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Pseudo-score confidence intervals for parameters in discrete statistical models

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  • Alan Agresti
  • Euijung Ryu

Abstract

We propose pseudo-score confidence intervals for parameters in models for discrete data. The confidence interval is obtained by inverting a test that uses a Pearson chi-squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values. For multinomial models, the pseudo-score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test-based inferences. For cases in which ordinary score methods are impractical, such as when the likelihood function is not an explicit function of model parameters, the pseudo-score method is feasible. We illustrate the method for four such examples. Generalizations of the method are also presented for future research, including inference for complex sampling designs using a quasilikelihood Pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model. Copyright 2010, Oxford University Press.

Suggested Citation

  • Alan Agresti & Euijung Ryu, 2010. "Pseudo-score confidence intervals for parameters in discrete statistical models," Biometrika, Biometrika Trust, vol. 97(1), pages 215-222.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:1:p:215-222
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    File URL: http://hdl.handle.net/10.1093/biomet/asp074
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    Cited by:

    1. Maricela Cruz & Hernando Ombao & Daniel L. Gillen, 2022. "A Generalized Interrupted Time Series Model for Assessing Complex Health Care Interventions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 582-610, December.
    2. Zhu, Qiansheng & Lang, Joseph B., 2022. "Test-inversion confidence intervals for estimands in contingency tables subject to equality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    3. Alan Agresti, 2014. "Two Bayesian/frequentist challenges for categorical data analyses," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 125-132, August.
    4. 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.

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