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Year 2019, Volume: 03 Issue: 1, 15 - 25, 31.08.2019
https://doi.org/10.34110/forecasting.514761

Abstract

References

  • [1] P. Royston and D. G. Altman, ‘Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling’, Appl. Stat., vol. 43, no. 3, pp. 429–467, 1994.
  • [2] P. Royston and W. Sauerbrei, ‘Multivariable model-building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables’. John Wiley & Sons, 2008.
  • [3] L. Breiman, ‘Bagging predictors’, Mach. Learn., vol. 24, no. 2, pp. 123–140, 1996.
  • [4] J. H. Friedman, ‘Multivariate adaptive regression splines’, Ann. Stat., pp. 1–67, 1991.
  • [5] B. Efron, T. Hastie, I. Johnstone, R. Tibshirani, and others, ‘Least angle regression’, Ann. Stat., vol. 32, no. 2, pp. 407–499, 2004.
  • [6] P. Royston and W. Sauerbrei, Multivariable model-building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables. John Wiley & Sons, 2008.
  • [7] G. Ambler and P. Royston, ‘Fractional polynomial model selection procedures: investigation of Type {I} error rate’, J. Stat. Comput. Simul., vol. 69, no. 1, pp. 89–108, 2001.
  • [8] W. Sauerbrei and P. Royston, ‘Corrigendum: Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials’, J. R. Stat. Soc. Ser. A (Statistics Soc., vol. 165, no. 2, pp. 399–400, 2002.
  • [9] C. Darwin, ‘The origin of species by means of natural selection, or, The preservation of favored races in the struggle for life. Vol. 1’, Int. Sci. Libr., 1897.
  • [10] J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press, 1975.
  • [11] S. Owais, P. Gajdoš, and V. Snášel, ‘Usage of genetic algorithm for lattice drawing’, Concept Lattices Appl., vol. 2005, pp. 82–91, 2005.
  • [12] D. E. Golberg, ‘Genetic algorithms in search, optimization, and machine learning’, Addion wesley, vol. 1989, p. 102, 1989.
  • [13] R. L. Haupt and H. S. Ellen, Practical genetic algorithms. John Wiley & Sons, 2004.
  • [14] L. Scrucca, ‘{GA}: A Package for Genetic Algorithms in {R}’, J. Stat. Softw., vol. 53, no. 4, pp. 1–37, 2013.
  • [15] M. Wahde, Biologically inspired optimization methods: an introduction. WIT press, 2008.
  • [16] G. Ambler and A. Benner, ‘mfp: Multivariable Fractional Polynomials.{ R} package version 1.4. 9’. 2010.
  • [17] A. A. Neath and J. E. Cavanaugh, ‘The Bayesian information criterion: background, derivation, and applications’, Wiley Interdiscip. Rev. Comput. Stat., vol. 4, no. 2, pp. 199–203, 2012.
  • [18] D. E. Goldberg and K. Deb, ‘A comparative analysis of selection schemes used in genetic algorithms’, Found. Genet. algorithms, vol. 1, pp. 69–93, 1991.
  • [19] T. Blickle and L. Thiele, ‘A comparison of selection schemes used in evolutionary algorithms’, Evol. Comput., vol. 4, no. 4, pp. 361–394, 1996.
  • [20] B. L. Miller and D. E. Goldberg, ‘Genetic algorithms, tournament selection, and the effects of noise’, Complex Syst., vol. 9, no. 3, pp. 193–212, 1995.

Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data

Year 2019, Volume: 03 Issue: 1, 15 - 25, 31.08.2019
https://doi.org/10.34110/forecasting.514761

Abstract

Fractional polynomials are powerful statistic tools used in
multivariable building model to select relevant variables and their functional
form. This selection of variables, together with their corresponding power is
performed through a multivariable fractional polynomials (MFP) algorithm that
uses a closed test procedure, called function selection procedure (FSP), based
on the statistical significance level α. In this paper, Genetic algorithms,
which are stochastic search and optimization methods based on string
representation of candidate solutions and various operators such as selection,
crossover and mutation; reproducing genetic processes in nature, are used as
alternative to MFP algorithm to select powers in an extended set of real
numbers (to be specified) by minimizing the Bayesian Information Criteria
(BIC). A simulation study and an application to a real dataset are performed to
compare the two algorithms in many scenarios. Both algorithms perform quite
well in terms of mean square error with Genetic algorithms that yied a more
parsimonious model comparing to MFP Algorithm
.

References

  • [1] P. Royston and D. G. Altman, ‘Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling’, Appl. Stat., vol. 43, no. 3, pp. 429–467, 1994.
  • [2] P. Royston and W. Sauerbrei, ‘Multivariable model-building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables’. John Wiley & Sons, 2008.
  • [3] L. Breiman, ‘Bagging predictors’, Mach. Learn., vol. 24, no. 2, pp. 123–140, 1996.
  • [4] J. H. Friedman, ‘Multivariate adaptive regression splines’, Ann. Stat., pp. 1–67, 1991.
  • [5] B. Efron, T. Hastie, I. Johnstone, R. Tibshirani, and others, ‘Least angle regression’, Ann. Stat., vol. 32, no. 2, pp. 407–499, 2004.
  • [6] P. Royston and W. Sauerbrei, Multivariable model-building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables. John Wiley & Sons, 2008.
  • [7] G. Ambler and P. Royston, ‘Fractional polynomial model selection procedures: investigation of Type {I} error rate’, J. Stat. Comput. Simul., vol. 69, no. 1, pp. 89–108, 2001.
  • [8] W. Sauerbrei and P. Royston, ‘Corrigendum: Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials’, J. R. Stat. Soc. Ser. A (Statistics Soc., vol. 165, no. 2, pp. 399–400, 2002.
  • [9] C. Darwin, ‘The origin of species by means of natural selection, or, The preservation of favored races in the struggle for life. Vol. 1’, Int. Sci. Libr., 1897.
  • [10] J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press, 1975.
  • [11] S. Owais, P. Gajdoš, and V. Snášel, ‘Usage of genetic algorithm for lattice drawing’, Concept Lattices Appl., vol. 2005, pp. 82–91, 2005.
  • [12] D. E. Golberg, ‘Genetic algorithms in search, optimization, and machine learning’, Addion wesley, vol. 1989, p. 102, 1989.
  • [13] R. L. Haupt and H. S. Ellen, Practical genetic algorithms. John Wiley & Sons, 2004.
  • [14] L. Scrucca, ‘{GA}: A Package for Genetic Algorithms in {R}’, J. Stat. Softw., vol. 53, no. 4, pp. 1–37, 2013.
  • [15] M. Wahde, Biologically inspired optimization methods: an introduction. WIT press, 2008.
  • [16] G. Ambler and A. Benner, ‘mfp: Multivariable Fractional Polynomials.{ R} package version 1.4. 9’. 2010.
  • [17] A. A. Neath and J. E. Cavanaugh, ‘The Bayesian information criterion: background, derivation, and applications’, Wiley Interdiscip. Rev. Comput. Stat., vol. 4, no. 2, pp. 199–203, 2012.
  • [18] D. E. Goldberg and K. Deb, ‘A comparative analysis of selection schemes used in genetic algorithms’, Found. Genet. algorithms, vol. 1, pp. 69–93, 1991.
  • [19] T. Blickle and L. Thiele, ‘A comparison of selection schemes used in evolutionary algorithms’, Evol. Comput., vol. 4, no. 4, pp. 361–394, 1996.
  • [20] B. L. Miller and D. E. Goldberg, ‘Genetic algorithms, tournament selection, and the effects of noise’, Complex Syst., vol. 9, no. 3, pp. 193–212, 1995.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Barnabe Ndabashinze This is me

Gülesen Ustundag Siray

Luca Scrucca This is me

Publication Date August 31, 2019
Submission Date January 18, 2019
Acceptance Date June 18, 2019
Published in Issue Year 2019 Volume: 03 Issue: 1

Cite

APA Ndabashinze, B., Ustundag Siray, G., & Scrucca, L. (2019). Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data. Turkish Journal of Forecasting, 03(1), 15-25. https://doi.org/10.34110/forecasting.514761
AMA Ndabashinze B, Ustundag Siray G, Scrucca L. Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data. TJF. August 2019;03(1):15-25. doi:10.34110/forecasting.514761
Chicago Ndabashinze, Barnabe, Gülesen Ustundag Siray, and Luca Scrucca. “Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data”. Turkish Journal of Forecasting 03, no. 1 (August 2019): 15-25. https://doi.org/10.34110/forecasting.514761.
EndNote Ndabashinze B, Ustundag Siray G, Scrucca L (August 1, 2019) Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data. Turkish Journal of Forecasting 03 1 15–25.
IEEE B. Ndabashinze, G. Ustundag Siray, and L. Scrucca, “Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data”, TJF, vol. 03, no. 1, pp. 15–25, 2019, doi: 10.34110/forecasting.514761.
ISNAD Ndabashinze, Barnabe et al. “Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data”. Turkish Journal of Forecasting 03/1 (August 2019), 15-25. https://doi.org/10.34110/forecasting.514761.
JAMA Ndabashinze B, Ustundag Siray G, Scrucca L. Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data. TJF. 2019;03:15–25.
MLA Ndabashinze, Barnabe et al. “Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data”. Turkish Journal of Forecasting, vol. 03, no. 1, 2019, pp. 15-25, doi:10.34110/forecasting.514761.
Vancouver Ndabashinze B, Ustundag Siray G, Scrucca L. Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data. TJF. 2019;03(1):15-2.

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