David Sanders and Malcolm Brynin
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198292371
- eISBN:
- 9780191600159
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198292376.003.0003
- Subject:
- Political Science, Reference
Setting out the basic regression model, and comparing the analytic efficacy of the OLS the model and its extension to logistic regression.
Setting out the basic regression model, and comparing the analytic efficacy of the OLS the model and its extension to logistic regression.
Dirk U. Pfeiffer, Timothy P. Robinson, Mark Stevenson, Kim B. Stevens, David J. Rogers, and Archie C. A. Clements
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198509882
- eISBN:
- 9780191709128
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509882.003.0007
- Subject:
- Biology, Disease Ecology / Epidemiology
This chapter presents analytical techniques of regression and discrimination as a means of quantifying the effect of a set of explanatory variables on the spatial distribution of a particular ...
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This chapter presents analytical techniques of regression and discrimination as a means of quantifying the effect of a set of explanatory variables on the spatial distribution of a particular outcome. The chapter is divided into four sections. The first outlines the principles of linear, Poisson, and logistic regression in order to provide a background to the material presented later in the chapter. The second section discusses the options available to identify and account for spatial dependency in data when modelling. The third section reviews the common analytical techniques available for dealing with the three major spatial data types (area, point, and continuous data), and the fourth deals with discriminant analysis.Less
This chapter presents analytical techniques of regression and discrimination as a means of quantifying the effect of a set of explanatory variables on the spatial distribution of a particular outcome. The chapter is divided into four sections. The first outlines the principles of linear, Poisson, and logistic regression in order to provide a background to the material presented later in the chapter. The second section discusses the options available to identify and account for spatial dependency in data when modelling. The third section reviews the common analytical techniques available for dealing with the three major spatial data types (area, point, and continuous data), and the fourth deals with discriminant analysis.
Elinor Scarbrough and Eric Tanenbaum (eds)
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198292371
- eISBN:
- 9780191600159
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198292376.001.0001
- Subject:
- Political Science, Reference
This volume is a collection of commissioned articles by 16 experts in social science methodology, each contribution introducing experienced social scientists to more advanced analytic techniques. The ...
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This volume is a collection of commissioned articles by 16 experts in social science methodology, each contribution introducing experienced social scientists to more advanced analytic techniques. The contributions explain the theoretical underpinnings of a particular technique, and illustrate the approach with a worked example. The techniques covered are the basic regression model and its extensions, linear structural equation modelling, log‐linear and latent class models, multi‐level modelling, and three extensions to modelling time series data. In these contributions, statistical notation is kept to a minimum; where necessary, it is consigned to footnotes or an appendix. Three final contributions introduce new developments in rational choice theory and discourse analysis.Less
This volume is a collection of commissioned articles by 16 experts in social science methodology, each contribution introducing experienced social scientists to more advanced analytic techniques. The contributions explain the theoretical underpinnings of a particular technique, and illustrate the approach with a worked example. The techniques covered are the basic regression model and its extensions, linear structural equation modelling, log‐linear and latent class models, multi‐level modelling, and three extensions to modelling time series data. In these contributions, statistical notation is kept to a minimum; where necessary, it is consigned to footnotes or an appendix. Three final contributions introduce new developments in rational choice theory and discourse analysis.
William R. Nugent
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780195369625
- eISBN:
- 9780199865208
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195369625.003.0002
- Subject:
- Social Work, Research and Evaluation
This chapter covers regression-discontinuity models for analyzing the data from single case designs. Auto-regressive-integrated-moving-average models are also described and illustrated. These ...
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This chapter covers regression-discontinuity models for analyzing the data from single case designs. Auto-regressive-integrated-moving-average models are also described and illustrated. These statistical methods are useful when there are a large number of observations in the phases of a single case design. These methods are described in detail and illustrated using data from a study of the implementation of an Aggression Replacement Training program implemented in a runaway shelter.Less
This chapter covers regression-discontinuity models for analyzing the data from single case designs. Auto-regressive-integrated-moving-average models are also described and illustrated. These statistical methods are useful when there are a large number of observations in the phases of a single case design. These methods are described in detail and illustrated using data from a study of the implementation of an Aggression Replacement Training program implemented in a runaway shelter.
John G. Orme and Terri Combs-Orme
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780195329452
- eISBN:
- 9780199864812
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195329452.003.0004
- Subject:
- Social Work, Research and Evaluation
This chapter discusses ordinal logistic regression (also known as the ordinal logit, ordered polytomous logit, constrained cumulative logit, proportional odds, parallel regression, or grouped ...
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This chapter discusses ordinal logistic regression (also known as the ordinal logit, ordered polytomous logit, constrained cumulative logit, proportional odds, parallel regression, or grouped continuous model), for modeling relationships between an ordinal dependent variable and multiple independent variables. Ordinal variables have three or more ordered categories, and ordinal logistic regression focuses on cumulative probabilities of the dependent variable and odds and odds ratios based on those cumulative probabilities, estimating a single common odds ratio. The chapter discusses the proportional odds or parallel regression assumption; this is the assumption that the odds ratios for each cumulative level are equal in the population (although they might be different in a sample due to sampling error). The concepts of threshold, sometimes called a cut-point, proportional odds or parallel regression assumption, are also discussed.Less
This chapter discusses ordinal logistic regression (also known as the ordinal logit, ordered polytomous logit, constrained cumulative logit, proportional odds, parallel regression, or grouped continuous model), for modeling relationships between an ordinal dependent variable and multiple independent variables. Ordinal variables have three or more ordered categories, and ordinal logistic regression focuses on cumulative probabilities of the dependent variable and odds and odds ratios based on those cumulative probabilities, estimating a single common odds ratio. The chapter discusses the proportional odds or parallel regression assumption; this is the assumption that the odds ratios for each cumulative level are equal in the population (although they might be different in a sample due to sampling error). The concepts of threshold, sometimes called a cut-point, proportional odds or parallel regression assumption, are also discussed.
Michio Hatanaka
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198773535
- eISBN:
- 9780191596360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198773536.003.0013
- Subject:
- Economics and Finance, Econometrics
This chapter analyses co-integrated regressions. It considers the cases where Δxt is i.i.d without a drift, Δxt is still i.i.d. but has a deterministic drift, and Δxt is serially correlated. It ...
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This chapter analyses co-integrated regressions. It considers the cases where Δxt is i.i.d without a drift, Δxt is still i.i.d. but has a deterministic drift, and Δxt is serially correlated. It discusses testing for co-integration, and co-integrated regression models’ assumption of some basic aspect of the co-integration space called the location of non-singular submatrices in B’.Less
This chapter analyses co-integrated regressions. It considers the cases where Δxt is i.i.d without a drift, Δxt is still i.i.d. but has a deterministic drift, and Δxt is serially correlated. It discusses testing for co-integration, and co-integrated regression models’ assumption of some basic aspect of the co-integration space called the location of non-singular submatrices in B’.
Harvey Checkoway, Neil Pearce, and David Kriebel
- Published in print:
- 2004
- Published Online:
- September 2009
- ISBN:
- 9780195092424
- eISBN:
- 9780199864553
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195092424.003.0009
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
Stratified analyses may not be feasible if there are multiple exposure categories or two or more than two or three confounders. In this situation, multiple regression methods are required. This ...
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Stratified analyses may not be feasible if there are multiple exposure categories or two or more than two or three confounders. In this situation, multiple regression methods are required. This chapter presents an overview of the methods that are used for analyzing occupational epidemiology data. It begins with a presentation of the basic multiple linear regression model used when the outcome of interest in measured as a continuous variable. This is followed by a presentation of generalized estimating equation (GEE) methods in the context of repeated measures analysis. The general form of the log-linear model is then introduced. The specific forms of Poisson regression (for cohort studies), the Cox proportional hazards model (for survival studies), and logistic regression (for case-control studies) are then defined and illustrated with occupational epidemiology examples. Various aspects of model specification are considered, including variable specification, estimation of joint effects, exposure-response estimation, and regression diagnostics.Less
Stratified analyses may not be feasible if there are multiple exposure categories or two or more than two or three confounders. In this situation, multiple regression methods are required. This chapter presents an overview of the methods that are used for analyzing occupational epidemiology data. It begins with a presentation of the basic multiple linear regression model used when the outcome of interest in measured as a continuous variable. This is followed by a presentation of generalized estimating equation (GEE) methods in the context of repeated measures analysis. The general form of the log-linear model is then introduced. The specific forms of Poisson regression (for cohort studies), the Cox proportional hazards model (for survival studies), and logistic regression (for case-control studies) are then defined and illustrated with occupational epidemiology examples. Various aspects of model specification are considered, including variable specification, estimation of joint effects, exposure-response estimation, and regression diagnostics.
Ludwig Fahrmeir and Thomas Kneib
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0005
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
This chapter provides an introduction to Bayesian spatial smoothing as a subject of interest in its own right, it points out the close relation between modelling interactions and spatial effects, and ...
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This chapter provides an introduction to Bayesian spatial smoothing as a subject of interest in its own right, it points out the close relation between modelling interactions and spatial effects, and it extends smoothing and regression to geoadditive regression models. Section 5.1 introduces the different types of spatial data in more detail and provides information on the corresponding modelling techniques. Section 5.2 describes Markov random fields as basic stochastic process models for discrete spatial data. Section 5.3 highlights relations between continuous spatial smoothing approaches and the modelling of interactions. Section 5.4 introduces Gaussian random fields as stochastic process models for continuous spatial data, including their use in classical geostatistics. Section 5.5 incorporates ideas from the previous sections in the general framework of geoadditive regression.Less
This chapter provides an introduction to Bayesian spatial smoothing as a subject of interest in its own right, it points out the close relation between modelling interactions and spatial effects, and it extends smoothing and regression to geoadditive regression models. Section 5.1 introduces the different types of spatial data in more detail and provides information on the corresponding modelling techniques. Section 5.2 describes Markov random fields as basic stochastic process models for discrete spatial data. Section 5.3 highlights relations between continuous spatial smoothing approaches and the modelling of interactions. Section 5.4 introduces Gaussian random fields as stochastic process models for continuous spatial data, including their use in classical geostatistics. Section 5.5 incorporates ideas from the previous sections in the general framework of geoadditive regression.
Judith D. Singer and John B. Willett
- Published in print:
- 2003
- Published Online:
- September 2009
- ISBN:
- 9780195152968
- eISBN:
- 9780199864980
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195152968.003.0015
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
This chapter begins by describing how to include time-varying predictors in the Cox regression model. It then introduces two methods for relaxing the proportionality assumption. Section 15.2 presents ...
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This chapter begins by describing how to include time-varying predictors in the Cox regression model. It then introduces two methods for relaxing the proportionality assumption. Section 15.2 presents the stratified Cox regression model, which stipulates that while the effects of each predictor are identical across strata, the baseline hazard functions can differ. Section 15.3 presents an alternative strategy that closely mirrors the approach used in discrete time: the inclusion of interactions with time as predictors in the model. Section 15.4 introduces a range of regression diagnostics useful for examining the underlying assumptions of the Cox model. Section 15.5 discusses what to do when modeling “competing risks”—multiple events that compete to terminate an individual's lifetime. Section 15.6 concludes by describing what to do when you have not observed the beginning of time for everyone in your sample and there are so-called late entrants to the risk set.Less
This chapter begins by describing how to include time-varying predictors in the Cox regression model. It then introduces two methods for relaxing the proportionality assumption. Section 15.2 presents the stratified Cox regression model, which stipulates that while the effects of each predictor are identical across strata, the baseline hazard functions can differ. Section 15.3 presents an alternative strategy that closely mirrors the approach used in discrete time: the inclusion of interactions with time as predictors in the model. Section 15.4 introduces a range of regression diagnostics useful for examining the underlying assumptions of the Cox model. Section 15.5 discusses what to do when modeling “competing risks”—multiple events that compete to terminate an individual's lifetime. Section 15.6 concludes by describing what to do when you have not observed the beginning of time for everyone in your sample and there are so-called late entrants to the risk set.
Ludwig Fahrmeir and Thomas Kneib
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0006
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
This chapter extends Bayesian approaches for smoothing and regression developed in previous chapters to regression models for survival and event history data with structured additive predictors. This ...
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This chapter extends Bayesian approaches for smoothing and regression developed in previous chapters to regression models for survival and event history data with structured additive predictors. This allows for the inclusion of nonlinear time-varying effects and flexible covariate effects, spatial effects, and random effects in addition to common linear predictors and to estimate them simultaneously based on full or empirical Bayes inference. Alternative approaches and other model types are outlined in Section 6.6.Less
This chapter extends Bayesian approaches for smoothing and regression developed in previous chapters to regression models for survival and event history data with structured additive predictors. This allows for the inclusion of nonlinear time-varying effects and flexible covariate effects, spatial effects, and random effects in addition to common linear predictors and to estimate them simultaneously based on full or empirical Bayes inference. Alternative approaches and other model types are outlined in Section 6.6.
Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David F. Hendry
- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198288107
- eISBN:
- 9780191595899
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198288107.003.0003
- Subject:
- Economics and Finance, Econometrics
Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit ...
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Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit roots, non‐stationarity, orders of integration, and near integration, and demonstrates the use of the theory in understanding the behaviour of least‐squares estimators in spurious regressions and in models involving integrated data. The theoretical analysis is accompanied by evidence from Monte Carlo simulations. Several examples are also provided to illustrate the use of Wiener distribution theory in deriving asymptotic results for such models.Less
Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit roots, non‐stationarity, orders of integration, and near integration, and demonstrates the use of the theory in understanding the behaviour of least‐squares estimators in spurious regressions and in models involving integrated data. The theoretical analysis is accompanied by evidence from Monte Carlo simulations. Several examples are also provided to illustrate the use of Wiener distribution theory in deriving asymptotic results for such models.
Luc Bauwens, Michel Lubrano, and Jean-François Richard
- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0005
- Subject:
- Economics and Finance, Econometrics
This chapter examines the application of the dynamic regression models for inference and prediction with dynamic econometric models. It shows how to extend to the dynamic case the notion of Bayesian ...
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This chapter examines the application of the dynamic regression models for inference and prediction with dynamic econometric models. It shows how to extend to the dynamic case the notion of Bayesian cut seen in the static case to justify conditional inference. The chapter also explains how Bayesian inference can be used for single-equation dynamic models. It discusses the particular case of models with autoregressive errors, discusses the issues of moving average errors, and illustrates the empirical use of the error correction model by an analysis of a money demand function for Belgium.Less
This chapter examines the application of the dynamic regression models for inference and prediction with dynamic econometric models. It shows how to extend to the dynamic case the notion of Bayesian cut seen in the static case to justify conditional inference. The chapter also explains how Bayesian inference can be used for single-equation dynamic models. It discusses the particular case of models with autoregressive errors, discusses the issues of moving average errors, and illustrates the empirical use of the error correction model by an analysis of a money demand function for Belgium.
Aman Ullah
- Published in print:
- 2004
- Published Online:
- August 2004
- ISBN:
- 9780198774471
- eISBN:
- 9780191601347
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774478.003.0005
- Subject:
- Economics and Finance, Econometrics
This chapter examines regression models with nonscalar covariance matrix of errors. This includes the estimators and test statistics in the context of linear regression with heteroskedasticity and ...
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This chapter examines regression models with nonscalar covariance matrix of errors. This includes the estimators and test statistics in the context of linear regression with heteroskedasticity and serial correlation, seemingly unrelated regressions, limited dependent variables, and panel data models.Less
This chapter examines regression models with nonscalar covariance matrix of errors. This includes the estimators and test statistics in the context of linear regression with heteroskedasticity and serial correlation, seemingly unrelated regressions, limited dependent variables, and panel data models.
Judith D. Singer and John B. Willett
- Published in print:
- 2003
- Published Online:
- September 2009
- ISBN:
- 9780195152968
- eISBN:
- 9780199864980
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195152968.003.0014
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
This chapter describes the conceptual underpinnings of the Cox regression model and demonstrates how to fit it to data. Section 14.1 begins by developing the Cox model specification itself, ...
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This chapter describes the conceptual underpinnings of the Cox regression model and demonstrates how to fit it to data. Section 14.1 begins by developing the Cox model specification itself, demonstrating why it is a sensible representation. Section 14.2 describes how the model is fit. Section 14.3 examines the results of model fitting, showing how to interpret parameters, test hypotheses, evaluate goodness-of-fit, and summarize effects. Section 14.4 concludes by presenting strategies for displaying results graphically.Less
This chapter describes the conceptual underpinnings of the Cox regression model and demonstrates how to fit it to data. Section 14.1 begins by developing the Cox model specification itself, demonstrating why it is a sensible representation. Section 14.2 describes how the model is fit. Section 14.3 examines the results of model fitting, showing how to interpret parameters, test hypotheses, evaluate goodness-of-fit, and summarize effects. Section 14.4 concludes by presenting strategies for displaying results graphically.
Luc Bauwens, Michel Lubrano, and Jean-François Richard
- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0004
- Subject:
- Economics and Finance, Econometrics
This chapter examines prior densities applicable for the regression model. It addresses the question of how to specify precisely the shape and the contents of the prior density in an empirical ...
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This chapter examines prior densities applicable for the regression model. It addresses the question of how to specify precisely the shape and the contents of the prior density in an empirical application and defines the concept of non-informative prior. It explains the restrictive properties of the natural conjugate prior in the regression model and discusses issues concerning the treatment of exact restrictions and exchangeable prior densities.Less
This chapter examines prior densities applicable for the regression model. It addresses the question of how to specify precisely the shape and the contents of the prior density in an empirical application and defines the concept of non-informative prior. It explains the restrictive properties of the natural conjugate prior in the regression model and discusses issues concerning the treatment of exact restrictions and exchangeable prior densities.
Steve Selvin
- Published in print:
- 2004
- Published Online:
- September 2009
- ISBN:
- 9780195172805
- eISBN:
- 9780199865697
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172805.003.08
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
The three basic features of the logistic regression model are the appropriateness of binary outcome variables, estimation of adjusted odd ratios as a measure of association, and the effective ...
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The three basic features of the logistic regression model are the appropriateness of binary outcome variables, estimation of adjusted odd ratios as a measure of association, and the effective analysis of both continuous and discrete risk factors. This chapter focuses on the last property. A logistic model allows the analysis of risk factors measured in their original units, producing a less arbitrary and more powerful analysis.Less
The three basic features of the logistic regression model are the appropriateness of binary outcome variables, estimation of adjusted odd ratios as a measure of association, and the effective analysis of both continuous and discrete risk factors. This chapter focuses on the last property. A logistic model allows the analysis of risk factors measured in their original units, producing a less arbitrary and more powerful analysis.
Marina Vannucci and Francesco C. Stingo
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0022
- Subject:
- Mathematics, Probability / Statistics
Variable selection has been the focus of much research in recent years. Bayesian methods have found many successful applications, particularly in situations where the amount of measured variables can ...
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Variable selection has been the focus of much research in recent years. Bayesian methods have found many successful applications, particularly in situations where the amount of measured variables can be much greater than the number of observations. One such example is the analysis of genomics data. In this paper we first review Bayesian variable selection methods for linear settings, including regression and classification models. We focus in particular on recent prior constructions that have been used for the analysis of genomic data and briefly describe two novel applications that integrate different sources of biological information into the analysis of experimental data. Next, we address variable selection for a different modeling context, i.e., mixture models. We address both clustering and discriminant analysis settings and conclude with an application to gene expression data for patients affected by leukemia.Less
Variable selection has been the focus of much research in recent years. Bayesian methods have found many successful applications, particularly in situations where the amount of measured variables can be much greater than the number of observations. One such example is the analysis of genomics data. In this paper we first review Bayesian variable selection methods for linear settings, including regression and classification models. We focus in particular on recent prior constructions that have been used for the analysis of genomic data and briefly describe two novel applications that integrate different sources of biological information into the analysis of experimental data. Next, we address variable selection for a different modeling context, i.e., mixture models. We address both clustering and discriminant analysis settings and conclude with an application to gene expression data for patients affected by leukemia.
Raymond L. Chambers and Robert G. Clark
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.003.0005
- Subject:
- Mathematics, Probability / Statistics
When there is a single continuous auxiliary variable, it is often reasonable to assume a simple linear regression model relating this variable to the variable of interest. This chapter describes the ...
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When there is a single continuous auxiliary variable, it is often reasonable to assume a simple linear regression model relating this variable to the variable of interest. This chapter describes the use of regression population models in sample surveys. Proportional models, where the intercept is assumed to be zero, have a long history in survey sampling and are discussed first. Empirical best and best linear unbiased predictors are derived. The ratio model is a special case of the proportional model, and this leads to the well known ratio estimator. Models with intercepts are then discussed, including best estimators of totals. Sample designs are developed. Under the ratio model, the optimal design is to select only the units with the largest values of the auxiliary variable. However this would not be robust to departures from the ratio model. The problem of robust design is discussed in Chapter 8. Optimal design is also discussed for the linear model with intercept. The combination of regression and stratification is discussed. It is possible to assume the same regression or ratio relationship in every stratum, or to allow different coefficients in each stratum. Data from an agriculture survey are used to illustrate this choice.Less
When there is a single continuous auxiliary variable, it is often reasonable to assume a simple linear regression model relating this variable to the variable of interest. This chapter describes the use of regression population models in sample surveys. Proportional models, where the intercept is assumed to be zero, have a long history in survey sampling and are discussed first. Empirical best and best linear unbiased predictors are derived. The ratio model is a special case of the proportional model, and this leads to the well known ratio estimator. Models with intercepts are then discussed, including best estimators of totals. Sample designs are developed. Under the ratio model, the optimal design is to select only the units with the largest values of the auxiliary variable. However this would not be robust to departures from the ratio model. The problem of robust design is discussed in Chapter 8. Optimal design is also discussed for the linear model with intercept. The combination of regression and stratification is discussed. It is possible to assume the same regression or ratio relationship in every stratum, or to allow different coefficients in each stratum. Data from an agriculture survey are used to illustrate this choice.
Luc Bauwens, Michel Lubrano, and Jean-François Richard
- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0009
- Subject:
- Economics and Finance, Econometrics
This chapter aims to review how Bayesian inference can be applied to some of the so-called systems of equations models. These models can be defined in several forms including multivariate regression ...
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This chapter aims to review how Bayesian inference can be applied to some of the so-called systems of equations models. These models can be defined in several forms including multivariate regression models, vector autoregressive (VAR) models, simultaneous equation models (SEM), and systems of seemingly unrelated regression equation (SURE) models. This chapter analyses VAR models which are formally equivalent to multivariate regression models and suggests that VAR models can be either open or closed depending on whether exogenous variables are included or not.Less
This chapter aims to review how Bayesian inference can be applied to some of the so-called systems of equations models. These models can be defined in several forms including multivariate regression models, vector autoregressive (VAR) models, simultaneous equation models (SEM), and systems of seemingly unrelated regression equation (SURE) models. This chapter analyses VAR models which are formally equivalent to multivariate regression models and suggests that VAR models can be either open or closed depending on whether exogenous variables are included or not.
Steve Selvin
- Published in print:
- 2004
- Published Online:
- September 2009
- ISBN:
- 9780195172805
- eISBN:
- 9780199865697
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172805.003.07
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
This chapter discusses the use of a logistic regression model to analyze data classified into a multiway table. Topics covered include the simplest model, the 2 x 2 x 2 table, the 2 x k table, the 2 ...
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This chapter discusses the use of a logistic regression model to analyze data classified into a multiway table. Topics covered include the simplest model, the 2 x 2 x 2 table, the 2 x k table, the 2 x 2 x k table, the multiway table, and goodness-of-fit.Less
This chapter discusses the use of a logistic regression model to analyze data classified into a multiway table. Topics covered include the simplest model, the 2 x 2 x 2 table, the 2 x k table, the 2 x 2 x k table, the multiway table, and goodness-of-fit.
