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Analysis of Categorical Data by Linear Models
Abstract
Assume there are ni., i = 1, 2, *--, s, samples from s multinomial distributions each having r categories of response. Then define any u functions of the unknown true cell probabilities {7rij: i = 1, 2, * , s; j = 1, 2, * , r, where E jrij l 1 } that have derivatives up to the second order with respect to 7rij, and for which the matrix of first derivatives is of rank u. A general noniterative procedure is described for fitting these functions to a linear model, for testing the goodness-of-fit of the model, and for testing hypotheses about the parameters in the linear model. The special cases of linear functions and logarithmic functions of the 7rin are developed in detail, and some examples of how the general approach can be used to analyze various types of categorical data are presented.
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Citations
Cites
THE COMPARISON OF PERCENTAGES IN MATCHED SAMPLES
COCHRAN, W. G. (1950) · Biometrika · doi:10.1093/biomet/37.3-4.256 · Cited by 1,465
Cited by
The Measurement of Observer Agreement for Categorical Data
Landis, J. R., & Koch, G. G. (1977) · Biometrics · doi:10.2307/2529310 · Cited by 81,148
Self-citationPsychopathology of Childhood Social Phobia
BEIDEL, D. C., TURNER, S. M., & MORRIS, T. L. (1999) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1097/00004583-199906000-00010 · Cited by 532
DiMarco, J. P., Miles, W., Akhtar, M., Milstein, S., Sharma, A. D., Platia, E., McGovern, B., Scheinman, M. M., & Govier, W. C. (1990) · Annals of Internal Medicine · doi:10.7326/0003-4819-113-2-104 · Cited by 306
SARAVOLATZ, L. D., POHLOD, D. J., & ARKING, L. M. (1982) · Annals of Internal Medicine · doi:10.7326/0003-4819-97-3-325 · Cited by 290
Tests for interaction in epidemiologic studies: A review and a study of power
Greenland, S. (1983) · Statistics in Medicine · doi:10.1002/sim.4780020219 · Cited by 280
Metadata
- Authors
- Grizzle, J. E., Starmer, C. F., & Koch, G. G.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1969-09
- Volume
- 25
- Issue
- 3
- Pages
- 489
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W2063803293
- Cited by
- 1,503
- References
- 1
- FWCI
- 19.18
- Type
- journal article
- Language
- en
- Open access
- closed
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