Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures

Name: Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures
ISBN: 9781446286104

doi:10.4135/9781446286104

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Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures

Edited by:W. Paul Vogt & R. Burke Johnson
Publisher: SAGE Publications Ltd
Series: SAGE Benchmarks in Social Research Methods
- Publication year: 2012
- Online pub date: February 05, 2015
Discipline: Regression & Correlation
DOI: https://doi.org/10.4135/9781446286104
Keywords:
attitudes, confirmatory factor analysis, correlation, counseling psychology, effect size, evaluation, exploratory factor analysis, factor analysis, five-factor model of personality, hypothesis testing, latent variables, logistic regression, measurement, mediation, missing data, multilevel modeling, multiple regression, personality, regression, regression analysis, research design, sample size, scaling, simulations, social work, sociology, structural equation modeling, structural equation modelling, structural models, testing
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Online ISBN: 9781446286104

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Rsuperscript 2is widely relied on in linear regression to index a model's discriminatory power. Many counterparts have been proposed for use in logistic regression, but no single measure is consistently used. Two potential criterion values are relevant: the explained variance in the latent scale underlying the binary indicator of event occurrence and the explained risk of the event itself. In this study, Monte Carlo methods were used to examine the performance, with respect to fixed theoretical levels of explained variance and explained risk, of eight Rsuperscript 2analogues. The McKelvey-Zavoina measure appears to be best at estimating explained variance and either the sample-estimated explained risk or the ordinary least squares Rsuperscript 2to be best at indexing explained risk. Other measures appear to be poor choices, primarily because asymptotic trends suggest they may be inconsistent estimators of the relevant criterion.

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‘Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures’, AlfredDeMaris Sociological Methods & Research, 31 (1) (2002): 27–74. Published by SAGE Publications, Inc. Reprinted with permission.

Chronology of Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures

Volume I
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- Regression and Its Correlational Foundations and Concomitants
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  - 1. Report on Certain Enteric Fever Inoculation Statistics
    
    Karl Pearson
    1904
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    The American Statistician
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    1954
    Journal of the American Statistical Association
  - 5. requivalent, Meta-Analysis, and Robustness: An Empirical Examination of Rosenthal and Rubin's Effect Size Indicator
    
    Andrew Gilpin
    2008
    Educational and Psychological Measurement
  - 6. Multiple Correlation versus Multiple Regression
    
    Carl Huberty
    2003
    Educational and Psychological Measurement
  - 7. Regression to the Mean, Murder Rates, and Shall-Issue Laws
    
    Patricia Grambsch
    2008
    The American Statistician
  - 8. A Regression Paradox for Linear Models: Sufficient Conditions and Relation to Simpson's Paradox
    
    Aiyou Chen | Thomas Bengtsson | Tin Ho
    2009
    The American Statistician
  - 9. Sample Sizes When Using Multiple Linear Regression for Prediction
    
    Gregory Knofczynski | Daniel Mundfrom
    2008
    Educational and Psychological Measurement
  - 10. Confidence Intervals for an Effect Size Measure in Multiple Linear Regression
    
    James Algina | H. Keselman | Randall Penfield
    2007
    Educational and Psychological Measurement
  - 11. History and Use of Relative Importance Indices in Organizational Research
    
    Jeff Johnson | James LeBreton
    2004
    Organizational Research Methods
  - 12. Variable Importance Assessment in Regression: Linear Regression versus Random Forest
    
    Ulrike Grömping
    2009
    ömping The American Statistician
  - 13. Modern Insights about Pearson's Correlation and Least Squares Regression
    
    Rand Wilcox
    2001
    International Journal of Selection and Assessment
- Linear Regression Designs and Model Building
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  - 14. Multiple Regression as a General Data-Analytic System
    
    Jacob Cohen
    1968
    Psychological Bulletin
  - 15. Multiple Regression Analyses in Clinical Child and Adolescent Psychology
    
    James Jaccard | Vincent Guilamo-Ramos | Margaret Johansson | Alida Bouris
    2006
    Vincent Guilamo-Ramos, Margaret Johansson and Alida Bouris Journal of Clinical Child & Adolescent Psychology
  - 16. Methodologist as Arbitrator: Five Models for Black-White Differences in the Causal Effect of Expectations on Attainment
    
    Stephen Morgan
    2004
    Sociological Methods & Research
  - 17. An Introduction to Ensemble Methods for Data Analysis
    
    Richard Berk
    2006
    Sociological Methods & Research
  - 18. Sparse Partial Least Squares Regression for On-Line Variable Selection with Multivariate Data Streams
    
    Brian McWilliams | Giovanni Montana
    2010
    Statistical Analysis and Data Mining
Volume II
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- Inherently Nonlinear Models – Log-Linear Models and Probit and Logistic Regression
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  - 19. Confronting Sociological Theory with Data: Regression Analysis, Goodman's Log-Linear Models and Comparative Research
    
    Bernice Pescosolido | Jonathan Kelley
    1983
    Sociology
  - 20. Suppression and Confounding in Action
    
    Henry Lynn
    2003
    The American Statistician
  - 21. Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures
    
    Alfred DeMaris
    2002
    Maris Sociological Methods & Research
  - 22. Coefficients of Determination in Logistic Regression Models – a New Proposal: The Coefficient of Discrimination
    
    Tue Tjur
    2009
    The American Statistician
  - 23. A Graphical Method for Assessing the Fit of a Logistic Regression Model
    
    Iain Pardoe | R. Cook
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    Cook The American Statistician
  - 24. Determining the Relative Importance of Predictors in Logistic Regression: An Extension of Relative Weight Analysis
    
    Scott Tonidandel | James LeBreton
    2010
    Organizational Research Methods
  - 25. Loss of Power in Logistic, Ordinal Logistic, and Probit Regression When an Outcome Variable Is Coarsely Categorized
    
    Aaron Taylor | Stephen West | Leona Aiken
    2006
    Educational and Psychological Measurement
  - 26. Using Heterogeneous Choice Models to Compare Logit and Probit Coefficients across Groups
    
    Richard Williams
    2009
    Sociological Methods & Research
  - 27. Large-scale Regression-based Pattern Discovery: The Example of Screening the WHO Global Drug Safety Database
    
    Ola Caster | G. Niklas | M. Norén | David Madigan | Andrew Bate
    2010
    Statistical Analysis and Data Mining
  - 28. Modeling Local Nonlinear Correlations Using Subspace Principal Curves
    
    Chandan Reddy | Mohammad Aziz
    2010
    Statistical Analysis and Data Mining
  - 29. A Primer for Social Worker Researchers on How to Conduct a Multinomial Logistic Regression
    
    Carrie Petrucci
    2009
    Journal of Social Service Research
  - 30. The Effect of Childhood Maltreatment on Adult Criminality: A Tobit Regression Analysis
    
    Andrew Grogan-Kaylor | Melanie Otis
    2003
    Child Maltreatment
- Multi-Level Regression Modeling (MLM)
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  - 31. Multiple-level Regression Analysis of Survey and Ecological Data
    
    Theodor Harder | Franz Pappi
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  - 32. Broadening the Scope of Regression Analysis
    
    Robert Bickel
    2007
    Multilevel Analysis for Applied Research: It's Just Regression
  - 33. Multilevel Modeling: Overview and Applications to Research in Counseling Psychology
    
    Jeffrey Kahn
    2011
    Journal of Counseling Psychology
  - 34. Acceptance of Other Religions in the United States: An HLM Analysis of Variability across Congregations
    
    Buster Smith
    2010
    Social Compass
  - 35. Multilevel Modeling of Social Segregation
    
    George Leckie | Rebecca Pillinger | Kelvyn Jones | Harvey Goldstein4
    2012
    Journal of Educational and Behavioral Statistics
  - 36. A New Approach for Estimating a Nonlinear Growth Component in Multilevel Modeling
    
    Asko Tolvanen | Noona Kiuru | Esko Leskinen | Kai Hakkarainen | Mikko Inkinen | Kirsti Lonka | Katariina Salmela-Aro
    2011
    International Journal of Behavioral Development
  - 37. Addressing Data Sparseness in Contextual Population Research: Using Cluster Analysis to Create Synthetic Neighborhoods
    
    Philippa Clarke | Blair Wheaton
    2007
    Sociological Methods & Research
  - 38. Effect Sizes in Three-level Cluster-Randomized Experiments
    
    Larry Hedges
    2011
    Journal of Educational and Behavioral Statistics
Volume III
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- Exploratory and Confirmatory Factor Analysis and Latent Class Modeling
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  - 39. Multiple Factor Analysis
    
    L. Thurstone
    1931
    Psychological Review
  - 40. Use of Exploratory Factor Analysis in Published Research: Common Errors and Some Comment on Improved Practice
    
    Robin Henson | J. Roberts
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  - 41. The Quality of Factor Solutions in Exploratory Factor Analysis: The Influence of Sample Size, Communality, and Overdetermination
    
    Kristine Hogarty | Constance Hines | Jeffrey Kromrey | John Ferron | Karen Mumford
    2005
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  - 42. Monte Carlo Experiments: Design and Implementation
    
    Pamela Paxton | Patrick Curran | Kenneth Bollen | Jim Kirby | Feinian Chen
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  - 43. Rotation Criteria and Hypothesis Testing for Exploratory Factor Analysis: Implications for Factor Pattern Loadings and Interfactor Correlations
    
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  - 44. Current Methodological Considerations in Exploratory and Confirmatory Factor Analysis
    
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  - 45. Reporting Practices in Confirmatory Factor Analysis: An Overview and Some Recommendations
    
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    J. Gustavsson | Anna-Karin Eriksson | Agneta Hilding | Mattias Gunnarsson | Claes-Göran Östensson
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Volume IV
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- Structural Equation Modeling (SEM)
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  - 53. Correlation and Causation
    
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    Peter Bentler
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    Kenneth Bollen
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    John Ferron | Melinda Hess
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    James Graham
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  - 59. Advanced Applications of Structural Equation Modeling in Counseling Psychology Research
    
    Matthew Martens | Richard Haase
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  - 60. Applications of Structural Equation Modeling in Psychological Research
    
    Robert MacCallum | James Austin
    2000
    Annual Review of Psychology
  - 61. Introduction to Structural Equation Modeling: Issues and Practical Considerations
    
    Pui-Wa Lei | Qiong Wu
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  - 62. Structural Equation Modeling: Reviewing the Basics and Moving Forward
    
    Jodie Ullman
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  - 63. Missing Data Techniques for Structural Equation Modeling
    
    Paul Allison
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  - 64. Working with Missing Values
    
    Alan Acock
    2005
    Journal of Marriage and Family
  - 65. Modeling Strategies: In Search of the Holy Grail
    
    Kenneth Bollen
    2000
    Structural Equation Modeling
  - 66. On Tests and Indices for Evaluating Structural Models
    
    Peter Bentler
    2007
    Personality and Individual Differences
  - 67. The Reliability Paradox in Assessing Structural Relations within Covariance Structure Models
    
    Gregory Hancock | Ralph Mueller
    2011
    Educational and Psychological Measurement
  - 68. Moderation and Mediation in Structural Equation Modeling: Applications for Early Intervention Research
    
    Christopher Hopwood
    2007
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  - 69. Latent Variable Interaction Modeling
    
    Randall Schumacker
    2002
    Structural Equation Modeling
  - 70. Parenting Efficacy and the Early School Adjustment of Poor and Near-Poor Black Children
    
    Aurora Jackson | Jeong-Kyun Choi | Peter Bentler
    2009
    Journal of Family Issues
  - 71. Neighborhood Social Disorganization, Families, and the Educational Behavior of Adolescents
    
    Natasha Bowen | Gary Bowen | William Ware
    2002
    Journal of Adolescent Research
  - 72. Intervention Effects on College Performance and Retention as Mediated by Motivational, Emotional, and Social Control Factors: Integrated Meta-Analytic Path Analyses
    
    Steven Robbins | In-Sue Oh | Huy Le | Christopher Button
    2009
    Journal of Applied Psychology

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Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures

Key Reading

All Readings

Entry

Table of Contents

Volume I

Regression and Its Correlational Foundations and Concomitants

Linear Regression Designs and Model Building

Volume II

Inherently Nonlinear Models – Log-Linear Models and Probit and Logistic Regression

Multi-Level Regression Modeling (MLM)

Volume III

Exploratory and Confirmatory Factor Analysis and Latent Class Modeling

Volume IV

Structural Equation Modeling (SEM)

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Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures

Key Reading

All Readings

Entry

Table of Contents

Volume I

Regression and Its Correlational Foundations and Concomitants

Linear Regression Designs and Model Building

Volume II

Inherently Nonlinear Models – Log-Linear Models and Probit and Logistic Regression

Multi-Level Regression Modeling (MLM)

Volume III

Exploratory and Confirmatory Factor Analysis and Latent Class Modeling

Volume IV

Structural Equation Modeling (SEM)

Sign in to access this content

Get a 30 day FREE TRIAL

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