Dichotomous Logistic Regression with Leave-One-Out Validation

In this paper, the concepts of dichotomous logistic regression (DLR) with leave-one-out (L-O-O) were discussed. To illustrate this, the L-O-O was run to determine the importance of the simulation conditions for robust test of spread procedures with good Type I error rates. The resultant model was then evaluated. The discussions included 1) assessment of the accuracy of the model, and 2) parameter estimates. These were presented and illustrated by modeling the relationship between the dichotomous dependent variable (Type I error rates) with a set of independent variables (the simulation conditions). The base SAS software containing PROC LOGISTIC and DATA step functions can be making used to do the DLR analysis.

Authors:

• Sin Yin Teh
• Abdul Rahman Othman
• Michael Boon Chong Khoo

Keywords:

• Dichotomous logistic regression
• leave-one-out
• testof spread.

References:

[1] A. Agresti, An Introduction to Categorical Data Analysis, 2nd ed. New
York: Wiley, 2002.
[2] J. M. Henshall, and M. E. Goddard, "Multiple-trait mapping of
quantitative trait loci after selective genotyping using logistic
regression," Genetics, vol.151, pp. 885-894, 1999.
[3] D. F. Levinson, P. Holmans, R. E. Straub, M. J. Owen, D. B.
Wildenauer, P. V. Gejman, A. E. Pulver, C. Laurent, K. S. Kendler, D.
Walsh, N. Norton, N. M. Williams, S. G. Schwab, B. Lerer, B. J.
Mowry, A. R. Sanders, S. E. Antonarakis, J. L. Blouin, , J. F. DeLeuze,
and J. Mallet, "Multicenter linkage study of schizophrenia candidate
regions on chromosomes 5q, 6q, 10p and 13q: Schizophrenia linkage
collaborative group III," American Journal of Human Genetics, vol. 67,
pp. 652-663.
[4] A. DeMaris, "Feedback: Interpreting logistic regression results: A
critical commentary," Journal of Marriage and the Family, vol. 52, pp.
271-277, 1990.
[5] P. S. Morgan, and J. D. Teachman, "Logistic regression: Description,
examples, and comparisons," Journal of Marriage and the Family,
vol.50, pp. 928-936, 1988.
[6] I. L. Lottes, M. A. Adler, and A. DeMaris, "Using and interpreting
logistic regression: A guide for teaching and students," Journal of
Teaching Sociology, vol. 24, pp. 284-298, 1996.
[7] D. R. Cox, and E. J. Snell, The Analysis of Binary Data, 2nd ed. London:
Chapman & Hall, 1989.
[8] D. W. Hosmer, and S. Lemeshow, Applied Logistic Regression. New
York: Wiley, 1989.
[9] F. Azuaje, "Genomic data sampling and its effect on classification
performance assessment," BMC Bioinformatics, vol.4, pp. 1-14, 2003.
[10] D. Pregibon, "Logistic regression diagnostics," The Annals of Statistics,
vol.9, pp. 705-724, 1981.
[11] P. McCullagh, and J. A. Nelder, Generalized linear models, 2nd ed.
London: Chapman and Hall, 1989.
[12] M. Crask, and Perreault, "Validation of discriminant analysis in
marketing research," Journal of Marketing Research, vol.14, pp.60-68,
1977.
[13] W. R. Dillon, and M. Goldstein, Multivariate Analysis: Methods and
Applications. New York: Wiley, 1984.
[14] P. A. Lachenbruch, Discriminant Analysis. New York: Hafner, 1975.
[15] G. Gong, "Cross-validation, the jackknife and the bootstrap excess error
estimation in forward regression logistic regression," Journal of the
American Statistical Association, vol.81, no.393, pp.108-113, 1986.
[16] C. J. Huberty, Applied Discriminant Analysis. New York: Wiley, 1994.
[17] R. A. Johnson, and D. W. Wichern, Applied Multivariate Statistical
Analysis, 5th ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
[18] C. J. Huberty, J. M. Wisenbaker, J. D. Smith, and J. C. Smith, "Using
categorical variables in discriminant analysis," Multivariate Behavioral
Research, vol.21, pp. 479-496, 1986.
[19] D. C. Montgomery, E. A. Peck, and G. Vinning, An Introduction to
Linear Regression Analysis, 3rd ed. New York: Wiley, 2001.
[20] S. Menard, Applied Logistic Regression Analysis, 2nd ed. Thousand
Oaks: Sage Publications, 2002.
[21] D. G. Kleinbaum, L. L. Kupper, K. E. Muller, and A. Nizam, Applied
Regression Analysis and Other Multivariate Methods. New York:
Duxbury Press, 1998.
[22] H. J. Keselman, R. R. Wilcox, J. Algina, A. R. Othman, and K. A.
Fradette, "Comparative study of robust tests for spread: asymmetric
trimming strategies," British Journal of Mathematical and Statistical
Psychology, vol.61, pp.235-253, 2008.
[23] A. I. Fleishman, "A method for simulating non-normal distributions,"
Psychometrika, vol.43, pp. 521-532, 1978.
[24] D. C. Hoaglin, Summarizing Shape Numerically: The g- and h-
Distributions. In D. C. Hoaglin, F. Mosteller & J. Tukey (Eds.),
Exploring Data Tables, Trends, and Shapes (pp. 461-513). New York:
Wiley, 1985.