Skip to main content
Log in

Dandelion plot: a method for the visualization of R-mode exploratory factor analyses

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

One of the important aspects of exploratory factor analysis (EFA) is to discover underlying structures in real life problems. Especially, R-mode methods of EFA aim to investigate the relationship between variables. Visualizing an efficient EFA model is as important as obtaining one. A good graph of an EFA should be simple, informative and easy to interpret. A few number of visualization methods exist. Dandelion plot, a novel method of visualization for R-mode EFA, is used in this study, providing a more effective representation of factors. With this method, factor variances and factor loadings can be plotted on a single window. The representation of both positivity and negativity among factor loadings is another strength of the method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Aypay A, Erdoğan M, Sözer MA (2007) Variation among schools on classroom practices in science based on timss-1999 in turkey. J Res Sci Teach 44(10):1417–1435

    Article  Google Scholar 

  • Basto M, Pereira JM (2012) An SPSS R-menu for ordinal factor analysis. J Stat Softw 46(4):1–29

    Google Scholar 

  • Bernaards C, Jennrich R (2012) GPArotation: GPA factor rotation. R package version 2012.3-1

  • Cattell RB (1966) The scree test for the number of factors. Multivar Behav Res 1(2):245–276

    Article  Google Scholar 

  • Chajewski M (2009) Rela: Item analysis package with standard errors. R package version 4.1

  • Choi J, Peters M, Mueller RO (2010) Correlational analysis of ordinal data: from Pearsons r to Bayesian polychoric correlation. Asia Pac Educ Rev 11(4):459–466

    Article  Google Scholar 

  • Conway JM, Huffcutt AI (2003) A review and evaluation of exploratory factor analysis practices in organizational research. Organ Res Methods 6(2):147–168

    Article  Google Scholar 

  • Cordeiro PMG, Figueira APC, da Silva JT, Matos L (2012) School motivation questionnaire for the portuguese population: structure and psychometric studies. Span J Psychol 15(3):1441–1455

    Article  Google Scholar 

  • Cotton S, McCann T, Gleeson J, Crisp K, Murphy B, Lubman D (2013) Coping strategies in carers of young people with a first episode of psychosis. Schizophr Res 146(1):118–124

    Article  Google Scholar 

  • Cudeck R, MacCallum RC (2007) Factor analysis at 100: historical developments and future directions. Lawrence Erlbaum Associates, Mahwah

    Google Scholar 

  • Dunn JG, Dunn JC, McDonald K (2012) Domain-specific perfectionism in intercollegiate athletes: Relationships with perceived competence and perceived importance in sport and school. Psychol Sport Exerc 13(6):747–755

    Article  Google Scholar 

  • Dziuban CD, Shirkey EC (1974) When is a correlation matrix appropriate for factor analysis? Some decision rules. Psychol Bull 81(6):358

    Article  Google Scholar 

  • Epskamp S, Cramer AO, Waldorp LJ, Schmittmann VD, Borsboom D (2012) Qgraph: Network visualizations of relationships in psychometric data. J Stat Softw 48(4):1–18

    Google Scholar 

  • Fox J (2007) Polycor: polychoric and polyserial correlations. R package version 0.7–8

  • Gabriel R (1971) The biplot graphic display of matrices with application to principal component analysis. Biometrika 58(3):453–467

    Article  MATH  MathSciNet  Google Scholar 

  • Gilley WF, Uhlig GE (1993) Factor analysis and ordinal data. Education 114(2):258–264

    Google Scholar 

  • Gorsuch RL (1990) Common factor analysis versus component analysis: some well and little known facts. Multivar Behav Res 25(1):33–39

    Article  Google Scholar 

  • Gorsuch RL (1997) Exploratory factor analysis: its role in item analysis. J Personal Assess 68(3):532–560

    Article  Google Scholar 

  • Greenacre MJ (2010) Biplots in practice. Fundacion BBVA/BBVA Foundation, Bilbao

    Google Scholar 

  • Hakstian AR, Abell RA (1974) A further comparison of oblique factor transformation methods. Psychometrika 39(4):429–444

    Article  MATH  Google Scholar 

  • Harman H, Jones W (1966) Factor analysis by minimizing residuals (minres). Psychometrika 31(3):351–368

    Article  MathSciNet  Google Scholar 

  • Harrington D (2009) Confirmatory factor analysis. Oxford University Press, New York

    Google Scholar 

  • Holgado-Tello FP, Chacón-Moscoso S, Barbero-García I, Vila-Abad E (2010) Polychoric versus pearson correlations in exploratory and confirmatory factor analysis of ordinal variables. Qual Quant 44(1):153–166

    Article  Google Scholar 

  • Horn JL (1965) A rationale and test for the number of factors in factor analysis. Psychometrika 30(2):179–185

    Article  Google Scholar 

  • IBM Corporation (2010) IBM SPSS Statistics 19. IBM Corporation, Armonk

  • IBM Corporation (2012) IBM SPSS Modeler 15 User’s Guide. IBM Corporation, Armonk

  • Jenkins EW, Nelson N (2005) Important but not for me: students attitudes towards secondary school science in england. Res Sci Technol Educ 23(1):41–57

    Article  Google Scholar 

  • Kaiser H (1958) The varimax criterion for analytic rotation in factor analysis. Psychometrika 23(3):187–200

    Article  MATH  Google Scholar 

  • Kaiser H (1960) The application of electronic computers to factor analysis. Educ Psychol Meas 20(1):141–151

    Article  Google Scholar 

  • Kaiser HF (1974) A note on the equamax criterion. Multivar Behav Res 9(4):501–503

    Article  Google Scholar 

  • Khodadady E, Ghallasi Fakhrabadi Z et al (2012) Designing and validating a comprehensive scale of english language teachers attributes and establishing its relationship with achievement. Am J Sci Res 82(12):113–125

    Google Scholar 

  • Klinke S, Wagner C (2008) Visualizing exploratory factor analysis models. In: Paulo B (ed) Compstat 2008: proceedings in computational statistics : 18th symposium held in Porto, Portugal

  • Kolence KW, Kiviat PJ (1973) Software unit profiles & kiviat figures. SIGMETRICS Perform Eval Rev 2(3):2–12

    Article  Google Scholar 

  • Lance CE, Butts MM, Michels LC (2006) The sources of four commonly reported cutoff criteria what did they really say? Organ Res Methods 9(2):202–220

    Article  Google Scholar 

  • Lawley DN (1940) The estimation of factor loadings by the method of maximum likelihood. Proc R Soc Edinb 60(2):64–82

    MathSciNet  Google Scholar 

  • Manukyan A, Demir I, Sedef A (2011) A new graphical approach to exploratory factor analysis. In: Papanikos GT (ed) Abstract book for the 5th annual international conference on mathematics, statistics & mathematical education, Greece, Athens 13–16 June 2011

  • Manukyan A, Sedef A, Cene E, Demir I (2012) DandEFA: Dandelion plot for R-mode exploratory factor analysis. R package version 1.5

  • Martin MO, Mullis IV, Foy P, Stanco GM (2012) TIMSS 2011 international results in science. TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, Boston

  • Misaki M, Wallace GL, Dankner N, Martin A, Bandettini PA (2012) Characteristic cortical thickness patterns in adolescents with autism spectrum disorders: interactions with age and intellectual ability revealed by canonical correlation analysis. NeuroImage 60(3):1890–1901

    Article  Google Scholar 

  • Neuhauss J, Wrigley C (1954) The quartimax method. Br J Stat Psychol 7(2):81–91

    Article  Google Scholar 

  • Oconnor BP (2000) SPSS and SAS programs for determining the number of components using parallel analysis and velicers map test. Behav Res Methods Instr Comput 32(3):396–402

    Article  MathSciNet  Google Scholar 

  • Park M, Lee JW, Lee JB, Song SH (2008) Several biplot methods applied to gene expression data. J Stat Plan Inference 138(2):500–515

    Article  MATH  MathSciNet  Google Scholar 

  • Peres-Neto PR, Jackson DA, Somers KM (2005) How many principal components? stopping rules for determining the number of non-trivial axes revisited. Comput Stat Data Anal 49(4):974–997

    Article  MATH  MathSciNet  Google Scholar 

  • R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/

  • Revelle W (2014) Psych: procedures for psychological, psychometric, and personality research. R package version 1.4.2.3

  • Revelle W, Rocklin T (1979) Very simple structure: an alternative procedure for estimating the optimal number of interpretable factors. Multivar Behav Res 14(4):403–414

    Article  Google Scholar 

  • Reyment R, Joreskog KG (1993) Applied factor analysis in the natural sciences. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Roberts LD, Allen PJ (2013) A brief measure of student perceptions of the educational value of research participation. Aust J Psychol 65(1):22–29

    Article  Google Scholar 

  • Saldivia S, Torres-Gonzalez F, Runte-Geidel A, Xavier M, Grandon P, Antonioli C, Ballester D, Gibbons R, Melipillan R, Caldas J et al (2013) Standardization of the maristán scale of informal care in people with schizophrenia and other psychoses. Acta Psychiatr Scand 128(6):468–474

    Article  Google Scholar 

  • SAS Institute Inc (2011) SAS/STAT software, Version 9.3. Cary, NC, USA. http://www.sas.com/

  • SAS Institute Inc (2013) SAS Text Miner 13.1. Cary, NC, USA

  • Selimović A, Tomić Selimović L (2012) Validation of existence of secondorder factors in Cattell’s 16pf personality inventory. Primenj Psihol 5(4):319–334

    Google Scholar 

  • Shen C (2002) Revisiting the relationship between students’ achievement and their self-perceptions: a cross-national analysis based on timss 1999 data. Assess Educ Princ Policy Pract 9(2):161–184

    Article  Google Scholar 

  • Shen C, Pedulla JJ (2000) The relationship between students’ achievement and their self-perception of competence and rigour of mathematics and science: a cross-national analysis. Assess Educ Princ Policy Pract 7(2):237–253

    Article  Google Scholar 

  • Sonmez M, Moorhouse A (2010) Purchasing professional services: which decision criteria? Manag Decis 48(2):189–206

    Article  Google Scholar 

  • Tahar NF, Ismail Z, Zamani ND, Adnan N (2010) Students attitude toward mathematics: the use of factor analysis in determining the criteria. Proced Soc Behav Sci 8:476–481

    Article  Google Scholar 

  • Udina F (2005) Interactive biplot construction. J Stat Softw 13(5):1–16

    Google Scholar 

  • Velicer WF (1976) Determining the number of components from the matrix of partial correlations. Psychometrika 41(3):321–327

    Article  MATH  Google Scholar 

  • Voudouris K, Lambrakis N, Papatheothorou G, Daskalaki P (1997) An application of factor analysis for the study of the hydrogeological conditions in Plio-Pleistocene aquifers of NW Achaia (NW Peloponnesus, Greece). Math Geol 29(1):43–59

    Article  Google Scholar 

  • Warne RT, Lazo M, Ramos T, Ritter N (2012) Statistical methods used in gifted education journals, 2006–2010. Gifted Child Q 56(3):134–149

    Article  Google Scholar 

  • Widaman KF (1993) Common factor analysis versus principal component analysis: differential bias in representing model parameters? Multivar Behav Res 28(3):263–311

    Article  Google Scholar 

  • Yan W, Hunt L, Sheng Q, Szlavnics Z (2000) Cultivar evaluation and mega-environment investigation based on the GGE biplot. Crop Sci 40(3):597–605

    Article  Google Scholar 

  • Yidana SM, Ophori D, Banoeng-Yakubo B (2008) A multivariate statistical analysis of surface water chemistry datathe ankobra basin, Ghana. J Environ Manage 86(1):80–87

    Article  Google Scholar 

  • Zandi P, Shirani-Rad AH, Daneshian J, Bazrkar-Khatibani L (2011) Agronomic and morphologic analysis of fenugreek (Trigonella foenum-graecum l.) under nitrogen fertilizer and plant density via factor analysis. Afr J Agric Res 6(5):1134–1140

    Google Scholar 

  • Zumbo BD, Gadermann AM, Zeisser C (2007) Ordinal versions of coefficients alpha and theta for likert rating scales. J Mod Appl Stat Methods 6(1):21–29

    Google Scholar 

  • Zwick WR, Velicer WF (1986) Comparison of five rules for determining the number of components to retain. Psychol Bull 99(3):432

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Artür Manukyan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manukyan, A., Çene, E., Sedef, A. et al. Dandelion plot: a method for the visualization of R-mode exploratory factor analyses. Comput Stat 29, 1769–1791 (2014). https://doi.org/10.1007/s00180-014-0518-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-014-0518-x

Keywords

Navigation