Factor Rotation Methods in Factor Analysis: An Application on Agricultural Data

Year 2023, Volume: 18 Issue: 2, 134 - 142, 18.12.2023

Ayşe Sümeyye Can , Özgür Koşkan , Malik Ergin

https://doi.org/10.54975/isubuzfd.1370165

Abstract

In this study, the rotation stage of factor analysis, which is one of the multivariate analysis methods, was examined. All stages of factor analysis have been defined. The material of the study consisted of a data set obtained from barley planted in 20 plots (replication) having 9 variables. In each plot, the average of 6 plants selected from that plot was used. The variables emphasized in the study were plant height, number of leaves, spike length, spike weight, grain yield, flowering period (days), harvest index, yield, and 1000-grain weight. Factors were obtained by principal component analysis, which is a factor extraction method, from the data set that met the prerequisites of the analysis. The criteria used in different factor rotations are given and based on these criteria, the formula that gives the optimum rotation angle for each data set was obtained. As a result, the formulas obtained for orthomax, varimax, quartimax, and equamax were applied to the factors obtained from the data set and the results were interpreted. As a result of factor rotation, when varimax, quartimax, and equamax methods were used, the values of the variables in terms of factor loads differed in each factor. This is a desirable situation for factor analysis results.

Keywords

Equamax, factor analysis, orthomax, rotation methods, varimax, quartimax

Ethical Statement

As the authors of this study, we declare that we do not have any ethics committee approval.

Thanks

This manuscript was generated from first author’s master thesis.

Faktör Analizinde Faktör Döndürme Yöntemleri: Ziraat Verisi Üzerinde Bir Uygulama

Abstract

Bu çalışmada, çok değişkenli analiz yöntemlerinden biri olan faktör analizinde döndürme aşaması incelenmiştir. Faktör analizinin tüm aşamaları tanımlanmıştır. Çalışmanın materyali, 9 değişken içeren 20 parsele (tekrarlama) ekilen arpadan elde edilen bir veri setinden oluşmaktadır. Her parselde, o parselde seçilen 6 bitkinin ortalaması kullanılmıştır. Çalışmada vurgulanan değişkenler bitki boyu, yaprak sayısı, başak uzunluğu, başak ağırlığı, tane verimi, çiçeklenme periyodu (gün), hasat indeksi, verim ve 1000 tane ağırlığıdır. Analizin ön koşullarını sağlayan veri setinden, faktör çıkarma yöntemi olan temel bileşen analizi ile faktörler elde edilmiştir. Farklı faktör döndürmeler için kullanılan kriterler verilmiş ve bu kriterlere dayanarak her veri seti için en uygun döndürme açısını veren formül elde edilmiştir. Sonuç olarak, orthomax, varimax, quartimax ve equamax için elde edilen formüller veri setinden elde edilen faktörlere uygulanmış ve sonuçlar yorumlanmıştır. Faktör döndürme sonucunda varimax, quartimax ve equamax yöntemleri kullanıldığında değişkenlerin faktör yükleri açısından değerleri her faktörde farklılık göstermiştir. Bu, faktör analizi sonuçları için arzu edilen bir durumdur.

Keywords

Equamax, faktör analizi, orthomax, döndürme yöntemleri, varimax, quartimax

Ethical Statement

As the authors of this study, we declare that we do not have any ethics committee approval.

Thanks

This manuscript was generated from first author’s master thesis.

References

• Akhtar-Danesh, N. (2017). A comparison between major factor extraction and factor rotation techniques in q-methodology. Open Journal of Applied Sciences, 7(4), 147-156. https://10.4236/ojapps.2017.74013
• Alpar, R. (2013). Çok Değişkenli istatistiksel yöntemler. Detay Yayıncılık, Ankara.
• Beniston, J. W., Lal, R., & Mercer, K. L. (2016). Assessing and managing soil quality for urban agriculture in a degraded vacant lot soil. Land Degradation & Development, 27(4), 996-1006.
• Brown, B. L., & Hendrix, S. B. (2005). Partial correlation coefficients. Encyclopedia of Statistics in Behavioral Science, 3, 1518-1523. https://doi.org/10.1002/0470013192.bsa469
• Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36(1), 111-150. https://doi.org/10.1207/ S15327906MBR3601_05 Darton, R. A. (1980). Rotation in factor analysis. The Statistician, 167-194. https://doi.org/10.2307/2988040
• Didia, J. U. D., & Idenedo, O. W. (2021). Customer orientation and loyalty behaviour of users of global system of mobile telecommunication services. International Journal of Marketing and Management, 7(3), 34-44.
• Finch, W. H. (2011). A comparison of factor rotation methods for dichotomous data. Journal of Modern Applied Statistical Methods, 10(2), 549-570. https://10.22237/jmasm/ 1320120780
• Goddard, M. E., & Beilharz, R. G. (1984). A factor analysis of fearfulness in potential guide dogs. Applied Animal Behaviour Science, 12(3), 253-265.
• İlhan, F. (2007). A study on factor analysis and its application to agricultural data. Master thesis, Selçuk Üniversitesi, Konya, 63 p.
• Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23(3), 1-14. https://10.1007/BF02289233
• Karaman, H., Atar, B., & Çobanoğlu, A. D. (2017). The comparison of factor extraction methods used in exploratory factor analysis. Gazi University Journal of Education Faculty, 37(3), 1173-1193.
• Khalaf, K. (2007). Factor analysis and an application. Master Thesis. Gazi University Institute of Science, Ankara, 63 p.
• Osborne, J. W. (2015). What is rotating in explor what is rotating in exploratory factor analysis? or analysis? Practical Assessment, Research, and Evaluation, 20(2), 1-7. https://10.7275/hb2g-m060
• Polat, Y. (2012). Examining factor analyses methods comparatively and applying to animal husbandry trial. PhD thesis, Çukurova Üniversitesi, Adana, 206 p.
• Sadek, M. H., Al‐Aboud, A. Z., & Ashmawy, A. A. (2006). Factor analysis of body measurements in Arabian horses. Journal of Animal Breeding and Genetics, 123(6), 369-377.
• Saraçlı, S. (2011). An application on comparison the extracting methods in factor analysis. Düzce Üniversitesi Sağlık Bilimleri Enstitüsü Dergisi, 1(3), 22-26.
• Shrestha, N. (2021). Factor analysis as a tool for survey analysis. American Journal of Applied Mathematics and Statistics, 9(1), 4-11. http:// 10.12691/ajams-9-1-2
• Süzülmüş, S. (2005). Identifying models of factor analysis and using of generalized inverses. PhD Thesis. Çukurova Üniversitesi, Adana, 159 p.
• Tan, Y., & Corke, H. (2002). Factor analysis of physicochemical properties of 63 rice varieties. Journal of the Science of Food and Agriculture, 82(7), 745-752.
• Wrigley, C., Saunders, D. R., & Neuhaus, J. O. (1958). Application of the quartimax method of rotation to thurstone's primary mental abilities study. Psychometrika, 23(2), 151-170. https://10.1007/BF02289011