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A new multidimensional model II regression based on bisector approach

Yıl 2023, Cilt: 72 Sayı: 4, 1187 - 1200, 29.12.2023
https://doi.org/10.31801/cfsuasmas.1292470

Öz

A new multidimensional Model II regression based on bisector point of view (BRM-II) is introduced for multivariate problems that may contain measurement error. The suggested method is constructed depending on using the bisector of the minor angle between two hyperplanes identified by linear regression. The performance of the proposed method are examined by simulations up to ten variables for different sample sizes and distribution types in terms of the Mean Square Error. Moreover, the BRM-II is applied to two real problems with two and three variables, and compared with the existing methods. The results indicate that the BRM-II is easy applicable and offers relatively better accuracy. The relevant method can be easily coded in any programming language provides convenience in its application. Thus, the proposed method provide powerful tool for prediction of relevant real life problems.

Kaynakça

  • Alexiades, A. V., Marcy-Quay, B., Sullivan, P. J., Kraft, C. E., Measurement error in angler creel surveys, North American Journal of Fisheries Management, 35 (2) (2015), 253–261. https://doi.org/10.1080/02755947.2014.996689.
  • Amado, A., Meirelles-Pereira, F., Vidal, L., Sarmento, H., Suhett, A., Farjalla, V., Cotner, J., Roland, F., Tropical freshwater ecosystems have lower bacterial growth efficiency than temperate ones, Frontiers in Microbiology, 4 (2013). https://doi.org/10.3389/fmicb.2013.00167.
  • Bradbury, J. W., Vehrencamp, S. L., Choice of regression model for isodar analysis, Evolutionary Ecology Research, 16 (2015), 689–704.
  • Chen, S.-C., Pahlevani, A. H., Malikova, L., Riina, R., Thomson, F. J., Giladi, I., Trade-off or coordination? correlations between ballochorous and myrmecochorous phases of diplochory, Functional Ecology, 33 (8) (2019), 1469–1479. https://doi.org/10.1111/1365-2435.13353.
  • Deming, W. E., Statistical Adjustment Of Data, J. Wiley & Sons, inc.; Chapman & Hall, ltd New York, London, 1943.
  • Downs, D. E., Cheng, Y. W., Length–length and width–length conversion of longnose skate and big skate off the pacific coast: Implications for the choice of alternative measurement units in fisheries stock assessment, North American Journal of Fisheries Management, 33 (5) (2013), 887–893. https://doi.org/10.1080/02755947.2013.818080.
  • Endo, H., Nishigaki, T., Yamamoto, Keigoand Takeno, K., Age- and size-based morphological comparison between the brown alga sargassum macrocarpum (heterokonta; fucales) from different depths at an exposed coast in northern kyoto, japan, Journal of Applied Phycology, 25 (6) (Dec 2013), 1815–1822. https://doi.org/10.1007/s10811-013-0002-y.
  • Fairchild, W., Hales, B., High-resolution carbonate system dynamics of netarts bay, or from 2014 to 2019, Frontiers in Marine Science, 7 (2021). https://doi.org/10.3389/fmars.2020.590236.
  • Formicola, V., Franceschi, M., Regression equations for estimating stature from long bones of early holocene european samples, Am J Phys Anthropol, 100 (1) (May 1996), 83–88.
  • Hou, A., DeLaune, Ronald D.and Tan, M., Reams, M., Laws, E., Toxic elements in aquatic sediments: Distinguishing natural variability from anthropogenic effects, Water, Air, and Soil Pollution, 203 (1) (Oct 2009), 179–191. https://doi.org/10.1007/s11270-009-0002-3.
  • Isobe, T., Feigelson, E. D., Akritas, M. G., Babu, G. J., Linear regression in astronomy. i., apj, 364 (Nov. 1990), 104. https://doi.org/10.1086/169390.
  • James, G., Witten, D., Hastie, T., Tibshirani, R., An Introduction To Statistical Learning, 1 ed., Springer texts in statistics, Springer, New York, NY, June 2013.
  • Laws, E. A., Archie, J. W., Appropriate use of regression analysis in marine biology, Marine Biology, 65 (1) (Nov 1981), 13–16, https://doi.org/10.1007/BF00397062.
  • Lewis-Beck, M. S., Applied Regression: An Introduction, Quantitative applications in the social sciences, SAGE, Newbury Park, London, 1980.
  • Ludbrook, J., Linear regression analysis for comparing two measurers or methods of measurement: But which regression?, Clinical and Experimental Pharmacology and Physiology, 37 (7) (2010), 692–699. https://doi.org/10.1111/j.1440-1681.2010.05376.x.
  • Ludbrook, J., A primer for biomedical scientists on how to execute model ii linear regression analysis, Clinical and Experimental Pharmacology and Physiology, 39 (4) (2012), 329–335. https://doi.org/10.1111/j.1440-1681.2011.05643.x.
  • Martinez, P. A., Bidau, C. J., A re-assessment of rensch’s rule in tuco-tucos (rodentia: Ctenomyidae: Ctenomys) using a phylogenetic approach, Mammalian Biology, 81 (1) (2016), 66–72. https://doi.org/10.1016/j.mambio.2014.11.008.
  • Passing, H., Bablok, W., A new biometrical procedure for testing the equality of measurements from two different analytical methods. application of linear regression procedures for method comparison studies in clinical chemistry, part i, 709–720. https://doi.org/10.1515/cclm.1983.21.11.709.
  • Rayner, J. M. V., Linear relations in biomechanics: the statistics of scaling functions, Journal of Zoology, 206 (3) (1985), 415–439. https://doi.org/10.1111/j.1469-7998.1985.tb05668.x.
  • Richter, S. J., Stavn, R. H., Determining functional relations in multivariate oceanographic systems: Model ii multiple linear regression, Journal of Atmospheric and Oceanic Technology, 31 (7) (2014), 1663 – 1672. https://doi.org/10.1175/JTECH-D-13-00210.1.
  • Ricker, W. E., Linear regressions in fishery research, Journal of the Fisheries Research Board of Canada, 30 (3) (1973), 409–434, 10.1139/f73-072.
  • Sokal, R. R., Rohlf, F. J., Biometry, W.H. Freeman, New York, NY, Aug. 1969.
  • Sprent, P., Dolby, G. R., Query: The geometric mean functional relationship, Biometrics, 36 (3) (1980), 547–550.
  • Stavn, R. H., Richter, S. J., Biogeo-optics: particle optical properties and the partitioning of the spectral scattering coefficient of ocean waters, Appl. Opt., 47 (14) (May 2008), 2660–2679. https://doi.org/10.1364/AO.47.002660.
  • Tao, J., Hill, P. S., Boss, E. S., Milligan, T. G., Evaluation of optical proxies for suspended particulate mass in stratified waters, Journal of Atmospheric and Oceanic Technology, 34 (10) (2017), 2203 – 2212. https://doi.org/10.1175/JTECH-D-17-0042.1.
  • Trujillo-Ortiz, A., Hernandez-Walls, R., gmregress: Geometric mean regression (reduced major axis regression). a matlab file. retrived august 10, 2021. http://www.mathworks.com/matlabcentral/fileexchange/27918-gmregress. Accessed, [Accessed 30-Mar-2023].
  • Warton, D. I., Wright, I. J., Falster, D. S., Westoby, M., Bivariate linefitting methods for allometry, Biological Reviews, 81 (2) (2006), 259–291. https://doi.org/10.1017/S1464793106007007.
  • Yang, X., Lauzon, C. B., Crainiceanu, C., Caffo, B., Resnick, S. M., Landman, B. A., Biological parametric mapping accounting for random regressors with regression calibration and model ii regression, NeuroImage, 62 (3) (2012), 1761–1768. https://doi.org/10.1016/j.neuroimage.2012.05.020.
  • York, D., Least-squares of fitting of a straight line, Canadian Journal of Physics, 44 (5) (1966), 1079–1086, https://doi.org/10.1139/p66-090.
Yıl 2023, Cilt: 72 Sayı: 4, 1187 - 1200, 29.12.2023
https://doi.org/10.31801/cfsuasmas.1292470

Öz

Kaynakça

  • Alexiades, A. V., Marcy-Quay, B., Sullivan, P. J., Kraft, C. E., Measurement error in angler creel surveys, North American Journal of Fisheries Management, 35 (2) (2015), 253–261. https://doi.org/10.1080/02755947.2014.996689.
  • Amado, A., Meirelles-Pereira, F., Vidal, L., Sarmento, H., Suhett, A., Farjalla, V., Cotner, J., Roland, F., Tropical freshwater ecosystems have lower bacterial growth efficiency than temperate ones, Frontiers in Microbiology, 4 (2013). https://doi.org/10.3389/fmicb.2013.00167.
  • Bradbury, J. W., Vehrencamp, S. L., Choice of regression model for isodar analysis, Evolutionary Ecology Research, 16 (2015), 689–704.
  • Chen, S.-C., Pahlevani, A. H., Malikova, L., Riina, R., Thomson, F. J., Giladi, I., Trade-off or coordination? correlations between ballochorous and myrmecochorous phases of diplochory, Functional Ecology, 33 (8) (2019), 1469–1479. https://doi.org/10.1111/1365-2435.13353.
  • Deming, W. E., Statistical Adjustment Of Data, J. Wiley & Sons, inc.; Chapman & Hall, ltd New York, London, 1943.
  • Downs, D. E., Cheng, Y. W., Length–length and width–length conversion of longnose skate and big skate off the pacific coast: Implications for the choice of alternative measurement units in fisheries stock assessment, North American Journal of Fisheries Management, 33 (5) (2013), 887–893. https://doi.org/10.1080/02755947.2013.818080.
  • Endo, H., Nishigaki, T., Yamamoto, Keigoand Takeno, K., Age- and size-based morphological comparison between the brown alga sargassum macrocarpum (heterokonta; fucales) from different depths at an exposed coast in northern kyoto, japan, Journal of Applied Phycology, 25 (6) (Dec 2013), 1815–1822. https://doi.org/10.1007/s10811-013-0002-y.
  • Fairchild, W., Hales, B., High-resolution carbonate system dynamics of netarts bay, or from 2014 to 2019, Frontiers in Marine Science, 7 (2021). https://doi.org/10.3389/fmars.2020.590236.
  • Formicola, V., Franceschi, M., Regression equations for estimating stature from long bones of early holocene european samples, Am J Phys Anthropol, 100 (1) (May 1996), 83–88.
  • Hou, A., DeLaune, Ronald D.and Tan, M., Reams, M., Laws, E., Toxic elements in aquatic sediments: Distinguishing natural variability from anthropogenic effects, Water, Air, and Soil Pollution, 203 (1) (Oct 2009), 179–191. https://doi.org/10.1007/s11270-009-0002-3.
  • Isobe, T., Feigelson, E. D., Akritas, M. G., Babu, G. J., Linear regression in astronomy. i., apj, 364 (Nov. 1990), 104. https://doi.org/10.1086/169390.
  • James, G., Witten, D., Hastie, T., Tibshirani, R., An Introduction To Statistical Learning, 1 ed., Springer texts in statistics, Springer, New York, NY, June 2013.
  • Laws, E. A., Archie, J. W., Appropriate use of regression analysis in marine biology, Marine Biology, 65 (1) (Nov 1981), 13–16, https://doi.org/10.1007/BF00397062.
  • Lewis-Beck, M. S., Applied Regression: An Introduction, Quantitative applications in the social sciences, SAGE, Newbury Park, London, 1980.
  • Ludbrook, J., Linear regression analysis for comparing two measurers or methods of measurement: But which regression?, Clinical and Experimental Pharmacology and Physiology, 37 (7) (2010), 692–699. https://doi.org/10.1111/j.1440-1681.2010.05376.x.
  • Ludbrook, J., A primer for biomedical scientists on how to execute model ii linear regression analysis, Clinical and Experimental Pharmacology and Physiology, 39 (4) (2012), 329–335. https://doi.org/10.1111/j.1440-1681.2011.05643.x.
  • Martinez, P. A., Bidau, C. J., A re-assessment of rensch’s rule in tuco-tucos (rodentia: Ctenomyidae: Ctenomys) using a phylogenetic approach, Mammalian Biology, 81 (1) (2016), 66–72. https://doi.org/10.1016/j.mambio.2014.11.008.
  • Passing, H., Bablok, W., A new biometrical procedure for testing the equality of measurements from two different analytical methods. application of linear regression procedures for method comparison studies in clinical chemistry, part i, 709–720. https://doi.org/10.1515/cclm.1983.21.11.709.
  • Rayner, J. M. V., Linear relations in biomechanics: the statistics of scaling functions, Journal of Zoology, 206 (3) (1985), 415–439. https://doi.org/10.1111/j.1469-7998.1985.tb05668.x.
  • Richter, S. J., Stavn, R. H., Determining functional relations in multivariate oceanographic systems: Model ii multiple linear regression, Journal of Atmospheric and Oceanic Technology, 31 (7) (2014), 1663 – 1672. https://doi.org/10.1175/JTECH-D-13-00210.1.
  • Ricker, W. E., Linear regressions in fishery research, Journal of the Fisheries Research Board of Canada, 30 (3) (1973), 409–434, 10.1139/f73-072.
  • Sokal, R. R., Rohlf, F. J., Biometry, W.H. Freeman, New York, NY, Aug. 1969.
  • Sprent, P., Dolby, G. R., Query: The geometric mean functional relationship, Biometrics, 36 (3) (1980), 547–550.
  • Stavn, R. H., Richter, S. J., Biogeo-optics: particle optical properties and the partitioning of the spectral scattering coefficient of ocean waters, Appl. Opt., 47 (14) (May 2008), 2660–2679. https://doi.org/10.1364/AO.47.002660.
  • Tao, J., Hill, P. S., Boss, E. S., Milligan, T. G., Evaluation of optical proxies for suspended particulate mass in stratified waters, Journal of Atmospheric and Oceanic Technology, 34 (10) (2017), 2203 – 2212. https://doi.org/10.1175/JTECH-D-17-0042.1.
  • Trujillo-Ortiz, A., Hernandez-Walls, R., gmregress: Geometric mean regression (reduced major axis regression). a matlab file. retrived august 10, 2021. http://www.mathworks.com/matlabcentral/fileexchange/27918-gmregress. Accessed, [Accessed 30-Mar-2023].
  • Warton, D. I., Wright, I. J., Falster, D. S., Westoby, M., Bivariate linefitting methods for allometry, Biological Reviews, 81 (2) (2006), 259–291. https://doi.org/10.1017/S1464793106007007.
  • Yang, X., Lauzon, C. B., Crainiceanu, C., Caffo, B., Resnick, S. M., Landman, B. A., Biological parametric mapping accounting for random regressors with regression calibration and model ii regression, NeuroImage, 62 (3) (2012), 1761–1768. https://doi.org/10.1016/j.neuroimage.2012.05.020.
  • York, D., Least-squares of fitting of a straight line, Canadian Journal of Physics, 44 (5) (1966), 1079–1086, https://doi.org/10.1139/p66-090.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Research Article
Yazarlar

Cengiz Gazeloğlu 0000-0002-8222-3384

Asuman Zeytinoğlu 0000-0001-5102-2152

Nurullah Yılmaz 0000-0001-6429-7518

Yayımlanma Tarihi 29 Aralık 2023
Gönderilme Tarihi 4 Mayıs 2023
Kabul Tarihi 7 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 4

Kaynak Göster

APA Gazeloğlu, C., Zeytinoğlu, A., & Yılmaz, N. (2023). A new multidimensional model II regression based on bisector approach. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(4), 1187-1200. https://doi.org/10.31801/cfsuasmas.1292470
AMA Gazeloğlu C, Zeytinoğlu A, Yılmaz N. A new multidimensional model II regression based on bisector approach. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2023;72(4):1187-1200. doi:10.31801/cfsuasmas.1292470
Chicago Gazeloğlu, Cengiz, Asuman Zeytinoğlu, ve Nurullah Yılmaz. “A New Multidimensional Model II Regression Based on Bisector Approach”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 4 (Aralık 2023): 1187-1200. https://doi.org/10.31801/cfsuasmas.1292470.
EndNote Gazeloğlu C, Zeytinoğlu A, Yılmaz N (01 Aralık 2023) A new multidimensional model II regression based on bisector approach. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 4 1187–1200.
IEEE C. Gazeloğlu, A. Zeytinoğlu, ve N. Yılmaz, “A new multidimensional model II regression based on bisector approach”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 4, ss. 1187–1200, 2023, doi: 10.31801/cfsuasmas.1292470.
ISNAD Gazeloğlu, Cengiz vd. “A New Multidimensional Model II Regression Based on Bisector Approach”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/4 (Aralık 2023), 1187-1200. https://doi.org/10.31801/cfsuasmas.1292470.
JAMA Gazeloğlu C, Zeytinoğlu A, Yılmaz N. A new multidimensional model II regression based on bisector approach. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:1187–1200.
MLA Gazeloğlu, Cengiz vd. “A New Multidimensional Model II Regression Based on Bisector Approach”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 4, 2023, ss. 1187-00, doi:10.31801/cfsuasmas.1292470.
Vancouver Gazeloğlu C, Zeytinoğlu A, Yılmaz N. A new multidimensional model II regression based on bisector approach. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(4):1187-200.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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