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Examination of Distance Based Regression Methods for Different Data Structures in Animal Science

Yıl 2025, Cilt: 8 Sayı: 2, 354 - 362, 15.03.2025

Burcu Kurnaz , Hasan Önder

https://doi.org/10.34248/bsengineering.1599606

Öz

Distance-based regression is an alternative method for parameter estimation in linear regression models when mixed-type explanatory variables are used. Distance-based regression is similar to classical linear regression, except that explanatory variables are measured by distance measures rather than raw values. In this study, datasets with sample sizes of 10, 25, 50, 100, 250 and 500 produced for Binomial, Normal, t, Chi-square and Poisson distributions of Euclidean, Gower and Manhattan distance measures and real data with discrete and continuous distribution that body weight at sixth months was used as outcome variable, body length and chest depth at sixth months of Saanen kids were used as explanatory variables as continuous data. Milk fat ratio was determined as the response variable, while the number of milking per day and the season of Polish Holstein Friesian cattle were determined as the explanatory variables as discrete data. It was aimed to determine the effect on the data sets (10, 50 and 100 sample sizes) by comparing the results obtained from the Linear Regression method. R packages "dbstats", "cluster" and "tidyverse" were used to perform the analysis. As a result, it has been determined that the use of Manhattan distance in data with Poisson distribution may produce unsuccessful results, especially in small sample sizes (n<50). Although there is no significant difference between Gower and Euclidean distances in different distributions according to sample sizes, it has been determined that the use of Euclidean distance measure in some distributions produces results that cause fluctuation. However, it has been understood that the Gower distance can be recommended as a more suitable choice since it has a more stable structure. For the applicability of the Least Square Estimation method, it may be recommended to use Distance Based Regression methods in cases where the necessary assumptions mentioned in this study cannot be met.

Anahtar Kelimeler

Distance measures Package dbstats Regression R software

Etik Beyan

Ethics committee approval was not required for this study because of there was no study on animals or humans.

Teşekkür

This study is short summary of MSc thesis of first author under the supervision of the second author.

Kaynakça

  • Adıgüzel MB. 2021. Çok değişkenli uyarlanabilir regresyon eğrilerinde alternatif bilgi kriterleri ile model seçimi. PhD Thesis, Ondokuz Mayıs University, Graduate Shool of Education, Department of Statistics, Samsun, Türkiye, pp: 86.
  • Aerts J, Sitkowska B, Piwczyński D, Kolenda M, Önder H. 2022. The optimal level of factors for high daily milk yield in automatic milking system. Livestock Sci, 264: 105035.
  • Alma ÖG, Vupa Ö. 2008. Regresyon analizinde kullanılan en küçük kareler ve en küçük medyan kareler yöntemlerinin karşılaştırılması. SDÜ Fen Ede Fak Fen Derg, 3(2): 2019-229.
  • Alpar R. 2010. Basit doğrusal regresyon çözümlemesi: Spor, sağlık ve eğitim bilimlerinden örneklerle uygulamalı istatistik ve geçerlik-güvenirlik. Detay Yayıncılık, Ankara, Türkiye, pp: 672.
  • Alpar R. 2013. Uygulamalı çok değişkenli istatistiksel yöntemler. Detay Yayıncılık, Ankara, Türkiye, pp: 853.
  • Anderson MJ. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecol, 26: 32-46.
  • Anonymous. 2011. Kümeleme analizinde kullanılan bazı farklılık ve benzerlik ölçülerinin incelenmesi. URL: http://emredunder.blogspot.com/2011/06/kumeleme-analizinde-kullanlan-baz.html (accessed date: June18, 2023).
  • Anonymous. 2023a. Ankara Üniversitesi açık ders. URL: https://acikders.ankara.edu.tr/pluginfile.php/130799/mod_resource/content/0/6-%20Matris.pdf (accessed date: May 12, 2023).
  • Anonymous. 2023b. Model ve dağılım seçme URL: https://avys.omu.edu.tr/storage/app/public/kamilal/108861/HPTZ.HF10.pdf (accessed date: May 16, 2023).
  • Arenas C, Cuadras M. 2002. Recent statistical methods based on distances. Contrib Sci, 2(2): 183-191.
  • Arı A, Önder H. 2013. Farklı veri yapılarında kullanılabilecek regresyon yöntemleri. Anadolu Tar Bil Derg, 28(3): 168-174.
  • Atkinson AC, Riani M. 2000. Robust diagnostic regression analysis. Springer, New York, US, pp: 328.
  • Boj E, Claramunt MM, Fortiana J, Vidiella A. 2002. The use of distance-based regression and generalized linear models in the rate making process: An empirical study. Universitat de Barcelona. Institut de Matemàtica [IMUB], Barcelona, Spain, pp: 47.
  • Chen J, Bittinger K, Charlson ES, Hoffmann C, Lewis J, Wu GD, Li H. 2012. Associating microbiome composition with environmental covariates using generalized UniFrac distances. Bioinf, 28(16): 2106-2113.
  • Cuadras CM, Arenas C. 1990. A distance based regression model for prediction with mixed data. Commun Stat A. Theory Methods, 19: 2261-2279.
  • Cuadras CM. 1988 Statistical distances. Estadística Española, 30: 295-378.
  • de Souza Jr AH, Corona F, Barreto GA, Miche Y, Lendase A. 2015. Minimal learning machine: A novel supervised distance-based approach for regression and classification. Neurocomputing, 164: 34-44.
  • Ferreira Barreto CDS, Zimeo Morais GA, Vanzella P, Sato JR. 2020. Combining the intersubject correlation analysis and the multivariate distance matrix regression to evaluate associations between fNIRS signals and behavioral data from ecological experiments. Experl Brain Res, 238: 2399-2408. https://doi: 10.1007/s00221-020-05895-8
  • Gower JC. 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53(3-4): 325-338.
  • Gower JC. 1971. A general coefficient of similarity and some of its properties. Biometrics, 1971: 857-871.
  • Haron NH, Ahad NA, Mahat NI. 2019. Distance-based regression for non-normal data. The 4th Innovation and Analytics Conference & Exhibition (IACE 2019), March 21-28, Kedah, Malaysia. https://doi.org/10.1063/1.5121118
  • Kim C, Lee Y, Park BU. 2001. Cook’s distance in local polynomial regression. Stat Probab Lett, 54: 33-40.
  • Kurnaz B, Önder H, Piwczynski D, Kolenda M, Sitkowska B. 2021. Determination of the best model to predict milk dry matter in high milk yielding dairy cattle. Acta Sci Pol Zootechnica, 20(3): 41-44. https://doi: 10.21005/asp.2021.20.3.05
  • Kurnaz B, Önder H. 2021. Distance based regression models. II. International Applied Statistics Conference (UYIK-2021), June 29- July 2, Tokat, Türkiye, pp: 120-126.
  • Li J, Zhang W, Zhang S, Li Q. 2019. A theoretic study of a distance-based regression model. Sci China Math, 62: 979-998.
  • Lichstein JW. 2007. Multiple regression on distance matrices: a multivariate spatial analysis tool. Plant Ecol, 188: 117-131.
  • McArdle BH, Anderson MJ. 2001. Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology, 82(1): 290-297.
  • McQuarrie AD, Tsai CL. 1998. Regression and time series model selection. World Scientific Publication Co Pte. Ltd., London, UK, pp:45
  • Okur S. 2009. Parametrik ve parametrik olmayan doğrusal regresyon analiz yöntemlerinin karşılaştırılmalı olarak incelenmesi. MSc Thesis, Çukurova University, Institute of Science, Department of Animal Science, Adana, Türkiye, pp: 62.
  • Orhunbilge N. 2017. Uygulamalı regresyon ve korelasyon analizi. Nobel Yayıncılık, Ankara, Türkiye, pp: 394.
  • Önder H, Abacı SH. 2015. Path analysis for body measurements on body weight of Saanen kids. Kafkas Üniv Vet Fak Derg, 21(3): 351-354.
  • R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2022, URL: https://www.R-project.org/.
  • Raftery AE. 1995. Bayesian model selection in social research. Sociol Methodol, 25: 111-163.
  • Schork NJ, Wessel J, Malo N. 2008. DNA sequence-based phenotypic association analysis. Adv Genet, 60: 195-217.
  • Servi T. 2009. Çok değişkenli karma dağılım modeline dayalı kümeleme analizi. PhD Thesis, Çukurova University, Institute of Science, Department of Statistics, Adana, Türkiye, pp: 266.
  • Shehzad Z, Kelly C, Reiss PT, Craddock RC, Emerson JW, McMahon K, Milham MP. 2014. A multivariate distance-based analytic framework for connectome-wide association studies. Neuroimage, 93: 74-94.
  • Timm NH. 2002. Applied Multivariate Analysis. Splinger-Verlag, New York, US, pp: 718.
  • Ucal MŞ. 2006. Ekonometrik Model seçim kriterleri üzerine kisa bir inceleme. CÜ İİBF Derg, 7(2): 41-57.
  • URL1: https://acikders.ankara.edu.tr/pluginfile.php/130799/mod_resource/content/0/6-%20Matris.pdf (accessed date: May 12, 2023).
  • URL2: http://emredunder.blogspot.com/2011/06/kumeleme-analizinde-kullanlan-baz.html (accessed date: June18, 2023).
  • URL3: https://avys.omu.edu.tr/storage/app/public/kamilal/108861/HPTZ.HF10.pdf (accessed date: May 16, 2023).
  • Ünlükaplan Y. 2008. Çok değişkenli istatistiksel yöntemlerin peyzaj ekolojisi araştırmalarında kullanımı. PhD Thesis, Çukurova University, Institute of Science, Department of Statistics, Adana, Türkiye, pp: 156.
  • Varoquaux G, Craddock RC. 2013. Learning and comparing functional connectomes across subjects. NeuroImage, 80: 405-415.
  • Vural A. 2007. Aykırı değerlerin regresyon modellerine etkileri ve sağlam kestiriciler. MSc Thesis, Marmara University, Institute of Social Sciecnes, Department of Econometry, İstanbul, Türkiye, pp: 73.
  • Wasserman L. 2000. Bayesian model selection and model averaging. J Math Psychol, 44(1): 92-107.
  • Weisberg S. 2005. Applied linear regression. John Wiley & Sons, New Jersey, US, pp: 340.
  • Wessel J, Schork NJ. 2006. Generalized genomic distance-based regression methodology for multilocus association analysis. Amer J Human Genet, 79(5): 792-806.
  • Xu Y, Guo X, Sun J, Zhao Z. 2015. Snowball: resampling combined with distance-based regression to discover transcriptional consequences of a driver mutation. Bioinformatics, 31(1): 84-93.
  • Yıldız M. 2022. Dolar ve Euro kurları üzerinde etkili faktörlerin iki bağımlı değişkenli MARS modeli ile belirlenmesi. Kastamonu Üniv İİBF Derg, 24(1): 6-29.
  • Zapala MA, Schork NJ. 2012. Statistical properties of multivariate distance matrix regression for high-dimensional data analysis. Front Genet, 3: 190. https/doi.org/10.3389/fgene.2012.00190

Examination of Distance Based Regression Methods for Different Data Structures in Animal Science

Yıl 2025, Cilt: 8 Sayı: 2, 354 - 362, 15.03.2025

Burcu Kurnaz , Hasan Önder

https://doi.org/10.34248/bsengineering.1599606

Öz

Distance-based regression is an alternative method for parameter estimation in linear regression models when mixed-type explanatory variables are used. Distance-based regression is similar to classical linear regression, except that explanatory variables are measured by distance measures rather than raw values. In this study, datasets with sample sizes of 10, 25, 50, 100, 250 and 500 produced for Binomial, Normal, t, Chi-square and Poisson distributions of Euclidean, Gower and Manhattan distance measures and real data with discrete and continuous distribution that body weight at sixth months was used as outcome variable, body length and chest depth at sixth months of Saanen kids were used as explanatory variables as continuous data. Milk fat ratio was determined as the response variable, while the number of milking per day and the season of Polish Holstein Friesian cattle were determined as the explanatory variables as discrete data. It was aimed to determine the effect on the data sets (10, 50 and 100 sample sizes) by comparing the results obtained from the Linear Regression method. R packages "dbstats", "cluster" and "tidyverse" were used to perform the analysis. As a result, it has been determined that the use of Manhattan distance in data with Poisson distribution may produce unsuccessful results, especially in small sample sizes (n<50). Although there is no significant difference between Gower and Euclidean distances in different distributions according to sample sizes, it has been determined that the use of Euclidean distance measure in some distributions produces results that cause fluctuation. However, it has been understood that the Gower distance can be recommended as a more suitable choice since it has a more stable structure. For the applicability of the Least Square Estimation method, it may be recommended to use Distance Based Regression methods in cases where the necessary assumptions mentioned in this study cannot be met.

Anahtar Kelimeler

Distance measures Package dbstats Regression R software

Etik Beyan

Ethics committee approval was not required for this study because of there was no study on animals or humans.

Teşekkür

This study is short summary of MSc thesis of first author under the supervision of the second author.

Kaynakça

  • Adıgüzel MB. 2021. Çok değişkenli uyarlanabilir regresyon eğrilerinde alternatif bilgi kriterleri ile model seçimi. PhD Thesis, Ondokuz Mayıs University, Graduate Shool of Education, Department of Statistics, Samsun, Türkiye, pp: 86.
  • Aerts J, Sitkowska B, Piwczyński D, Kolenda M, Önder H. 2022. The optimal level of factors for high daily milk yield in automatic milking system. Livestock Sci, 264: 105035.
  • Alma ÖG, Vupa Ö. 2008. Regresyon analizinde kullanılan en küçük kareler ve en küçük medyan kareler yöntemlerinin karşılaştırılması. SDÜ Fen Ede Fak Fen Derg, 3(2): 2019-229.
  • Alpar R. 2010. Basit doğrusal regresyon çözümlemesi: Spor, sağlık ve eğitim bilimlerinden örneklerle uygulamalı istatistik ve geçerlik-güvenirlik. Detay Yayıncılık, Ankara, Türkiye, pp: 672.
  • Alpar R. 2013. Uygulamalı çok değişkenli istatistiksel yöntemler. Detay Yayıncılık, Ankara, Türkiye, pp: 853.
  • Anderson MJ. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecol, 26: 32-46.
  • Anonymous. 2011. Kümeleme analizinde kullanılan bazı farklılık ve benzerlik ölçülerinin incelenmesi. URL: http://emredunder.blogspot.com/2011/06/kumeleme-analizinde-kullanlan-baz.html (accessed date: June18, 2023).
  • Anonymous. 2023a. Ankara Üniversitesi açık ders. URL: https://acikders.ankara.edu.tr/pluginfile.php/130799/mod_resource/content/0/6-%20Matris.pdf (accessed date: May 12, 2023).
  • Anonymous. 2023b. Model ve dağılım seçme URL: https://avys.omu.edu.tr/storage/app/public/kamilal/108861/HPTZ.HF10.pdf (accessed date: May 16, 2023).
  • Arenas C, Cuadras M. 2002. Recent statistical methods based on distances. Contrib Sci, 2(2): 183-191.
  • Arı A, Önder H. 2013. Farklı veri yapılarında kullanılabilecek regresyon yöntemleri. Anadolu Tar Bil Derg, 28(3): 168-174.
  • Atkinson AC, Riani M. 2000. Robust diagnostic regression analysis. Springer, New York, US, pp: 328.
  • Boj E, Claramunt MM, Fortiana J, Vidiella A. 2002. The use of distance-based regression and generalized linear models in the rate making process: An empirical study. Universitat de Barcelona. Institut de Matemàtica [IMUB], Barcelona, Spain, pp: 47.
  • Chen J, Bittinger K, Charlson ES, Hoffmann C, Lewis J, Wu GD, Li H. 2012. Associating microbiome composition with environmental covariates using generalized UniFrac distances. Bioinf, 28(16): 2106-2113.
  • Cuadras CM, Arenas C. 1990. A distance based regression model for prediction with mixed data. Commun Stat A. Theory Methods, 19: 2261-2279.
  • Cuadras CM. 1988 Statistical distances. Estadística Española, 30: 295-378.
  • de Souza Jr AH, Corona F, Barreto GA, Miche Y, Lendase A. 2015. Minimal learning machine: A novel supervised distance-based approach for regression and classification. Neurocomputing, 164: 34-44.
  • Ferreira Barreto CDS, Zimeo Morais GA, Vanzella P, Sato JR. 2020. Combining the intersubject correlation analysis and the multivariate distance matrix regression to evaluate associations between fNIRS signals and behavioral data from ecological experiments. Experl Brain Res, 238: 2399-2408. https://doi: 10.1007/s00221-020-05895-8
  • Gower JC. 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53(3-4): 325-338.
  • Gower JC. 1971. A general coefficient of similarity and some of its properties. Biometrics, 1971: 857-871.
  • Haron NH, Ahad NA, Mahat NI. 2019. Distance-based regression for non-normal data. The 4th Innovation and Analytics Conference & Exhibition (IACE 2019), March 21-28, Kedah, Malaysia. https://doi.org/10.1063/1.5121118
  • Kim C, Lee Y, Park BU. 2001. Cook’s distance in local polynomial regression. Stat Probab Lett, 54: 33-40.
  • Kurnaz B, Önder H, Piwczynski D, Kolenda M, Sitkowska B. 2021. Determination of the best model to predict milk dry matter in high milk yielding dairy cattle. Acta Sci Pol Zootechnica, 20(3): 41-44. https://doi: 10.21005/asp.2021.20.3.05
  • Kurnaz B, Önder H. 2021. Distance based regression models. II. International Applied Statistics Conference (UYIK-2021), June 29- July 2, Tokat, Türkiye, pp: 120-126.
  • Li J, Zhang W, Zhang S, Li Q. 2019. A theoretic study of a distance-based regression model. Sci China Math, 62: 979-998.
  • Lichstein JW. 2007. Multiple regression on distance matrices: a multivariate spatial analysis tool. Plant Ecol, 188: 117-131.
  • McArdle BH, Anderson MJ. 2001. Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology, 82(1): 290-297.
  • McQuarrie AD, Tsai CL. 1998. Regression and time series model selection. World Scientific Publication Co Pte. Ltd., London, UK, pp:45
  • Okur S. 2009. Parametrik ve parametrik olmayan doğrusal regresyon analiz yöntemlerinin karşılaştırılmalı olarak incelenmesi. MSc Thesis, Çukurova University, Institute of Science, Department of Animal Science, Adana, Türkiye, pp: 62.
  • Orhunbilge N. 2017. Uygulamalı regresyon ve korelasyon analizi. Nobel Yayıncılık, Ankara, Türkiye, pp: 394.
  • Önder H, Abacı SH. 2015. Path analysis for body measurements on body weight of Saanen kids. Kafkas Üniv Vet Fak Derg, 21(3): 351-354.
  • R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2022, URL: https://www.R-project.org/.
  • Raftery AE. 1995. Bayesian model selection in social research. Sociol Methodol, 25: 111-163.
  • Schork NJ, Wessel J, Malo N. 2008. DNA sequence-based phenotypic association analysis. Adv Genet, 60: 195-217.
  • Servi T. 2009. Çok değişkenli karma dağılım modeline dayalı kümeleme analizi. PhD Thesis, Çukurova University, Institute of Science, Department of Statistics, Adana, Türkiye, pp: 266.
  • Shehzad Z, Kelly C, Reiss PT, Craddock RC, Emerson JW, McMahon K, Milham MP. 2014. A multivariate distance-based analytic framework for connectome-wide association studies. Neuroimage, 93: 74-94.
  • Timm NH. 2002. Applied Multivariate Analysis. Splinger-Verlag, New York, US, pp: 718.
  • Ucal MŞ. 2006. Ekonometrik Model seçim kriterleri üzerine kisa bir inceleme. CÜ İİBF Derg, 7(2): 41-57.
  • URL1: https://acikders.ankara.edu.tr/pluginfile.php/130799/mod_resource/content/0/6-%20Matris.pdf (accessed date: May 12, 2023).
  • URL2: http://emredunder.blogspot.com/2011/06/kumeleme-analizinde-kullanlan-baz.html (accessed date: June18, 2023).
  • URL3: https://avys.omu.edu.tr/storage/app/public/kamilal/108861/HPTZ.HF10.pdf (accessed date: May 16, 2023).
  • Ünlükaplan Y. 2008. Çok değişkenli istatistiksel yöntemlerin peyzaj ekolojisi araştırmalarında kullanımı. PhD Thesis, Çukurova University, Institute of Science, Department of Statistics, Adana, Türkiye, pp: 156.
  • Varoquaux G, Craddock RC. 2013. Learning and comparing functional connectomes across subjects. NeuroImage, 80: 405-415.
  • Vural A. 2007. Aykırı değerlerin regresyon modellerine etkileri ve sağlam kestiriciler. MSc Thesis, Marmara University, Institute of Social Sciecnes, Department of Econometry, İstanbul, Türkiye, pp: 73.
  • Wasserman L. 2000. Bayesian model selection and model averaging. J Math Psychol, 44(1): 92-107.
  • Weisberg S. 2005. Applied linear regression. John Wiley & Sons, New Jersey, US, pp: 340.
  • Wessel J, Schork NJ. 2006. Generalized genomic distance-based regression methodology for multilocus association analysis. Amer J Human Genet, 79(5): 792-806.
  • Xu Y, Guo X, Sun J, Zhao Z. 2015. Snowball: resampling combined with distance-based regression to discover transcriptional consequences of a driver mutation. Bioinformatics, 31(1): 84-93.
  • Yıldız M. 2022. Dolar ve Euro kurları üzerinde etkili faktörlerin iki bağımlı değişkenli MARS modeli ile belirlenmesi. Kastamonu Üniv İİBF Derg, 24(1): 6-29.
  • Zapala MA, Schork NJ. 2012. Statistical properties of multivariate distance matrix regression for high-dimensional data analysis. Front Genet, 3: 190. https/doi.org/10.3389/fgene.2012.00190
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistiksel Analiz, Uygulamalı İstatistik
Bölüm Research Articles
Yazarlar

Burcu Kurnaz 0000-0001-5613-6992

Hasan Önder 0000-0002-8404-8700

Yayımlanma Tarihi 15 Mart 2025
Gönderilme Tarihi 11 Aralık 2024
Kabul Tarihi 16 Ocak 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 2

Kaynak Göster

APA Kurnaz, B., & Önder, H. (2025). Examination of Distance Based Regression Methods for Different Data Structures in Animal Science. Black Sea Journal of Engineering and Science, 8(2), 354-362. https://doi.org/10.34248/bsengineering.1599606
AMA Kurnaz B, Önder H. Examination of Distance Based Regression Methods for Different Data Structures in Animal Science. BSJ Eng. Sci. Mart 2025;8(2):354-362. doi:10.34248/bsengineering.1599606
Chicago Kurnaz, Burcu, ve Hasan Önder. “Examination of Distance Based Regression Methods for Different Data Structures in Animal Science”. Black Sea Journal of Engineering and Science 8, sy. 2 (Mart 2025): 354-62. https://doi.org/10.34248/bsengineering.1599606.
EndNote Kurnaz B, Önder H (01 Mart 2025) Examination of Distance Based Regression Methods for Different Data Structures in Animal Science. Black Sea Journal of Engineering and Science 8 2 354–362.
IEEE B. Kurnaz ve H. Önder, “Examination of Distance Based Regression Methods for Different Data Structures in Animal Science”, BSJ Eng. Sci., c. 8, sy. 2, ss. 354–362, 2025, doi: 10.34248/bsengineering.1599606.
ISNAD Kurnaz, Burcu - Önder, Hasan. “Examination of Distance Based Regression Methods for Different Data Structures in Animal Science”. Black Sea Journal of Engineering and Science 8/2 (Mart 2025), 354-362. https://doi.org/10.34248/bsengineering.1599606.
JAMA Kurnaz B, Önder H. Examination of Distance Based Regression Methods for Different Data Structures in Animal Science. BSJ Eng. Sci. 2025;8:354–362.
MLA Kurnaz, Burcu ve Hasan Önder. “Examination of Distance Based Regression Methods for Different Data Structures in Animal Science”. Black Sea Journal of Engineering and Science, c. 8, sy. 2, 2025, ss. 354-62, doi:10.34248/bsengineering.1599606.
Vancouver Kurnaz B, Önder H. Examination of Distance Based Regression Methods for Different Data Structures in Animal Science. BSJ Eng. Sci. 2025;8(2):354-62.
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