R-optimal design strategies for logistic regression models with complementary log-log link

Tofan Kumar  Biswal

doi:https://doi.org/10.59139/stattrans-2026-024

R-optimal design strategies for logistic regression models with complementary log-log link

Tofan Kumar Biswal Department of Statistics, Central University of Odisha, Sunabeda 763004, India ORCID:https://orcid.org/0000-0003-4379-1298 Statistics in Transition new series, vol. 27, 2026, 2, pages: 205-218 Published online: 9 June 2026 https://doi.org/10.59139/stattrans-2026-024 Citation: Biswal T. K., 2026. R-optimal design strategies for logistic regression models with complementary log-log link. Statistics in Transition new series, 27(2), pp. 205-218. https://doi.org/10.59139/stattrans-2026-024

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ABSTRACT

The manuscript explores optimal experimental design strategies, specifically R-optimality, for two-parameter logistic regression (2PLR) models using the complementary log-log (c-loglog) link function. The study seeks to establish efficient designs that minimize the average width of confidence bands across the range of p redictor variables. The general equivalence theorem validates the necessary and sufficient conditions of this optimality criterion.

KEYWORDS

logistic regression model, link function, R-optimality, equivalence theorem

REFERENCES

Agresti, A., (2002). Logistic regression. Categorical data analysis.

Atkinson, A., Donev, A., and Tobias, R., (2007). Optimum Experimental Designs, with SAS. 34, Oxford University Press, Oxford.

Bailey, R. A., and Simon, L. J., (1960). Two studies in automobile insurance ratemaking. ASTIN Bulletin: The Journal of the IAA, 1(4), pp. 192–217.

Biswal, T. K., (2024). R-optimal designs for Poisson regression model with two parameters. Pakistan journal of statistics, 40(3), pp. 285–300.

Biswal, T. K., (2024). R-optimal designs for Linear regression model in two explanatory variables. International Journal of Statistics and Reliability Engineering, pp. 1–12.

Chaloner, K., Larntz, K., (1989). Optimal Bayesian design applied to logistic regression experiments. Journal of Statistical Planning and Inference, 21(2), pp. 191–208.

Chernoff, H., (1953). Locally optimal designs for estimating parameters. The Annals of Mathematical Statistics, pp. 586–602.

De Jong, P., Heller, G. Z., (2008). Generalized linear models for insurance data. Cambridge Books.

Dette, H., Haines, L. M., (1994). E-optimal designs for linear and nonlinear models with two parameters. Biometrika, 81(4), pp. 739–754.

Dette, H., (1997). Designing experiments with respect to some ‘standardized’ optimality criteria. Journal of Royal Statistical Society, 59(B), pp. 97–110.

Dror, H. A., and Steinberg, D. M., (2006). Robust experimental design for multivariate generalized linear models. Technometrics, 48(4), pp. 520–529.

Ford, I., Torsney, B. and Wu, C. J., (1992). The use of a canonical form in the construction of locally optimal designs for non-linear problems. Journal of the Royal Statistical Society: Series B (Methodological), 54(2), pp. 569–583.

Fox, J., (2015). Applied Regression Analysis and Generalized Linear Models. Sage Publications.

Goldburd, M., Khare, A., Tevet, D. and Guller, D., (2016). Generalized linear models for insurance rating. Casualty Actuarial Society, Virginia.

Haines, L. M., Kabera, G. M., (2018). D-optimal designs for the two-variable binary logistic regression model with interaction. Journal of Statistical Planning and Inference, 193, pp. 136–150.

Kiefer, J., (1959). Optimum experimental designs. Journal of the Royal Statistical Society: Series B (Methodological), 21(2), pp. 272–304.

Kiefer, J., Wolfowitz, J., (1959). Optimal designs in regression problems. Annals of Mathematical Statistics, 30, pp. 271–294.

Lee, Y., and Nelder, J. A., (2002). Analysis of ulcer data using hierarchical generalized linear models. Statistics in Medicine, 21(2), pp. 191–202.

Liu, P., Gao, L. L. and Zhou, J., (2022). R-optimal designs for multi-response regression models with multi-factors. Communications in Statistics-Theory and Methods, 51(2), pp. 340–355.

Mathew, T., Sinha, B. K., (2001). Optimal designs for binary data under logistic regression. Journal of Statistical Planning and Inference, 93(1-2), pp. 295–307.

McCullough, P., Nelder, J. A., (1989). Generalized linear models. Chapman and hall. New York.

Myers, R. H., and Montgomery, D. C., (1997). A tutorial on generalized linear models. Journal of Quality Technology, 29(3), pp. 274–291.

Nelder, J. A., Wedderburn, R. W., (1972). Generalized linear models. Journal of the Royal Statistical Society Series A: Statistics in Society, 135(3), pp. 370–384.

Panda, M. K., Sahoo, R. P., (2022). R-optimal designs for linear log contrast model with mixture experiments. Communications in Statistics-Theory and Methods, 53(7), pp. 2355–2368.

Panda, M. K., Biswal, T. K., (2024). R-optimal designs for logistic regression model with two variables, Statistics and Applications, 23(1), pp. 1–12 .

Panda, M. K., Biswal, T. K. and Gupta V. K., (2024). R-Optimal Designs for Gamma Regression Model with Two Parameters. Statistics and Applications, 23(1), pp. 33–53.

Russell, K. G., (2018). Design of experiments for generalized linear models, CRC Press.

Shiboski, S. C. and Jewell, N. P., (1992). Statistical analysis of the time dependence of HIV infectivity based on partner study data. Journal of the American Statistical Association, 87(418), pp. 360–372.

Silvey, S. D., (1980). Optimal Design, London: Chapman and Hall.

Sitter, R. R. and Wu, C. F. J., (1993). Optimal designs for binary response experiments: Fieller, D, and A criteria. Scandinavian Journal of Statistics, pp. 329–341.