Application of tetrachoric and polychoric correlation coefficients to forecasts verification

Geofizika

Volumn 23, Issue 1, 2006, Pages 59-82

  Juras, Josip ^a   Pasarić, Zoran ^a  

^a UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Contingency table; Forecast evaluation; Tetrachoric correlation coefficient

Indexed keywords

CORRELATION; PRECIPITATION (CLIMATOLOGY); WEATHER FORECASTING;

EID: 33746087650     PISSN: 03523659     EISSN: 18466346     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Barnston, A. G. (1992): Correspondence among the correlation, RMSE, and Heidke forecast verification measures; refinement of the Heidke score, Weather Forecast., 7, 699-709.
2. Brooks, C. E. P. and Carruthers, N. (1953): Handbook of Statistical Methods in Meteorology. Her Majesty's Stationery Office, London, 412 pp.
3. Brown, M. B. (1977): Algorithm AS 116: The tetrachoric correlation and its asymptotic standard error, Appl. Stat-J. Roy. St. C., 26, 345-351.
4. Daan, H. (1984): Scoring Rules in Forecast Verification. Number 4 in PSMP Publication Series, WMO, 62 pp.
5. Doswell, C. A., III, Davies-Jones, R. P. and Keller, D. L. (1990): On summary measures of skill in rare event forecasting based on contingency tables, Weather Forecast., 5, 576-585.
6. Gandin, L. S. and Murphy, A. H. (1992): Equitable skill scores for categorical forecasts. Mon. Weather Rev., 120, 361-370.
7. Gerrity, J. P., Jr. (1992): A note on Gandin and Murphy's equitable skill score, Mon. Weather Rev., 120, 2709-2712.
8. Gringorten, I. I. (1971): Modeling conditional probability, J. Appl. Meteorol., 10, 646-657.
9. Gringorten, I. I. (1972): Conditional probability for an exact noncategorized initial condition, Mon. Weather Rev., 100, 796-798.
10. Hamdan, M. A. (1970): The equivalence of tetrachoric and maximum likelihood estimates of ρ in 2×2 tables. Biometrika, 57, 212-215.
11. IMSL Library 1 (1975): International Mathematical and Statistical Libraries, Houston, Texas, 5 edition.
12. Johnson, N. L. and Kotz, S. (1972): Distributions in Statistics. 4. Continuous Multivariate Distributions. Wiley, New York 333 pp.
13. Juras, J. (1982): Comparison of models for estimating the joint probability of a weather event, J. Appl. Meteorol., 21, 1926-1928.
14. Kendall, M. G. and Stuart, A. (1973): The Advanced Theory of Statistics, volume 2. Griffin, London, 723 pp.
15. Kruizinga, S., Blaauboer, D. and van Vliet., K. (1989): Statistical input for a fog forecasting system. Preprints, 11th Conference on probability and statistics, Amer. Meteor. Soc., Montrey, California, 84-87.
16. Martinson, E. O. and Hamdan, M. A. (1971): Maximum likelihood and some other asymptotically efficient estimators of correlation in two way tables. J. Stat. Comput. Sim., 1, 45-54.
17. Marzban, C. (1998): Scalar measures of performance in rare-event situations, Weather Forecast., 13, 753-763.
18. Marzban, C. and Lakshmanan, V. (1999): On the uniqueness of Gandin and Murphy's equitable performance measures, Mon. Weather Rev., 127, 1134-1136.
19. Murphy, A. H. (1995): The coefficient of correlation and determination as measures of performance in forecast verification, Weather Forecast., 10, 681-688.
20. Murphy, A. H. (1996): The Finley affair: A signal event in the history of forecast verification, Weather Forecast., 11, 3-20.
21. Murphy, A. H. and Epstein, S. (1989): Skill scores and correlation coefficients in model verification, Mon. Weather Rev., 117, 572-581.
22. National Bureau of Standards (1959): Tables of Bivariate Normal Distribution Function and Related Functions. Number 50 in NBS Appl. Math. Series, Govt. Printing Office, Washington, D. C., 258 pp.
23. Olsson, U. (1979): Maximum likelihood estimation of the polychoric correlation coefficient, Psichometrika, 44, 443-460.
24. Panofsky, H. A. and Brier, G. W. (1958): Some Applications of Statistics to Meteorology. Pennsylvania State University, University Park, 224 pp.
25. Pearson, K. (1900): Mathematical contributions to the theory of evolution. VII. On the correlation of characters not quantitatively measurable, Philos. Tr. R. Soc. S.-A, 195, 1-47.
26. Pearson, K. and Heron, D. (1913): On theories of association. Biometrika, 9, 159-315.
27. Potts, J. M., Folland, C. K, Jolliffe, I. T. and Sexton, D. (1996): Revised «LEPS» scores for assessing climate model simulations and long-range forecasts. J. Climate, 9, 34-53.
28. Reed, R. J. (1983): A note on the relationship between relative precipitation frequency and percent of correct forecasts. B. Am. Meteorol. Soc., 64, 148-149.
29. Rousseau, D. (1980): A new skill score for the evaluation of yes/no forecasts. Proc. WWO Symposium on Probabilistic and Statistical Methods in Weather Forecasting, WMO, Nice, France, 167-174.
30. Sheppard, W. F. (1898): On the application of the theory of error to cases of normal distributions and normal correlations, Philos. Tr. R. Soc. S.-A, 192, 101-167.
31. Stansky, H. R., Wilson, L. J. and Burrows, W. R. (1989): Survey of Common Verification Methods in Meteorology. Number 358 in WMO/TD., WMO, Geneva, Switzerland, 114 pp.
32. Stephenson, D. B. (2000): Use of the «odds ratio» for diagnosing forecast skill, Weather Forecast., 15, 221-232.
33. Ward, M. N. and Folland, C. K. (1991): Prediction of seasonal rainfall in the north nordeste of Brazil using eigenvectors of sea-surface temperature, Int. J. Climatol., 11, 711-743.
34. Wilks, D. (1995): Statistical Methods in the Atmospheric Sciences, Academic Press, San Diego, 464 pp.
35. Woodcock, F. (1976): The evaluation of yes/no forecasts for scientific and administrative purposes, Mon. Weather Rev., 104, 1209-1214.