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Regression and ANOVA with Zero-One Data: Measures of Residual Variation
Abstract
We consider regression situations for which the response variable is dichotomous. The most common analysis fits successively richer linear logistic models and measures the residual variation from the model by minus twice the maximized log likelihood. General measures of residual variation are considered here, including ordinary squared error and prediction error as well as the log likelihood. All of these are shown to be satisfactory in a certain primitive sense, unlike quantitative regression theory where only squared error is logically satisfactory. The relation of Goodman and Kruskal's measures of categorical association to the theory of penalty functions and probability elicitation is demonstrated.
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Good, I. J. (1952) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1952.tb00104.x · Cited by 976
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The use of logit and probit models in strategic management research: Critical issues
Hoetker, G. (2007) · Strategic Management Journal · doi:10.1002/smj.582 · Cited by 1,519
How Biased is the Apparent Error Rate of a Prediction Rule?
Efron, B. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478291 · Cited by 587
Self-citationA Better Coefficient of Determination for Genetic Profile Analysis
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Identifying adolescents at risk for hard drug use: racial/ethnic variations
Ellickson, P. L., & Morton, S. C. (1999) · Journal of Adolescent Health · doi:10.1016/s1054-139x(98)00144-x · Cited by 143
Metadata
- Authors
- Efron, B.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1978-03
- Volume
- 73
- Issue
- 361
- Pages
- 113-121
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2028520303
- Cited by
- 360
- References
- 1
- FWCI
- 3.14
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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