Multiple imputation of industry and occupation codes in census public-use samples using Bayesian logistic regression

Journal of the American Statistical Association

Volumn 86, Issue 413, 1991, Pages 68-78

  Clogg, Clifford C ^a   Rubin, Donald B ^b   Schenker, Nathaniel ^c   Schultz, Bradley ^d   Weidman, Lynn ^e  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d U S ENVIRONMENTAL PROTECTION AGENCY   (United States)

^e U S CENSUS BUREAU   (United States)

Author keywords

Maximum likelihood; Missing data; Multiple imputation; Prior distribution; Sparse data; Structural zeros

Indexed keywords

EID: 0001913059     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1991.10475005     Document Type: Article

References (65)

1. Albert, A., and Anderson, J. A. (1984), “On the Existence of Maximum Likelihood Estimates in Logistic Regression Models,” Biometrika, 71, 1–10.
2. Anderson, J. A. (1980), “Logistic Discrimination,” in Handbook of Statistics (Vol. 2: Classification, Pattern Recognition, and Reduction of Dimension), eds. P. R. Krishnaiah, and L. Kanal, New York: North-Holland.
3. Anscombe, F. J. (1956), “On Estimating Binomial Response Relations,” Biometrika, 43, 461–464.
4. Bartlett, M. S. (1935), “Contingency Table Interactions,” Journal of the Royal Statistical Society, Supplement, 2, 248–252.
5. Begg, C. B., and Gray, R. (1984), “Calculation of Polychotomous Logistic Regression Parameters Using Individualized Regressions,” Biometrika, 71, 11–18.
6. Birch, M. W. (1963), “Maximum Likelihood in Three-Way Contingency Tables,” Journal of the Royal Statistical Society, Ser. B, 25, 220–233.
7. Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: MIT Press.
8. Box, G. E. P., and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis, Reading, MA: Addison-Wesley.
9. Bull, S. B., and Donner, A. (1987), “The Efficiency of Multinomial Logistic Regression Compared With Multiple Group Discriminant Analysis, “Journal of the American Statistical Association, 82, 111 8–1122.
10. X,” in Computer Science and Statistics: 17th Symposium on the Interface, ed. D. M. Allen, Amsterdam: North-Holland.
11. Clogg, C. C., and Eliason, S. R. (1987), “Some Common Problems in LogLinear Analysis,” Sociological Methods and Research, 15, 8–44.
12. 2 Test,” Biometrics, 10, 417–451.
13. Cox, D. R. (1970), Analysis of Binary Data, London: Methuen.
14. Cox, D. R., and Hinkley, D. A. (1974), Theoretical Statistics, London: Chapman and Hall.
15. Das Gupta, S. (1980), “Discriminant Analysis,” in R. A. Fisher: An Appreciation, eds. S. E. Fienberg, and D. V. Hinkley, New York: SpringerVerlag.
16. Davis, L. J. (1985), “Modification of the Empirical Logit to Reduce Bias in Simple Linear Logistic Regression,” Biometrika, 72, 199–202.
17. Dillon, W. R., and Goldstein, M. (1984), Multivariate Analysis, New York: John Wiley.
18. Efron, B. (1975), “The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis,” Journal of the American Statistical Association, 70, 892–898.
19. Fienberg, S. E. (1980), The Analysis of Cross-Classified Categorical Data (2nd ed.), Cambridge, MA: MIT Press.
20. Fienberg, S. E., and Holland, P. W. (1972), “On the Choice of Flattening Constants for Estimating Multinomial Probabilities,” Journal of Multivariate Analysis, 2, 127–134.
21. —— (1973), “Simultaneous Estimation of Multinomial Cell Probabilities,” Journal of the American Statistical Association, 68, 683–691.
22. Gart, J. J., and Zweifel, J. R. (1967), “On the Bias of Various Estimators of the Logit and Its Variance With Application to Quantal Bioassay,” Biometrika, 54, 181–187.
23. Gart, J. J., Pettigrew, H. M., and Thomas, D. G. (1985), “The Effect of Bias, Variance Estimation, Skewness and Kurtosis of the Empirical Logit on Weighted Least Squares Analyses,” Biometrika, 72, 179–190.
24. Geisser, S. (1984), “On Prior Distributions for Binary Trials,” The American Statistician, 38, 244–247.
25. Good, I. J. (1965), The Estimation of Probabilities, Cambridge, MA: MIT Press.
26. Goodman, L. A. (1964), “Simultaneous Confidence Limits for Cross-Product Ratios in Contingency Tables,” Journal of the Royal Statistical Society, Ser. B, 26, 86–102.
27. —— (1968), “The Analysis of Cross-Classified Data: Independence, Quasi-Independence, and Interactions in Contingency Tables With or Without Missing Entries,” Journal of the American Statistical Association, 63, 1091–1131.
28. —— (1970), “The Multivariate Analysis of Qualitative Data: Interactions Among Multiple Classifications,” Journal of the American Statistical Association, 65, 226–256.
29. Gunel, E., and Dickey, J. (1974), “Bayes Factors for Independence in Contingency Tables,” Biometrika, 61, 545–557.
30. Haberman, S. J. (1973), “Loglinear Models for Frequency Data: Sufficient Statistics and Likelihood Equations,” The Annals of Statistics, 1, 617–632.
31. —— (1974), The Analysis of Frequency Data, Chicago: University of Chicago Press.
32. —— (1977), “Log-Linear Models and Frequency Tables With Small Expected Counts,” The Annals of Statistics, 5, 1148–1169.
33. —— (1978), Analysis of Qualitative Data (Vol. 1. Introductory Topics), New York: Academic Press.
34. —— (1988), “A Warning on the Use of Chi-Squared Statistics With Frequency Tables With Small Expected Cell Counts,” Journal of the American Statistical Association, 83, 555–560.
35. Haldane, J. B. S. (1955), “The Estimation and Significance of the Logarithm of a Ratio of Frequencies,” Annals of Human Genetics, 20, 309–311.
36. 2 Method,” Biometrika, 49, 250–252.
37. Leonard, T. (1975), “Bayesian Estimation Methods for Two-Way Contingency Tables,” Journal of the Royal Statistical Society, Ser. B, 37, 23–37.
38. Li, K. H. (1985), “Hypothesis Testing in Multiple Imputation—With Emphasis on Mixed-Up Frequencies in Contingency Tables,” unpublished Ph.D. dissertation, University of Chicago, Department of Statistics.
39. Lindley, D. V. (1964), “The Bayesian Analysis of Contingency Tables,” The Annals of Mathematical Statistics, 35, 1622–1643.
40. Little, R. J. A., and Rubin, D. B. (1987), Statistical Analysis with Missing Data, New York: John Wiley.
41. McCullagh, P., and Neider, J. A. (1983), Generalized Linear Models, London: Chapman & Hall.
42. McFadden, D. (1976), “A Comment on Discriminant Analysis ‘versus’ Logit Analysis,” Annals of Economic and Social Measurement, 5, 511–523.
43. Plackett, R. L. (1981), The Analysis of Categorical Data (2nd ed.), New York: Macmillan.
44. Prentice, R. L. (1986), “Binary Regression Using an Extended Beta-Binomial Distribution, With Discussion of Correlation Induced by Covariate Measurement Errors,” Journal of the American Statistical Association, 81, 321–327.
45. Press, S. J. and Wilson, S. (1978), “Choosing Between Logistic Regression and Discriminant Analysis,” Journal of the American Statistical Association, 73, 699–705.
46. Raghunathan, T. E. (1987), Large Sample Significance Levels from Multiply-Imputed Data, unpublished Ph.D. dissertation, Harvard University, Dept. of Statistics.
47. Rubin, D. B. (1974), “Characterizing the Estimation of Parameters in Incomplete Data Problems,” Journal of the American Statisticial Association, 69, 467–474.
48. —— (1980), Handling Nonresponse in Sample Surveys by Multiple Imputation, Washington, DC: U.S. Bureau of the Census.
49. —— (1983), Progress Report on Project for Multiple Imputation of 1980 Codes, unpublished manuscript distributed to the U.S. Bureau of the Census, the National Science Foundation, and the Social Science Research Council.
50. —— (1986), “Statistical Matching Using File Concatenation With Adjusted Weights and Multiple Imputations,” Journal of Business and Economic Statistics, 4, 87–94.
51. —— (1987a), Multiple Imputation for Nonresponse in Surveys, New York: John Wiley.
52. —— (1987b), “Discussion of Tanner and Wong,” Journal of the American Statistical Association, 82, 543–546.
53. Rubin, D. B., and Schenker, N. (1986), “Multiple Imputation for Interval Estimation From Simple Random Samples with Ignorable Nonresponse,” Journal of the American Statistical Association, 81, 366–374.
54. —— (1987a), “Interval Estimation From Multiply-Imputed Data: A Case Study Using Census Agriculture Industry Codes,” Journal of Official Statistics, 3, 375–387.
55. —— (1987b), “Logit-Based Interval Estimation for Binomial Data Using the Jeffreys Prior,” in Sociological Methodology 1987, ed. C. C. Clogg, Washington, D.C.: American Sociologicial Association.
56. Schenker, N., and Welsh, A. H. (1988), “Asymptotic Results for Multiple Imputation,” The Annals of Statistics, 16, 1550–66.
57. Schenker, N., Treiman, D. J., and Weidman, L. (1989) “Analysis of Public-Use Data with Multiply-Imputed Industry and Occupation Codes,” UCLA Statistics Series, #39.
58. Silverstone, H. (1957), “Estimating the Logistic Curve,” Journal of the American Statistical Association, 52, 567–577.
59. Subcommittee on Comparability of Occupational Measurement (1983), Alternative Methods for Effecting the Comparability of Occupation Measurement Over Time, Report to the Social Science Research Council and the U.S. Bureau of the Census.
60. Treiman, D. J., Bielby, W., and Cheng, M. (1988), “Evaluating a Multiple-Imputation Method for Recalibrating 1970 U.S. Census Detailed Industry Codes to the 1980 Standard,” in Sociological Methodology 1988, ed. C. C. Clogg, Washington, DC: American Sociological Association.
61. Treiman, D. J., and Rubin, D. B. (1983), Multiple Imputation of Categorical Data to Achieve Calibrated Public-Use Samples, unpublished proposal to the National Science Foundation.
62. U.S. Bureau of Census (1983), Detailed Occupation and Years of School Completed by Age, for the Civilian Labor Force by Sex, Race, and Spanish Origin: 1980, Supplementary Report PC80-S1-8, Washington, DC: U.S. Government Printing Office.
63. U.S. Bureau of Census (1984), Detailed Occupation of the Experienced Civilian Labor Force by Sex for the United States and Regions: 1980 and 1970, Supplementary Report PC80-S1-15, Washington, DC: U.S. Government Printing Office.
64. Weld, L. H. (1987), Significance Levels from Public Use Data With Multiply-Imputed Industry Codes, unpublished Ph.D. dissertation, Harvard University, Dept. of Statistics.
65. Wong, G. Y., and Mason, W. M. (1985), “The Hierarchical Logistic Regression Model for Multilevel Analysis,” Journal of the American Statistical Association, 80, 513–524.