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A Review of Score-Test-Based Inference for Categorical Data

Author

Listed:
  • Alan Agresti

    (University of Florida)

  • Sabrina Giordano

    (University of Calabria)

  • Anna Gottard

    (University of Florence)

Abstract

One of C. R. Rao’s many important contributions to statistical science was his introduction of the score test, based on the derivative of the log-likelihood function at the null hypothesis value of the parameter of interest. This article reviews methods for constructing score tests and score-test-based confidence intervals for analyzing parameters that arise in analyzing categorical data. A considerable literature indicates that score tests and their inversion for constructing confidence intervals perform well in a variety of settings and sometimes much better than Wald-test and likelihood-ratio test-based methods. We also discuss extensions of score-based inference and potential future research on generalizations for longitudinal data, complex sampling, and high-dimensional data.

Suggested Citation

  • Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.
    • Handle: RePEc:spr:jqecon:v:20:y:2022:i:1:d:10.1007_s40953-022-00309-8
    DOI: 10.1007/s40953-022-00309-8
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    References listed on IDEAS

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    1. Santner, Thomas J. & Pradhan, Vivek & Senchaudhuri, Pralay & Mehta, Cyrus R. & Tamhane, Ajit, 2007. "Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5791-5799, August.
    2. R. Colombi & A. Forcina, 2016. "Testing order restrictions in contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 73-90, January.
    3. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    4. Agresti, Alan & Gottard, Anna, 2007. "Nonconservative exact small-sample inference for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6447-6458, August.
    5. Molenberghs, Geert & Verbeke, Geert, 2007. "Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space," The American Statistician, American Statistical Association, vol. 61, pages 22-27, February.
    6. Alan Agresti & Matilde Bini & Bruno Bertaccini & Euijung Ryu, 2008. "Simultaneous Confidence Intervals for Comparing Binomial Parameters," Biometrics, The International Biometric Society, vol. 64(4), pages 1270-1275, December.
    7. Stuart R. Lipsitz & Garrett M. Fitzmaurice & Debajyoti Sinha & Nathanael Hevelone & Edward Giovannucci & Jim C. Hu, 2015. "Testing for independence in J×K contingency tables with complex sample survey data," Biometrics, The International Biometric Society, vol. 71(3), pages 832-840, September.
    8. Gianfranco Lovison, 2005. "On Rao score and PearsonX 2 statistics in generalized linear models," Statistical Papers, Springer, vol. 46(4), pages 555-574, October.
    9. Alan Agresti & Yongyi Min, 2001. "On Small-Sample Confidence Intervals for Parameters in Discrete Distributions," Biometrics, The International Biometric Society, vol. 57(3), pages 963-971, September.
    10. Torsten Hothorn & Lisa Möst & Peter Bühlmann, 2018. "Most Likely Transformations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(1), pages 110-134, March.
    11. Colombi, Roberto & Giordano, Sabrina & Cazzaro, Manuela, 2014. "hmmm: An R Package for Hierarchical Multinomial Marginal Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i11).
    12. Shi, Chengchun & Song, Rui & Lu, Wenbin & Li, Runzi, 2020. "Statistical inference for high-dimensional models via recursive online-score estimation," LSE Research Online Documents on Economics 103043, London School of Economics and Political Science, LSE Library.
    13. Ivan S. F. Chan & Zhongxin Zhang, 1999. "Test-Based Exact Confidence Intervals for the Difference of Two Binomial Proportions," Biometrics, The International Biometric Society, vol. 55(4), pages 1202-1209, December.
    14. Alan Agresti & Bernhard Klingenberg, 2005. "Multivariate tests comparing binomial probabilities, with application to safety studies for drugs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(4), pages 691-706, August.
    15. Alan Agresti & Euijung Ryu, 2010. "Pseudo-score confidence intervals for parameters in discrete statistical models," Biometrika, Biometrika Trust, vol. 97(1), pages 215-222.
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