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Genelleştirilmiş lineer modellerde kısmi ve augmented kısmi artıklar ve grafikleri

Year 2021, Volume: 11 Issue: 4, 1145 - 1153, 15.10.2021
https://doi.org/10.17714/gumusfenbil.863338

Abstract

Genelleştirilmiş lineer modeller; fen, mühendislik ve sosyal alanlarda sıkça karşılaşılan bağımlı değişkenin kesikli veya sürekli dağılıma sahip olması durumunun, bağımsız değişken(ler)le modellenmesine olanak veren yöntemlerden biridir. Bu çalışmada, bağımsız değişkenlerin modelde yer alma biçimlerinin belirlenmesinde tanısal grafiklerden yararlanılmıştır. Bu amaçla kısmi ve augmented kısmi artıklar ile bu artıklara ait grafikler tanıtılarak, modellemede sıkça kullanılan artık grafikleri ile karşılaştırılmıştır. Uygulama olarak, 1965-1998 yılları arasındaki grev sayılarının sendikalaşma oranı, ücret oranı, işyeri ve kapanan işyeri sayılarıyla olan ilişkisi analiz edilmiş ve en uygun model seçilmeye çalışılmıştır. Analiz sonucunda; kısmi artık ve augmented kısmi artık grafiklerinin, ele alınan tüm bağımsız değişkenlerin modelde yer alma biçimini daha belirgin biçimde gösterdiği sonucuna varılmıştır.

References

  • Aitken, M., Anderson, D., Francis, B. and Hinde, J. (1989). Statistical modelling in GLIM. Clarendon Press, Oxford.
  • Cai, Z. and Tsai, C. (1999). Diagnostics for nonlinearity in generalized linear models. Computational Statistics&Data Analysis, 29, 445-469. https://doi.org/10.1016/S0167-9473(98)00079-6
  • Cook, R.D. (1993). Exploring partial residual plots. Technometrics, 35, 351-362.
  • Cook, R.D. and Croos-Dabrera, R. (1998). Partial residual plots in generalized linear models. American Statistical Association, 93, 442, 730-739. https://doi.org/10.1080/01621459.1998.10473725
  • Dobson, A.J. (2002). An iıntroduction to generalized linear models (2nd ed). Chapman and Hall, London.
  • Landwehr, J.M., Pregibon, D. and Shoemaker, A.C. (1984). Graphical methods for assessing logistic regression models. Journal of the American Statistical Association, 79 (385), 61-71.
  • Larsen, W.A. and McCleary, S.J. (1972). The use of partial residual plot in regression analysis. Technometrics, 14, 781-790.
  • Lewis, S.L., Montgomery, D.C. and Myers, R.H. (2001). Examples of designed experiments with nonnormal responses. Journal of Quality Technology, 33, 265-278. https://doi.org/10.1080/00224065.2001.11980078
  • Lindsey, J.K. (1997). Applying generalized linear model. Springer Verlag, Newyork.
  • Mallows, C.L. (1986). Augmented partial residuals. Technometrics, 28, 313-319.
  • McCullagh, C.E. and Searle, S.R. (2001). Generalized linear and mixed effects. John Wiley&Sons, Inc., America.
  • McCullagh, P. and Nelder, J.A. (1989). Background an outline of generalized linear models. İçinde: Generalized linear models (2nd ed.). Chapman and Hall, London, 30-35.
  • Myers, R.H., Montogomery, D.C. and Vining G.G. (2001). Generalized linear models with applications in engineering and science. John Wiley and Sons. Inc.
  • Nelder, A.J. and Wedderburn, R.W.M. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A, 135, 370-384.
  • O’Hara Hinest, R.J. and Carter, E.M. (1993). Improved added variable and partial residual plots for the detection of influential observations in generalized linear models. Applied. Statistics, 42, 1, 3-20. https://doi.org/10.2307/2347405
  • Uusipaikka, E. (2000). Confidence intervals in generalized regressions models. CRC Press, Boca Raton.

Partial and augmented partial residuals and plots in generalized linear models

Year 2021, Volume: 11 Issue: 4, 1145 - 1153, 15.10.2021
https://doi.org/10.17714/gumusfenbil.863338

Abstract

Generalized linear models; It is one of the methods that allows the modeling of the dependent variable having discrete or continuous distribution, which is frequently encountered in science, engineering and social fields, with independent variable(s). In this study, diagnostic graphics were used to determine the form of the independent variables were included in the model. For this purpose, partial and augmented partial residuals and graphs of these residuals were introduced and compared with the residual graphs that are frequently used in modeling. As an application, the relationship between the number of strikes between 1965 and 1998 with the unionization rate, wage rate, number of workplaces and closed workplaces was analyzed and the most suitable model was chosen. It is concluded that partial residual and augmented partial residual graphs show the functions of all the independent variables are included in the model more accurately.

References

  • Aitken, M., Anderson, D., Francis, B. and Hinde, J. (1989). Statistical modelling in GLIM. Clarendon Press, Oxford.
  • Cai, Z. and Tsai, C. (1999). Diagnostics for nonlinearity in generalized linear models. Computational Statistics&Data Analysis, 29, 445-469. https://doi.org/10.1016/S0167-9473(98)00079-6
  • Cook, R.D. (1993). Exploring partial residual plots. Technometrics, 35, 351-362.
  • Cook, R.D. and Croos-Dabrera, R. (1998). Partial residual plots in generalized linear models. American Statistical Association, 93, 442, 730-739. https://doi.org/10.1080/01621459.1998.10473725
  • Dobson, A.J. (2002). An iıntroduction to generalized linear models (2nd ed). Chapman and Hall, London.
  • Landwehr, J.M., Pregibon, D. and Shoemaker, A.C. (1984). Graphical methods for assessing logistic regression models. Journal of the American Statistical Association, 79 (385), 61-71.
  • Larsen, W.A. and McCleary, S.J. (1972). The use of partial residual plot in regression analysis. Technometrics, 14, 781-790.
  • Lewis, S.L., Montgomery, D.C. and Myers, R.H. (2001). Examples of designed experiments with nonnormal responses. Journal of Quality Technology, 33, 265-278. https://doi.org/10.1080/00224065.2001.11980078
  • Lindsey, J.K. (1997). Applying generalized linear model. Springer Verlag, Newyork.
  • Mallows, C.L. (1986). Augmented partial residuals. Technometrics, 28, 313-319.
  • McCullagh, C.E. and Searle, S.R. (2001). Generalized linear and mixed effects. John Wiley&Sons, Inc., America.
  • McCullagh, P. and Nelder, J.A. (1989). Background an outline of generalized linear models. İçinde: Generalized linear models (2nd ed.). Chapman and Hall, London, 30-35.
  • Myers, R.H., Montogomery, D.C. and Vining G.G. (2001). Generalized linear models with applications in engineering and science. John Wiley and Sons. Inc.
  • Nelder, A.J. and Wedderburn, R.W.M. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A, 135, 370-384.
  • O’Hara Hinest, R.J. and Carter, E.M. (1993). Improved added variable and partial residual plots for the detection of influential observations in generalized linear models. Applied. Statistics, 42, 1, 3-20. https://doi.org/10.2307/2347405
  • Uusipaikka, E. (2000). Confidence intervals in generalized regressions models. CRC Press, Boca Raton.
There are 16 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Esin Avcı 0000-0002-9173-0142

Publication Date October 15, 2021
Submission Date January 18, 2021
Acceptance Date July 30, 2021
Published in Issue Year 2021 Volume: 11 Issue: 4

Cite

APA Avcı, E. (2021). Genelleştirilmiş lineer modellerde kısmi ve augmented kısmi artıklar ve grafikleri. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 11(4), 1145-1153. https://doi.org/10.17714/gumusfenbil.863338