nach oben

Journal of Quantitative Economics

Erschienen in:

26.05.2022 | Original Article

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

verfasst von: Alan Agresti, Sabrina Giordano, Anna Gottard

Erschienen in: Journal of Quantitative Economics | Sonderheft 1/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

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.

Vorheriger Artikel Causal Inference of Social Experiments Using Orthogonal Designs

Nächster Artikel Bootstrap Version of Rao–Blackwellization to Two-Step and Instrumental Variable Estimators

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Agresti, A. 2003. Dealing with discreteness: Making ‘exact’ confidence intervals for proportions, differences of proportions, and odds ratios more exact. Statistical Methods in Medical Research 12 (1): 3–21.

Agresti, A. 2011. Score and pseudo-score confidence intervals for categorical data analysis. Statistics in Biopharmaceutical Research 3 (2): 163–172.

Agresti, A. 2013. Categorical Data Analysis. Oxford: Wiley.

Agresti, A., M. Bini, B. Bertaccini, and E. Ryu. 2008. Simultaneous confidence intervals for comparing binomial parameters. Biometrics 64 (4): 1270–1275.

Agresti, A., and B. Coull. 1998. Approximate is better than exact for interval estimation of binomial proportions. The American Statistician 52: 119–126.

Agresti, A., and A. Gottard. 2007. Nonconservative exact small-sample inference for discrete data. Computational Statistics and Data Analysis 51 (12): 6447–6458.

Agresti, A., and B. Klingenberg. 2005. Multivariate tests comparing binomial probabilities, with application to safety studies for drugs. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (4): 691–706.

Agresti, A., and Y. Min. 2001. On small-sample confidence intervals for parameters in discrete distributions. Biometrics 57 (3): 963–971.

Agresti, A., and Y. Min. 2005. Frequentist performance of Bayesian confidence intervals for comparing proportions in 2\(\times\) 2 contingency tables. Biometrics 61 (2): 515–523.

Agresti, A., and Y. Min. 2005. Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 24 (5): 729–740.

Agresti, A., and E. Ryu. 2010. Pseudo-score confidence intervals for parameters in discrete statistical models. Biometrika 97 (1): 215–222.

Bartolucci, F., R. Colombi, and A. Forcina. 2007. An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints. Statistica Sinica 17 (2): 691–711.

Birch, M. 1964. The detection of partial association, I: the 2\(\times\)2 case. Journal of the Royal Statistical Society: Series B (Methodological) 26 (2): 313–324.

Birch, M. 1965. The detection of partial association, II: the general case. Journal of the Royal Statistical Society: Series B (Methodological) 27 (1): 111–124.

Boos, D. 1992. On generalized score tests. The American Statistician 46 (4): 327–333.

Chan, I.S., and Z. Zhang. 1999. Test-based exact confidence intervals for the difference of two binomial proportions. Biometrics 55 (4): 1202–1209.

Coe, P.R., and A.C. Tamhane. 1993. Small sample confidence intervals for the difference, ratio and odds ratio of two success probabilities. Communications in Statistics - Simulation and Computation 22 (4): 925–938. https://doi.org/10.1080/03610919308813135CrossRef

Colombi, R., and A. Forcina. 2016. Testing order restrictions in contingency tables. Metrika 79 (1): 73–90.

Colombi, R., S. Giordano, and M. Cazzaro. 2014. hmmm: an R package for hierarchical multinomial marginal models. Journal of Statistical Software 59 (1): 1–25.

Cornfield, J. 1956. A statistical problem arising from retrospective studies. In Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, pp. 135–148. ed. J. Neyman.

Cox, D.R., and D.V. Hinkley. 1974. Theoretical Statistics. London: Chapman & Hall.

Cytel,. 2005. StatXact 7 User Manual and LogXact 7 User Manual. Cambridge, Massachusetts: Cytel Inc.

Dardanoni, V., and A. Forcina. 1998. A unified approach to likelihood inference on stochastic orderings in a nonparametric context. Journal of the American Statistical Association 93 (443): 1112–1123.

Darroch, J.N. 1981. The Mantel-Haenszel test and tests of marginal symmetry; fixed-effects and mixed models for a categorical response, correspondent paper. International Statistical Review/Revue Internationale de Statistique 49 (3): 285–307.

Day, N., and D. Byar. 1979. Testing hypotheses in case-control studies-equivalence of Mantel-Haenszel statistics and logit score tests. Biometrics 35 (3): 623–630.

Fagerland, M., S. Lydersen, and P. Laake. 2017. Statistical Analysis of Contingency Tables. Boca Raton: CRC Press.

Fagerland, M.W., S. Lydersen, and P. Laake. 2013. The McNemar test for binary matched-pairs data: mid-p and asymptotic are better than exact conditional. BMC Medical Research Methodology 13 (1): 1–8.

Fagerland, M.W., S. Lydersen, and P. Laake. 2015. Recommended confidence intervals for two independent binomial proportions. Statistical Methods in Medical Research 24 (2): 224–254.

Firth, D. 1993. Bias reduction of maximum likelihood estimates. Biometrika 80 (1): 27–38.

Grizzle, J.E., C.F. Starmer, and G.G. Koch. 1969. Analysis of categorical data by linear models. Biometrics 25: 489–504.

Grömping, U. 2010. Inference with linear equality and inequality constraints using R: The package ic-infer. Journal of Statistical Software 33 (1): 1–31.

Haberman, S.J. 1977. Log-linear models and frequency tables with small expected cell counts. The Annals of Statistics 5: 1148–1169.

Hothorn, T., L. Moest, and P. Buehlmann. 2018. Most likely transformations. Scandinavian Journal of Statistics 45 (1): 110–134.

Iannario, M., and J.B. Lang. 2016. Testing conditional independence in sets of I\(\times\)J tables by means of moment and correlation score tests with application to hpv vaccine. Statistics in Medicine 35 (25): 4573–4587.

Koopman, P. 1984. Confidence intervals for the ratio of two binomial proportions. Biometrics 40: 513–517.

Lancaster, H.O. 1961. Significance tests in discrete distributions. Journal of the American Statistical Association 56 (294): 223–234.

Lang, J.B. 2008. Score and profile likelihood confidence intervals for contingency table parameters. Statistics in Medicine 27 (28): 5975–5990.

Lang, J.B., J.W. McDonald, and P.W. Smith. 1999. Association-marginal modeling of multivariate categorical responses: A maximum likelihood approach. Journal of the American Statistical Association 94 (448): 1161–1171.

Lipsitz, S.R., G.M. Fitzmaurice, D. Sinha, N. Hevelone, E. Giovannucci, and J.C. Hu. 2015. Testing for independence in contingency tables with complex sample survey data. Biometrics 71 (3): 832–840.

Lovison, G. 2005. On Rao score and Pearson \(\chi ^2\) statistics in generalized linear models. Statistical Papers 46 (4): 555–574.

Mee, R.W. 1984. Confidence bounds for the difference between two probabilities (letter). Biometrics 40: 1175–1176.

Mehta, C.R., and N.R. Patel. 1995. Exact logistic regression: Theory and examples. Statistics in Medicine 14 (19): 2143–2160.

Miettinen, O., and M. Nurminen. 1985. Comparative analysis of two rates. Statistics in Medicine 4 (2): 213–226.

Molenberghs, G., and G. Verbeke. 2007. Likelihood ratio, score, and wald tests in a constrained parameter space. The American Statistician 61 (1): 22–27.

Newcombe, R.G. 1998. Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine 17 (8): 873–890.

Newcombe, R.G. 1998. Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine 17 (8): 857–872.

Ning, Y., H. Liu, et al. 2017. A general theory of hypothesis tests and confidence regions for sparse high dimensional models. Annals of Statistics 45 (1): 158–195.

Price, R.M., and D.G. Bonett. 2008. Confidence intervals for a ratio of two independent binomial proportions. Statistics in Medicine 27 (26): 5497–5508.

R Core Team. 2022. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.

Rao, C. R. 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. In Mathematical Proceedings of the Cambridge Philosophical Society, Volume 44: 50–57. Cambridge University Press.

Rao, C. R. 1961. A study of large sample test criteria through properties of efficient estimates: Part I: Tests for goodness of fit and contingency tables. Sankhyā: The Indian Journal of Statistics, Series A 23(1): 25–40.

Rao, J.N., and A.J. Scott. 1981. The analysis of categorical data from complex sample surveys: Chi-squared tests for goodness of fit and independence in two-way tables. Journal of the American Statistical Association 76 (374): 221–230.

Rotnitzky, A., and N.P. Jewell. 1990. Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data. Biometrika 77 (3): 485–497.

Ryu, E., and A. Agresti. 2008. Modeling and inference for an ordinal effect size measure. Statistics in Medicine 27 (10): 1703–1717.

Santner, T.J., V. Pradhan, P. Senchaudhuri, C.R. Mehta, and A. Tamhane. 2007. Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions. Computational Statistics and Data Analysis 51 (12): 5791–5799.

Shi, C., R. Song, W. Lu, and R. Li. 2020. Statistical inference for high-dimensional models via recursive online-score estimation. Journal of the American Statistical Association 116 (535): 1–12.

Siino, M., S. Fasola, and V.M. Muggeo. 2018. Inferential tools in penalized logistic regression for small and sparse data: A comparative study. Statistical Methods in Medical Research 27 (5): 1365–1375.

Silvapulle, M.J., and P.K. Sen. 2005. Constrained Statistical Inference: Inequality, Order and Shape Restrictions. Oxford: Wiley.

Silvey, S.D. 1959. The Lagrangian multiplier test. The Annals of Mathematical Statistics 30 (2): 389–407.

Smyth, G. K. 2003. Pearson’s goodness of fit statistic as a score test statistic. In Statistics and Science: a Festschrift for Terry Speed. Lecture notes-monograph series 40: 115–126, Institute of Mathematical Statistics, Hayward, CA.

Tang, Y. 2020. Score confidence intervals and sample sizes for stratified comparisons of binomial proportions. Statistics in Medicine 39 (24): 3427–3457.

Tango, T. 1998. Equivalence test and confidence interval for the difference in proportions for the paired-sample design. Statistics in Medicine 17 (8): 891–908.

Tarone, R.E., and J.J. Gart. 1980. On the robustness of combined tests for trends in proportions. Journal of the American Statistical Association 75 (369): 110–116.

Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 (1): 267–288.

Van de Geer, S., P. Bühlmann, Y. Ritov, and R. Dezeure. 2014. On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics 42 (3): 1166–1202.

Wald, A. 1943. Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54 (3): 426–482.

Wilks, S.S. 1938. The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9 (1): 60–62.

Wilson, E.B. 1927. Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association 22 (158): 209–212.

Zou, G., and A. Donner. 2008. Construction of confidence limits about effect measures: A general approach. Statistics in Medicine 27 (10): 1693–1702.

Titel: A Review of Score-Test-Based Inference for Categorical Data
verfasst von: Alan Agresti
Sabrina Giordano
Anna Gottard
Publikationsdatum: 26.05.2022
Verlag: Springer India
Erschienen in: Journal of Quantitative Economics / Ausgabe Sonderheft 1/2022
Print ISSN: 0971-1554
Elektronische ISSN: 2364-1045
DOI: https://doi.org/10.1007/s40953-022-00309-8

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Sonderheft 1/2022

Probabilistic Frontier Regression Models for Count Type Output Data

Bootstrap Version of Rao–Blackwellization to Two-Step and Instrumental Variable Estimators

Factor Analysis Regression for Predictive Modeling with High-Dimensional Data

Frequentist Model-based Statistical Induction and the Replication Crisis

Reverse Regressions, Symmetry and Test Distributions in Linear Models

Comparing the Secular Increasing Trend and Effect of the Response to the 2008 Financial Recession on Wealth Inequality in the U.S. with Other Nations Using the Median-based Gini Index

Premium Partner