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Dandelion plot: a method for the visualization of R-mode exploratory factor analyses. (English) Zbl 1306.65096
Summary: 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.

MSC:
65C60 Computational problems in statistics (MSC2010)
62H25 Factor analysis and principal components; correspondence analysis
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[1] Aypay, A; Erdoğan, M; Sözer, MA, Variation among schools on classroom practices in science based on timss-1999 in Turkey, J Res Sci Teach, 44, 1417-1435, (2007)
[2] Basto, M; Pereira, JM, An SPSS R-menu for ordinal factor analysis, J Stat Softw, 46, 1-29, (2012)
[3] Bernaards C, Jennrich R (2012) GPArotation: GPA factor rotation. R package version 2012.3-1
[4] Cattell, RB, The scree test for the number of factors, Multivar Behav Res, 1, 245-276, (1966)
[5] Chajewski M (2009) Rela: Item analysis package with standard errors. R package version 4.1
[6] Choi, J; Peters, M; Mueller, RO, Correlational analysis of ordinal data: from pearsons r to Bayesian polychoric correlation, Asia Pac Educ Rev, 11, 459-466, (2010)
[7] Conway, JM; Huffcutt, AI, A review and evaluation of exploratory factor analysis practices in organizational research, Organ Res Methods, 6, 147-168, (2003)
[8] Cordeiro, PMG; Figueira, APC; Silva, JT; Matos, L, School motivation questionnaire for the portuguese population: structure and psychometric studies, Span J Psychol, 15, 1441-1455, (2012)
[9] Cotton, S; McCann, T; Gleeson, J; Crisp, K; Murphy, B; Lubman, D, Coping strategies in carers of Young people with a first episode of psychosis, Schizophr Res, 146, 118-124, (2013)
[10] Cudeck R, MacCallum RC (2007) Factor analysis at 100: historical developments and future directions. Lawrence Erlbaum Associates, Mahwah
[11] Dunn, JG; Dunn, JC; McDonald, K, Domain-specific perfectionism in intercollegiate athletes: relationships with perceived competence and perceived importance in sport and school, Psychol Sport Exerc, 13, 747-755, (2012)
[12] Dziuban, CD; Shirkey, EC, When is a correlation matrix appropriate for factor analysis? some decision rules, Psychol Bull, 81, 358, (1974)
[13] Epskamp, S; Cramer, AO; Waldorp, LJ; Schmittmann, VD; Borsboom, D, Qgraph: network visualizations of relationships in psychometric data, J Stat Softw, 48, 1-18, (2012)
[14] Fox J (2007) Polycor: polychoric and polyserial correlations. R package version 0.7-8
[15] Gabriel, R, The biplot graphic display of matrices with application to principal component analysis, Biometrika, 58, 453-467, (1971) · Zbl 0228.62034
[16] Gilley, WF; Uhlig, GE, Factor analysis and ordinal data, Education, 114, 258-264, (1993)
[17] Gorsuch, RL, Common factor analysis versus component analysis: some well and little known facts, Multivar Behav Res, 25, 33-39, (1990)
[18] Gorsuch, RL, Exploratory factor analysis: its role in item analysis, J Personal Assess, 68, 532-560, (1997)
[19] Greenacre MJ (2010) Biplots in practice. Fundacion BBVA/BBVA Foundation, Bilbao
[20] Hakstian, AR; Abell, RA, A further comparison of oblique factor transformation methods, Psychometrika, 39, 429-444, (1974) · Zbl 0295.92021
[21] Harman, H; Jones, W, Factor analysis by minimizing residuals (minres), Psychometrika, 31, 351-368, (1966)
[22] Harrington D (2009) Confirmatory factor analysis. Oxford University Press, New York
[23] Holgado-Tello, FP; Chacón-Moscoso, S; Barbero-García, I; Vila-Abad, E, Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables, Qual Quant, 44, 153-166, (2010)
[24] Horn, JL, A rationale and test for the number of factors in factor analysis, Psychometrika, 30, 179-185, (1965) · Zbl 1367.62186
[25] IBM Corporation (2010) IBM SPSS Statistics 19. IBM Corporation, Armonk
[26] IBM Corporation (2012) IBM SPSS Modeler 15 User’s Guide. IBM Corporation, Armonk
[27] Jenkins, EW; Nelson, N, Important but not for me: students attitudes towards secondary school science in england, Res Sci Technol Educ, 23, 41-57, (2005)
[28] Kaiser, H, The varimax criterion for analytic rotation in factor analysis, Psychometrika, 23, 187-200, (1958) · Zbl 0095.33603
[29] Kaiser, H, The application of electronic computers to factor analysis, Educ Psychol Meas, 20, 141-151, (1960)
[30] Kaiser, HF, A note on the equamax criterion, Multivar Behav Res, 9, 501-503, (1974)
[31] Khodadady, E; Ghallasi Fakhrabadi, Z; etal., Designing and validating a comprehensive scale of English language teachers attributes and establishing its relationship with achievement, Am J Sci Res, 82, 113-125, (2012)
[32] 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
[33] Kolence, KW; Kiviat, PJ, Software unit profiles & kiviat figures, SIGMETRICS Perform Eval Rev, 2, 2-12, (1973)
[34] Lance, CE; Butts, MM; Michels, LC, The sources of four commonly reported cutoff criteria what did they really say?, Organ Res Methods, 9, 202-220, (2006)
[35] Lawley, DN, The estimation of factor loadings by the method of maximum likelihood, Proc R Soc Edinb, 60, 64-82, (1940) · Zbl 0027.23503
[36] 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
[37] Manukyan A, Sedef A, Cene E, Demir I (2012) DandEFA: Dandelion plot for R-mode exploratory factor analysis. R package version 1.5 · Zbl 1306.65096
[38] 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
[39] Misaki, M; Wallace, GL; Dankner, N; Martin, A; Bandettini, PA, Characteristic cortical thickness patterns in adolescents with autism spectrum disorders: interactions with age and intellectual ability revealed by canonical correlation analysis, NeuroImage, 60, 1890-1901, (2012)
[40] Neuhauss, J; Wrigley, C, The quartimax method, Br J Stat Psychol, 7, 81-91, (1954)
[41] Oconnor, BP, SPSS and SAS programs for determining the number of components using parallel analysis and velicers map test, Behav Res Methods Instr Comput, 32, 396-402, (2000)
[42] Park, M; Lee, JW; Lee, JB; Song, SH, Several biplot methods applied to gene expression data, J Stat Plan Inference, 138, 500-515, (2008) · Zbl 1138.62080
[43] Peres-Neto, PR; Jackson, DA; Somers, KM, How many principal components? stopping rules for determining the number of non-trivial axes revisited, Comput Stat Data Anal, 49, 974-997, (2005) · Zbl 1429.62223
[44] R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/ · Zbl 0295.92021
[45] Revelle W (2014) Psych: procedures for psychological, psychometric, and personality research. R package version 1.4.2.3
[46] Revelle, W; Rocklin, T, Very simple structure: an alternative procedure for estimating the optimal number of interpretable factors, Multivar Behav Res, 14, 403-414, (1979)
[47] Reyment R, Joreskog KG (1993) Applied factor analysis in the natural sciences. Cambridge University Press, Cambridge · Zbl 0868.62051
[48] Roberts, LD; Allen, PJ, A brief measure of student perceptions of the educational value of research participation, Aust J Psychol, 65, 22-29, (2013)
[49] Saldivia, S; Torres-Gonzalez, F; Runte-Geidel, A; Xavier, M; Grandon, P; Antonioli, C; Ballester, D; Gibbons, R; Melipillan, R; Caldas, J; etal., Standardization of the maristán scale of informal care in people with schizophrenia and other psychoses, Acta Psychiatr Scand, 128, 468-474, (2013)
[50] SAS Institute Inc (2011) SAS/STAT software, Version 9.3. Cary, NC, USA. http://www.sas.com/
[51] SAS Institute Inc (2013) SAS Text Miner 13.1. Cary, NC, USA
[52] Selimović, A; Tomić Selimović, L, Validation of existence of secondorder factors in cattell’s 16pf personality inventory, Primenj Psihol, 5, 319-334, (2012)
[53] Shen, C, 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, 161-184, (2002)
[54] Shen, C; Pedulla, JJ, 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, 237-253, (2000)
[55] Sonmez, M; Moorhouse, A, Purchasing professional services: which decision criteria?, Manag Decis, 48, 189-206, (2010)
[56] Tahar, NF; Ismail, Z; Zamani, ND; Adnan, N, Students attitude toward mathematics: the use of factor analysis in determining the criteria, Proced Soc Behav Sci, 8, 476-481, (2010)
[57] Udina, F, Interactive biplot construction, J Stat Softw, 13, 1-16, (2005)
[58] Velicer, WF, Determining the number of components from the matrix of partial correlations, Psychometrika, 41, 321-327, (1976) · Zbl 0336.62041
[59] Voudouris, K; Lambrakis, N; Papatheothorou, G; Daskalaki, P, 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, 43-59, (1997)
[60] Warne, RT; Lazo, M; Ramos, T; Ritter, N, Statistical methods used in gifted education journals, 2006-2010, Gifted Child Q, 56, 134-149, (2012)
[61] Widaman, KF, Common factor analysis versus principal component analysis: differential bias in representing model parameters?, Multivar Behav Res, 28, 263-311, (1993)
[62] Yan, W; Hunt, L; Sheng, Q; Szlavnics, Z, Cultivar evaluation and mega-environment investigation based on the GGE biplot, Crop Sci, 40, 597-605, (2000)
[63] Yidana, SM; Ophori, D; Banoeng-Yakubo, B, A multivariate statistical analysis of surface water chemistry datathe ankobra basin, ghana, J Environ Manage, 86, 80-87, (2008)
[64] Zandi, P; Shirani-Rad, AH; Daneshian, J; Bazrkar-Khatibani, L, Agronomic and morphologic analysis of fenugreek (trigonella foenum-graecum l.) under nitrogen fertilizer and plant density via factor analysis, Afr J Agric Res, 6, 1134-1140, (2011)
[65] Zumbo, BD; Gadermann, AM; Zeisser, C, Ordinal versions of coefficients alpha and theta for likert rating scales, J Mod Appl Stat Methods, 6, 21-29, (2007)
[66] Zwick, WR; Velicer, WF, Comparison of five rules for determining the number of components to retain, Psychol Bull, 99, 432, (1986)
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