiving an increasing attention in political science and other fields of sciences. Having developed under the focus on static network analysis, however, the research community suffers from the lack of a conceptual framework and a statistical methodology for modeling fundamental aspects of dynamic networks. In this paper, we present a general statistical framework to detect and model structural changes in network time series data using Bayesian inference. We first define what constitutes "structural changes" in network dynamics and discuss different strategies to model them in network time series data. Then, we present a network changepoint model that detects fundamental changes in latent node traits, in particular, their group structure, of dynamic networks using a hidden Markov model. After testing our method using simulated data sets, we apply our method to the analysis of historical voting data and text data. Using the 20th century United States Senate roll call voting data, we uncover the transition of three hidden regimes in the voting coalitions of United States Senate legislators. We also apply our method to new year addresses by North Korean leaders from 1946 to 2015 and find four dramatic changes in the semantic group structure of word associations.

Flexible Prior Specifications for Factor Analytic Models with an Application to the Measurement of American Political Ideology
Quinn, Kevin M.

Uploaded 04-20-2000
Keywords factor analysis
intrinsic autoregression
hierarchical modeling
Bayesian inference
political ideology
Abstract Factor analytic measurement models are widely used in the social sciences to measure latent variables and functions thereof. Examples include the measurement of: political preferences, liberal democracy, latent determinants of exchange rates, and latent factors in arbitrage pricing theory models and the corresponding pricing deviations. Oftentimes, the results of these measurement models are sensitive to distributional assumptions that are made regarding the latent factors. In this paper I demonstrate how prior distributions commonly used in image processing and spatial statistics provide a flexible means to model dependencies among the latent factor scores that cannot be easily captured with standard prior distributions that treat the factor scores as (conditionally) exchangeable. Markov chain Monte Carlo techniques are used to fit the resulting models. These modeling techniques are illustrated with a simulated data example and an analysis of American political attitudes drawn from the 1996 American National Election Study.

Post-stratification without population level information on the post-stratifying variable, with application to political polling
Gelman, Andrew
Katz, Jonathan
Riley, Cavan

Uploaded 02-10-2000
Keywords Bayesian Inference
Sample surveys
State-space models
Abstract We investigate the construction of more precise estimates of a collection of population means using information about a related variable in the context of repeated sample surveys. The method is illustrated using poll results concerning presidential approval rating (our related variable is political party identification). We use post-stratification to construct these improved estimates, but since we don't have population level information on the post-stratifying variable, we construct a model for the manner in which the post-stratifier develops over time. In this manner, we obtain more precise estimates without making possibly untenable assumptions about the dynamics of our variable of interest, the presidential approval rating.

Operationalizing and Testing Spatial Theories of Voting
Quinn, Kevin M.
Martin, Andrew D.

Uploaded 04-15-1998
Keywords spatial voting
factor analysis
multinomial probit
multinomial logit
Bayesian inference
model comparison
Bayes factors
Dutch politics
Danish politics
Abstract Spatial models of voting behavior provide the foundation for a substantial number of theoretical results. Nonetheless, empirical work involving the spatial model faces a number of potential difficulties. First, measures of the latent voter and candidate issue positions must be obtained. Second, evaluating the fit of competing statistical models of voter choice is often more complicated than previously realized. In this paper, we discuss precisely these issues. We argue that confirmatory factor analysis applied to mass-level issue preference questions is an attractive means of measuring voter ideal points. We also show how party issue positions can be recovered using a variation of this strategy. We go on to discuss the problems of assessing the fit of competing statistical models (multinomial logit vs. multinomial probit) and competing explanations (those based on spatial theory vs. those derived from other theories of voting such as sociological theories). We demonstrate how the Bayesian perspective not only provides computational advantages in the case of fitting the multinomial probit model, but also how it facilitates both types of comparison mentioned above. Results from the Netherlands and Denmark suggest that even when the computational cost of multinomial probit is disregarded, the decision whether to use multinomial probit (MNP) or multinomial logit (MNL) is not clear-cut.

Not Asked and Not Answered: Multiple Imputation for Multiple Surveys
Gelman, Andrew
King, Gary
Liu, Chuanhai

Uploaded 10-27-1997
Keywords Bayesian inference
cluster sampling
hierarchical models
ignorable nonresponse
missing data
political science
sample surveys
stratified sampling
multiple imputation
Abstract We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked, or different sampling methods used, in different strata or clusters. Our method involves multiply-imputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. Information from survey weights is exploited by including in the analysis the variables on which the weights were based, and then reweighting individual responses (observed and imputed) to estimate population quantities. We also develop diagnostics for checking the fit of the imputation model based on comparing imputed to non-imputed data. We illustrate with the example that motivated this project --- a study of pre-election public opinion polls, in which not all the questions of interest are asked in all the surveys, so that it is infeasible to impute each survey separately.

Multilevel (hierarchical) modeling: what it can and can't do
Gelman, Andrew

Uploaded 01-26-2005
Keywords Bayesian inference
hierarchical model
multilevel regression
Abstract Multilevel (hierarchical) modeling is a generalization of linear and generalized linear modeling in which regression coefficients are themselves given a model, whose parameters are also estimated from data. We illustrate the strengths and limitations of multilevel modeling through an example of the prediction of home radon levels in U.S. counties. The multilevel model is highly effective for predictions at both levels of the model but could easily be misinterpreted for causal inference.

Validation of software for Bayesian models using posterior quantiles
Cook, Samantha
Gelman, Andrew
Rubin, Donald

Uploaded 08-16-2005
Keywords Bayesian inference
Markov chain Monte Carlo
hierarchical models
Abstract We present a simulation-based method designed to establish the computational correctness of software developed to fit a specific Bayesian model, capitalizing on properties of Bayesian posterior distributions. We illustrate the validation technique with two examples. The validation method is shown to find errors in software when they exist and, moreover, the validation output can be informative about the nature and location of such errors.

Designing and Analyzing Randomized Experiments
Horiuchi, Yusaku
Imai, Kosuke
Taniguchi, Naoko

Uploaded 07-05-2005
Keywords Bayesian inference
causal inference
randomized block design
Abstract In this paper, we demonstrate how to effectively design and analyze randomized experiments, which are becoming increasingly common in political science research. Randomized experiments provide researchers with an opportunity to obtain unbiased estimates of causal effects because the randomization of treatment guarantees that the treatment and control groups are on average equal in both observed and unobserved characteristics. Even in randomized experiments, however, complications can arise. In political science experiments, researchers often cannot force subjects to comply with treatment assignment or to provide the information necessary for the estimation of causal effects. Building on the recent statistical literature, we show how to make statistical adjustments for these noncompliance and nonresponse problems when analyzing randomized experiments. We also demonstrate how to design randomized experiments so that the potential impact of such complications is minimized.

Modeling Foreign Direct Investment as a Longitudinal Social Network
Jensen, Nathan
Martin, Andrew
Westveld, Anton

Uploaded 07-13-2007
Keywords foreign direct investment
social network data
longitudinal data
hierarchical modeling
mixture modeling
Bayesian inference.
Abstract An extensive literature in international and comparative political economy has focused on the how the mobility of capital affects the ability of governments to tax and regulate firms. The conventional wisdom holds that governments are in competition with each other to attract foreign direct investment (FDI). Nation-states observe the fiscal and regulatory decisions of competitor governments, and are forced to either respond with policy changes or risk losing foreign direct investment, along with the politically salient jobs that come with these investments. The political economy of FDI suggests a network of investments with complicated dependencies. We propose an empirical strategy for modeling investment patterns in 24 advanced industrialized countries from 1985-2000. Using bilateral FDI data we estimate how increases in flows of FDI affect the flows of FDI in other countries. Our statistical model is based on the methodology developed by Westveld & Hoff (2007). The model allows the temporal examination of each notion's activity level in investing, attractiveness to investors, and reciprocity between pairs of nations. We extend the model by treating the reported inflow and outflow data as independent replicates of the true value and allowing for a mixture model for the fixed effects portion of the network model. Using a fully Bayesian approach, we also impute missing data within the MCMC algorithm used to fit the model.

Bayesian Analysis of Structural Changes: Historical Changes in US Presidential Uses of Force Abroad
Park, Jong Hee

Uploaded 07-16-2007
Keywords structural changes
changepoint models
discrete time series data
use of force data
state space models
time-varying parameter models
Bayesian inference
Abstract While many theoretical models in political science are inspired by structural changes in politics, most empirical methods assume stable patterns of causal processes and fail to capture dynamic changes in theoretical relationships. In this paper, I introduce an efficient Bayesian approach to the multiple changepoint problem presented by Chib (1998) and discuss the utility of the Bayesian changepoint models in the context of generalized linear models. As an illustration, I revisit the debate over whether and how U.S. presidents have used forces abroad in response to domestic factors since 1890.

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.

Why we (usually) don't have to worry about multiple comparisons
Gelman, Andrew
Hill, Jennifer
Yajima, Masanao

Uploaded 06-01-2008
Keywords Bayesian inference
hierarchical modeling
multiple comparisons
type S error
statistical significance
Abstract The problem of multiple comparisons can disappear when viewed from a Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. These address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the p-values corresponding to intervals of fixed width). Multilevel estimates make comparisons more conservative, in the sense that intervals for comparisons are more likely to include zero; as a result, those comparisons that are made with confidence are more likely to be valid.

Nonparametric Priors For Ordinal Bayesian Social Science Models: Specification and Estimation
Gill, Jeff
Casella, George

Uploaded 08-21-2008
Keywords generalized linear mixed model
ordered probit
Bayesian approaches
nonparametric priors
Dirichlet process mixture models
nonparametric Bayesian inference
Abstract A generalized linear mixed model, ordered probit, is used to estimate levels of stress in presidential political appointees as a means of understanding their surprisingly short tenures. A Bayesian approach is developed, where the random effects are modeled with a Dirichlet process mixture prior, allowing for useful incorporation of prior information, but retaining some vagueness in the form of the prior. Applications of Bayesian models in the social sciences are typically done with ``noninformative'' priors, although some use of informed versions exists. There has been disagreement over this, and our approach may be a step in the direction of satisfying both camps. We give a detailed description of the data, show how to implement the model, and describe some interesting conclusions. The model utilizing a nonparametric prior fits better and reveals more information in the data than standard approaches.

Prior Distributions for Variance Parameters in Hierarchical Models
Gelman, Andrew

Uploaded 03-28-2004
Keywords Bayesian inference
hierarchical model
multilevel model
noninformative prior distribution
weakly informative prior distribution
Abstract Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-$t$ family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of "noninformative" prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-$t$ family when the number of groups is small and in other settings where a weakly informative prior is desired.

What Can Be Learned from a Simple Table? Bayesian Inference and Sensitivity Analysis for Causal Effects from 2x2 and 2x2xK Tables in the Presence of Unmeasured Confounding
Quinn, Kevin

Uploaded 09-07-2008
Keywords causal inference
bayesian inference
sensitivity analysis
unmeasured confounding
Abstract What, if anything, should one infer about the causal effect of a binary treatment on a binary outcome from a $2 imes 2$ cross-tabulation of non-experimental data? Many researchers would answer ``nothing'' because of the likelihood of severe bias due to the lack of adjustment for key confounding variables. This paper shows that such a conclusion is unduly pessimistic. Because the complete data likelihood under arbitrary patterns of confounding factorizes in a particularly convenient way, it is possible to parameterize this general situation with four easily interpretable parameters. Subjective beliefs regarding these parameters are easily elicited and subjective statements of uncertainty become possible. This paper also develops a novel graphical display called the confounding plot that quickly and efficiently communicates all patterns of confounding that would leave a particular causal inference relatively unchanged.

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