29
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Improved likelihood ratio test for multinomial goodness of fit

Pages 3185-3198 | Received 01 Jul 1986, Published online: 27 Jun 2007

References

  • Berkson , J. 1953 . A Statistically precise and relatively simple method of estimating the bio-assay with quantal response, based on the logistic functions . Journal of the American Statistical Association , 48 : 565 – 599 .
  • Bishop , Y.M.M. , Feinberg , S.E. and Holland , P.W. 1975 . Discrete Multivariate Analysis , Cambridge, Massachusettes : The M.I.I. Press .
  • Chapman , J.W. 1976 . 1fA Comparison of the X2, -2 log R and Multinomial Probability Criteria for Significance Tests When Expected Frequencies are Small . Journal of the American Statistical Association , 71 : 854 – 863 .
  • Cochran , W.G. 1952 . The X2 Test of Goodness of Fit . Annals of Mathematical Statistics , 23 : 313 – 345 .
  • Cox , D.R. 1970 . The Analysis of Binary Data , London : Mathuen and Co., Ltd .
  • Good , I.J. , Cover , T.N. and Mitchell , G.J. 1970 . Exact Distri¬butions for X and for the Likelihood-Ratio Statistic for the Equiprobable Multinomial Distribution . Journal of the Americal Statistical Association , 65 : 267 – 283 .
  • Goodman , L.A. 1970 . The multivariate analysis of qualitative data: Interactions among multiple classifications . Journal of the American Statistical Association , 65 : 226 – 256 .
  • Grizzle , J.E. , Starmer , C.F. and Koch , C.E. 1969 . Analysis of categorical data by linear models . Biometrics , 25 : 489 – 504 .
  • Hauck , W.W. , Anderson , S. and Leahy , F.J. 1982 . Finite-Sample Properties of Some Old and Some New Estimators of a Common Odds Ratio from Multiple 2x2 Tables . Journal of the American Statistical Association , 77 : 145 – 152 .
  • Holtzman , G.I. and Good , I.J. 1986 . The Poisson and chi-squared approximations as compared with the true upper-tail probability of Pearson's for equiprobable multinom¬ials . Journal of Statistical Planning and Inference , 13 : 283 – 295 .
  • Hosmane , B.S. 1986 . Improved Likelihood Ratio Tests and Pear¬son Chi-square Tests for Independence in Two Dimensional Contingency Tables . Communications in Statistics, Theory and Methods , 15 : 1875 – 1888 .
  • Jennings , D.E. 1986 . Judging inference adequacy in logistic regression . Journal of the American Statistical Association , 81 : 471 – 476 .
  • Koehler , K.J. 1986 . Goodness-of-fit tests for log-linear models in sparse contingency tables . Journal of the American Statistical Association , 81 : 483 – 493 .
  • Koehler , K.J. and Larntz , K. 1980 . An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials . Journal of the American Statistical Association , 75 : 336 – 342 .
  • Larntz , K. 1978 . Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit Statistics . Journal of the American Statistical Association , 73 : 253 – 263 .
  • Lawal , H.B. 1984 . Comparison of the X , Y , Freeman-Tukey and Williams*s Improved G Test Statistics in Small samples . Biometrika , 71 : 415 – 418 .
  • Lawley , D.N. 1956 . A General Method for Approximating to the Distribution of Likelihood Ratio Criteria . Biometrika , 43 : 295 – 303 .
  • Mccullagh , P. 1986 . The conditional distribution of goodness-of-f it statistics for discrete data . Journal of the American Statistical Association , 81 : 104 – 107 .
  • Minkin , S. 1983 . Assessing the quadratic approximation to the log likelihood function in non-normal linear models . Biometrika , 70 : 367 – 372 .
  • Smith , P.J. , Rae , D.S. , Mander Scheid , R.W. and Silbergeld , S. 1981 . Approximating the Moments and distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit . Journal of the American Statistical Association , 76 : 737 – 740 .
  • Spruill , M.C. 1977 . Equally Likely Intervals in the Chi-square Test . Sankhya , 39 : 299 – 302 .
  • West , E.N. and Kempthorne , 0 . 1971 . A Comparison of the Chi and Likelihood Ratio Tests for Composite Alternatives . Journal of Statistical Computation and Simulation , 1 : 1 – 33 .
  • Williams , D.A. 1976 . Improved Likelihood Ratio Tests for Complete Contingency Tables . Biometrika , 63 : 33 – 37 .
  • Yarnold , J.K. 1970 . The Minimum Expectation of X2 Goodness of Fit Tests and the Accuracy of Approximations for the Null Distribution . Journal of the American Statistical Association , 65 : 864 – 886 .
  • Zelterman , D. 28 . Goodness of fit tests for large sparse tables of categorical data , New York at Albany : Technical Report .
  • Zelterman , D. 1984 . Approximating the distribution of goodness of fit tests for discrete data . Computational Statistics and Data Analysis , 2 : 207 – 214 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.