123
Views
0
CrossRef citations to date
0
Altmetric
Articles

Effects of dichotomizing continuous outcome on efficiencies of measures of explained variation in logistic regression: Simulation study and application

ORCID Icon

References

  • Aldrich, J. H., and F. D. Nelson. 1984. Linear Probability, Logit, and Probit Models. Beverly Hills: SAGE.
  • Altman, D. G., and P. Royston. 2006. “The Cost of Dichotomizing Continuous Variables.” British Medical Journal 332:1080.
  • Bakhshi, E., B. McArdle, K. Mohammad, B. Seifi, and A. Biglarian. 2012. “Let Continuous Outcome Variables Remain Continuous.” Computational and Mathematical Methods in Medicine 2012:1–13. doi: 10.1155/2012/639124..
  • Begg, M. D., and S. Lagakos. 1990. “On The Consequences of Model Misspecification in Logistic Regression.” Environmental Health Perspectives 87:69–75. doi: 10.1289/ehp.908769.
  • Bozkirli, E., M. E. Ertorer, O. Bakiner, N. B. Tutuncu, and N. G. Demirag. 2007. “The Validity of The World Health Organization’s Obesity Body Mass Index Criteria in a Turkish Population: A Hospital-Based Study.” Asia Pacific Journal of Clinical Nutrition 16(3):443–447.
  • Connor, R. J. 1972. “Grouping for Testing Trends in Categorical Data.” Journal of the American Statistical Association 67(339):601–604. doi: 10.1080/01621459.1972.10481256.
  • Cox, D. R., and D. V. Hinkley. 1974. Theoretical Statistics. London: Chapman and Hall.
  • Cox, D. R., and E. J. Snell. 1989. The Analysis of Binary Data. London: Chapman and Hall.
  • DasGupta, A. 2008. Asymptotic Theory of Statistics and Probability. New York: Springer.
  • DeMaris, A. 2002. “Explained Variance in Logistic Regression a Monte Carlo Study of Proposed Measures.” Sociological Methods & Research 31(1):27–74. doi: 10.1177/0049124102031001002.
  • Efron, B. 1975. “The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis.” Journal of the American Statistical Association 70(352):892–898. doi: 10.1080/01621459.1975.10480319.
  • Erees, S., and A. Alin. 2017. “Influences of Misspecification on Asymptotic Relative Efficiency of Coefficients of Determination: Application to Agriculture.” Communications in Statistics - Simulation and Computation 46(3):1842–1857. doi: 10.1080/03610918.2015.1016238..
  • Fedorov, V., F. Mannino, and R. Zhang. 2009. “Consequences of Dichotomization.” Pharmaceutical Statistics 8(1):50–61. doi: 10.1002/pst.331.
  • Hagle, T. M., and G. E. Mitchell. 1992. “Goodness-of-Fit Measures for Probit and Logit.” American Journal of Political Science 36(3):762–784. doi: 10.2307/2111590.
  • Harel, O. 2009. “The Estimation of R2 and Adjusted R2 in Incomplete Data Sets Using Multiple Imputation.” Journal of Applied Statistics 36 (10):1109–1118. doi: 10.1080/02664760802553000..
  • Hu, B., J. Shao, and M. Palta. 2006. “Pseudo-R2 in Logistic Regression Model.” Statistica Sinica 16:847–860.
  • Hu, B., M. Palta, and J. Shao. 2006. “Properties of R2 Statistics for Logistic Regression.” Statistics in Medicine 25 (8):1383–1395. doi: 10.1002/sim.2300.
  • Johnson, R. 1996. “Fitting Percentage of Body Fat to Simple Body Measurements.” Journal of Statistics Education 4(1). www.amstat.org/publications/jse/v4n1/datasets.johnson.html. doi: 10.1080/10691898.1996.11910505..
  • Kvalseth, T. O. 1985. “Cautionary Note About R2.” The American Statistician 39(4):279–285.
  • Lagakos, S. W. 1988. “Effects of Mismodelling and Mismeasuring Explanatory Variables on Tests of Their Association with a Response Variable.” Statistics in Medicine 7 (1–2):257–274. doi: 10.1002/sim.4780070126.
  • MacCallum, R. C., S. Zhang, K. J. Preacher, and D. D. Rucker. 2002. “On The Practice of Dichotomization of Quantitative Variables.” Psychological Methods 7(1):19–40. doi: 10.1037/1082-989x.7.1.19.
  • Maddala, G. S. 1983. Limited Dependent and Qualitative Variables in Economics. New York: Cambridge Press.
  • McFadden, D. 1974. “The Measurement of Urban Travel Demand.” Journal of Public Economics 3(4):303–328. doi: 10.1016/0047-2727(74)90003-6.
  • McKelvey, R. D., and W. Zavoina. 1975. “A Statistical Model for the Analysis of Ordinal Level Dependent Variables.” The Journal of Mathematical Sociology 4(1):103–120. doi: 10.1080/0022250X.1975.9989847.
  • Menard, S. 2000. “Coefficients of Determination for Multiple Logistic Regression Analysis.” The American Statistician 54(1):17–24.
  • Mittlböck, M., and M. Schemper. 1996. “Explained Variation for Logistic Regression.” Statistics in Medicine 15(19):1987–1997. doi: 10.1002/(SICI)1097-0258(19961015)15:19<1987::AID-SIM318>3.0.CO;2-9.
  • Moser, B. K., and L. P. Coombs. 2004. “Odds Ratios for a Continuous Outcome Variable without Dichotomizing.” Statistics in Medicine 23(12):1843–1860. doi: 10.1002/sim.1776.
  • Nagelkerke, N. J. D. 1991. “A Note on a General Definition of the Coefficient of Determination.” Biometrika 78(3):691–692. doi: 10.1093/biomet/78.3.691.
  • Naggara, O., J. Raymond, F. Guilbert, D. Roy, A. Weill, and D. G. Altman. 2011. “Analysis by Categorizing or Dichotomizing Continuous Variables is Inadvisable: An Example from the Natural History of Unruptured Aneurysms.” AJNR. American Journal of Neuroradiology 32(3):437–440. doi: 10.3174/ajnr.A2425.
  • Noether, G. E. 1955. “On a Theorem of Pitman.” The Annals of Mathematical Statistics 26(1): 64–68. doi: 10.1214/aoms/1177728593.
  • Penrose, K., A. Nelson, and A. Fisher. 1985. “Generalized Body Composition Prediction Equation for Men Using Simple Measurement Techniques.” Medicine and Science in Sports and Exercise 17(2):189.
  • Pitman, E. J. G. 1948. Lecture Notes on Non-Parametric Statistical Inference. New York: Colombia University.
  • Ragland, D. R. 1992. “Dichotomizing Continuous Outcome Variables: Dependence of the Magnitude of Association and Statistical Power on the Cutpoint.” Epidemiology 3(5):434–440.
  • Ramírez-Vélez, R.,. J. E. Correa-Bautista, A. Sanders-Tordecilla, M. L. Ojeda-Pardo, E. A. Cobo-Mejía, R. P. Castellanos-Vega, A. García-Hermoso, E. González-Jiménez, J. Schmidt-RioValle, and K. González-Ruíz. 2017. “Percentage of Body Fat and Fat Mass Index as a Screening Tool for Metabolic Syndrome Prediction in Colombian University Students.” Nutrients 9(9):1009. doi: 10.3390/nu9091009..
  • Romero-Corral, A., V. K. Somers, J. Sierra-Johnson, R. J. Thomas, M. L. Collazo-Clavell, J. Korinek, T. G. Allison, J. A. Batsis, F. H. Sert-Kuniyoshi, and F. Lopez-Jimenez. 2008. “Accuracy of Body Mass Index in Diagnosing Obesity in the Adult General Population.” International Journal of Obesity 32(6):959–966. doi: 10.1038/ijo.2008.11.
  • Royston, P., D. G. Altman, and W. Sauerbrei. 2006. “Dichotomizing Continuous Predictors in Multiple Regression: A Bad Idea.” Statistics in Medicine 25(1):127–141. doi: 10.1002/sim.2331.
  • Saikkonen, P. 1989. “Asymptotic Relative Efficiency of the Classical Test Statistics under Misspecification.” Journal of Econometrics 42(3):351–369. doi: 10.1016/0304-4076(89)90058-4.
  • Senn, S. 2013. “Being Efficient About Efficiency Estimation.” Statistics in Biopharmaceutical Research 5(3):204–210. doi: 10.1080/19466315.2012.754726.
  • Serfling, R. 1980. Approximation Theorems of Mathematical Statistics. New York: Wiley.
  • Shentu, Y., and M. Xie. 2010. “A Note on Dichotomization of Continuous Response Variable in the Presence of Contamination and Model Misspecification.” Statistics in Medicine 29(21):2200–2214. doi: 10.1002/sim.3966.
  • Stuart, A. 1954. “Asymptotic Relative Efficiencies of Distribution-Free Tests of Randomness against Normal Alternatives.” Journal of the American Statistical Association 49(265):147–157. doi: 10.1080/01621459.1954.10501221.
  • Taylor, A. B., S. G. West, and L. S. Aiken. 2006. “Loss of Power in Logistic, Ordinal Logistic and Probit Regression When an Outcome Variable is Coarsely Categorized.” Educational and Psychological Measurement 66(2):228–239. doi: 10.1177/0013164405278580.
  • Tosteson, T. D., and A. A. Tsiatis. 1988. “The Asymptotic Relative Efficiency of Score Tests in a Generalized Linear Model with Surrogate Covariates.” Biometrika 75(3):507–514. doi: 10.1093/biomet/75.3.507.
  • Vander Vaart, A. W. 2000. Asymptotic Statistics. Cambridge: Cambridge University Press.
  • Veall, M. R., and K. F. Zimmermann. 1996. “Pseudo-R2 Measures for Some Common Limited Dependent Variable Models.” Journal of Economic Surveys 10(3):241–259. doi: 10.1111/j.1467-6419.1996.tb00013.x.
  • Yoo, B. 2010. “The Impact of Dichotomization in Longitudinal Data Analysis: A Simulation Study.” Pharmaceutical Statistics 9(4):298–312. doi: 10.1002/pst.396.

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.