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An Introduction to Applied Multivariate Analysis
Abstract
This comprehensive text introduces readers to the most commonly used multivariate techniques at an introductory, non-technical level. By focusing on the fundamentals, readers are better prepared for more advanced applied pursuits, particularly on topics that are most critical to the behavioral, social, and educational sciences. Analogies betwe
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“For multivariate normality, the Mardia's coefficient in this study was 294.28, lesser than the requisite maximum of 37 × 39 = 1443, which was suggested should be lesser than (k [k + 2], k is the number of observed variables) [46].”
From An Extended Theory of Planned Behavior for the Modelling of Chinese Secondary School Students’ Intention to Learn Artificial Intelligence (2020) · cites this paper as [46]
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Okuda, P. M. M., Pangelinan, M. M., Capellini, S. A., & Cogo‐Moreira, H. (2019) · Trends in Psychiatry and Psychotherapy · doi:10.1590/2237-6089-2018-0014 · Cited by 21
PELLEGRINO, M. A., Pinto, M., Marson, F., et al. (2019) · Experimental Brain Research · doi:10.1007/s00221-019-05617-9 · Cited by 21
Vega, M. D. L., Baez-Lopez, Y. A., Limón-Romero, J., Tlapa, D., Flores, D., Borbón, M. I. R., & Maldonado-Macías, A. A. (2020) · IEEE Access · doi:10.1109/access.2020.3023633 · Cited by 21
Cogo‐Moreira, H., & Lamont, A. M. (2017) · Psychology of Music · doi:10.1177/0305735617710322 · Cited by 20
“…a more conservative approach than the circulated guidelines, which consider a loading larger than 0.3 to be relevantly correlated to the factor (Raykov & Marcoulides, 2012), so here we adopted a more restricted cutoff of 0.4 to create a very short scale with highly relevant items to capture…”
MethodInfluentialJofre, J. M. M., Hinojosa, S. A., Mascle-Allemand, A.-L., et al. (2023) · Journal of Environmental Management · doi:10.1016/j.jenvman.2023.117564 · Cited by 20
“In this sense, the EFA makes it possible to reduce the variables while minimising the distortion that this process may cause, and facilitates the management and interpretation of the data set (Costello and Osborne, 2005; Raykov and Marcoulides, 2008).”
Doo, M. Y. (2023) · Education and Information Technologies · doi:10.1007/s10639-023-11878-3 · Cited by 21
“According to Raykov and Marcoulides (2008), multivariate normality is satisfied when Mardia’s coefficient is lower than p ( p + 2) (i.e., p is the number of observed variables).”
BackgroundAssessing metacognitive writing strategies and the predictive effects on multimedia writing
Teng, M. F., & Qin, C. (2024) · Asia Pacific Journal of Education · doi:10.1080/02188791.2024.2325132 · Cited by 26
“The Cronbach’s alpha coefficient for each strategy was much higher than the benchmark value of .70, indicating robust internal consistency (Raykov & Marcoulides, 2008).”
Group Comparisons in the Presence of Missing Data Using Latent Variable Modeling Techniques
Raykov, T., & Marcoulides, G. A. (2010) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705510903439136 · Cited by 20
“However, the MCAR assumption is rarely fulfilled in empirical research (Raykov & Marcoulides, 2008).”
BackgroundMethodInfluentialSelf-citationExploring E-Learning Acceptance among University Students in Thailand: A National Survey
Teo, T. P., Ruangrit, N., Khlaisang, J., Thammetar, T., & Sunphakitjumnong, K. (2014) · Journal of Educational Computing Research · doi:10.2190/ec.50.4.c · Cited by 20
“The Mardia’s coefficient (Mardia, 1970) for the sample data was 165.63, which is lower than the value of 483 computed based on the formula p ( p + 2), where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialTechnology Acceptance Measure for Teachers:T-TAM
Şahin, S., McIlroy, D., & Ursavaş, Ö. F. (2014) · Cited by 20
Mina, R. J. L., Lerma, M. B., Litan, P. L. B., et al. (2019) · Journal of Advanced Nursing · doi:10.1111/jan.13964 · Cited by 20
Examining the Psychometric Properties of the Epistemic Belief Inventory (EBI)
Teo, T. P. (2012) · Journal of Psychoeducational Assessment · doi:10.1177/0734282912449436 · Cited by 20
“The Mardia’s coefficient for the data in this study was 171.86, and this is lower than that of 899 computed from the formula p(p+2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008), indicative of multivariate normality.”
MethodInfluentialThe Institutionalization of Multicultural Education as a Global Policy Agenda
Cha, Y., & Ham, S. (2013) · The Asia-Pacific Education Researcher · doi:10.1007/s40299-013-0088-7 · Cited by 20
The Importance of the Assumption of Uncorrelated Errors in Psychometric Theory
Raykov, T., Marcoulides, G. A., & Patelis, T. (2014) · Educational and Psychological Measurement · doi:10.1177/0013164414548217 · Cited by 20
Self-citationChen, P.-H., Teo, T., & Zhou, M. (2016) · Learning and Individual Differences · doi:10.1016/j.lindif.2016.06.017 · Cited by 20
Sun, Q., & Zhang, L. J. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.986301 · Cited by 42
“In reference to the convergent validity of the PWMEQ, the recommended value of standardized regression weights (i.e., factor loading) adopted in this research was 0.50 (Raykov and Marcoulides, 2008; Awang, 2012).”
MethodInfluentialDestination experiencescape for Hanfu tourism: Scale development and validation
Zong, Y., Chen, J. S., & Tsaur, S. (2023) · Journal Of Vacation Marketing · doi:10.1177/13567667231200905 · Cited by 20
“Sample 2 was also found to reach the criteria of multivariate normality (Mardia coef fi cient = 129.415 < 26 (26 + 2)) (Mardia, 1970; Raykov and Marcoulides, 2008).”
InfluentialHuang, F. (2023) · The Asia-Pacific Education Researcher · doi:10.1007/s40299-023-00797-z · Cited by 20
Soriano-Alcantara, J. M., Guillén‐Gámez, F. D., & Ruiz‐Palmero, J. (2024) · Technology Knowledge and Learning · doi:10.1007/s10758-024-09741-6 · Cited by 29
“For this, multivariate normality was verified by comparing the Mardia coefficient, which is considered acceptable when its value is less than the result of the formula p( p + 2) (Raykov & Marcoulides, 2008 ), where p is the number of items.”
Examining culture and performance at different middle school level structures
Gomez, M. O., Marcoulides, G. A., & Heck, R. H. (2012) · International Journal of Educational Management · doi:10.1108/09513541211202004 · Cited by 19
Self-citationKasapoğlu, K. (2020) · İnönü Üniversitesi Eğitim Fakültesi Dergisi · doi:10.17679/inuefd.709688 · Cited by 19
Plonsky, L. (2011) · ProQuest LLC eBooks · Cited by 19
Measuring User-Perceived Characteristics for Banking Services: Proposing a Methodology
Bitkina, O. V., Park, J., & Kim, H. K. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19042358 · Cited by 18
Usage Patterns of Telepsychology and Face-to-Face Psychotherapy: Clients’ Profiles and Perceptions
Sora, B., Nieto, R., Montesano, A., & Armayones, M. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.821671 · Cited by 20
“This is a method used in a multi-group setting to demonstrate whether several independent variables (nominal and/or continuous) are related to group membership and how they are combined to better understand group differences (Raykov and Marcoulides, 2012).”
MethodSpeed Matters: What to Prioritize in Optimization for Faster Websites
Xilogianni, C., Doukas, F.-R., Drivas, I. C., & Kouis, D. (2022) · Analytics · doi:10.3390/analytics1020012 · Cited by 18
Teo, T. P. (2010) · Multicultural Education & Technology Journal · doi:10.1108/17504971011075165 · Cited by 18
“49, which is lower than the value of 288 computed based on the formula p( p þ 2) where p equals the number of observed variables in the model (Raykov and Marcoulides, 2008).”
MethodComparing Between- and Within-Group Variances in a Two-Level Study
Raykov, T., Marcoulides, G. A., & Akaeze, H. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416634166 · Cited by 18
“…interest to a researcher, a test of the hypothesis H0 : r = r0 ð7Þ at a prefixed significance level a against the bidirectional alternative of r not being equal to r0, is directly carried out by checking if r0 is contained in the corresponding otherwise (e.g., Raykov & Marcoulides, 2008).”
BackgroundSelf-citationCross-validation: What is it and how is it used in regression?
Morin, K. L., & Davis, J. L. (2016) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2015.1099672 · Cited by 19
“In addition, although the focus of this article is how cross-validation can be used in regression, cross-validation has also been used in other situations to investigate concepts such as linear model selection (Harrell, 2013), comparing alternate models for covariance matrices (Raykov and Marcoulides, 2012), density e…”
MethodShrinkage estimation of non-negative mean vector with unknown covariance under balance loss
Karamikabir, H., Afshari, M., & Arashi, . (2018) · Journal of Inequalities and Applications · doi:10.1186/s13660-018-1919-0 · Cited by 18
Lu, J., Li, C., Potts, C. A., & Ufomadu, J. (2019) · International Journal for the Advancement of Counselling · doi:10.1007/s10447-019-09391-9 · Cited by 18
Altınsoy, F., & Aypay, A. (2021) · Current Psychology · doi:10.1007/s12144-021-02466-0 · Cited by 28
“…(812.77/98) =8.29, p = 0.001, SRMR: 0.055, NNFI = 0.91, CFI = 0.93, and GFI = 0.91; it was also determined that RMSEA = 0.083 (confidence interval for RMSEA = 0.077–0.088) and was within acceptable limits (for details of the fit criteria, see Jöreskog & Sörbom, 1993; Raykov & Marcoulides, 2008).”
MethodInfluentialFernández‐Pérez, L., Santana‐Farré, R., de Mirecki-Garrido, M., García, I., Guerra, B., Mateos-Dı́az, C., Iglesias‐Gato, D., Díaz-Chico, J. C., Flores‐Morales, A., & Díaz, M. L. (2014) · PLoS ONE · doi:10.1371/journal.pone.0096305 · Cited by 17
“133% compared with the TXOX group), points to a substantial stimulation of hepatic lipogenesis by the combination of E2 and GH. Finally, we performed PCA to identify data that discriminate groups.”
InfluentialSu, M., Zhao, J., Qi, G., Kim, J., & Park, K.-S. (2021) · International Journal of Logistics Research and Applications · doi:10.1080/13675567.2021.1961214 · Cited by 20
Examining learning management system success: a multiperspective framework
Bećirović, S. (2023) · Education and Information Technologies · doi:10.1007/s10639-023-12308-0 · Cited by 17
“Thus, the data in this investigation were assumed to be multivariate normal (Raykov & Marcoulides, 2008).”
A sampling design for a Sentinel General Practitioner Network
Pérez-Farinós, N., Galán, I., Ordobás, M., et al. (2009) · Gaceta Sanitaria · doi:10.1016/j.gaceta.2008.05.010 · Cited by 17
Park, R., Pituch, K. A., Kim, J., et al. (2015) · Methodology · doi:10.1027/1614-2241/a000096 · Cited by 17
Perspectives on flipped L2 classes: implications for learner training
Tecedor, M., & Pérez, A. B. (2019) · Computer Assisted Language Learning · doi:10.1080/09588221.2019.1626439 · Cited by 17
“Standardized estimates factor loadings higher than the benchmark value 0.50 suggest an acceptable effect size (Raykov & Marcoulides, 2008).”
BackgroundInfluentialUslu, S., & Aktaş, H. (2017) · Eskişehir Osmangazi Üniversitesi İktisadi ve İdari Bilimler Dergisi · doi:10.17153/oguiibf.298772 · Cited by 17
Wang, Y., Zhang, X., & Wang, L. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.846594 · Cited by 22
“According to Mardia’s (1970) and Raykov and Marcoulides (2008) Average variances extracted (AVE) and composite reliability (CR) were employed to evaluate the validity and reliability of internal constructs.”
MethodYe, W., & Ren, W. (2023) · Reading and Writing · doi:10.1007/s11145-023-10419-1 · Cited by 16
“1, all standardized estimates of the hypothesized latent constructs were greater than the threshold value of 0.50, suggesting an acceptable effect size (Raykov & Marcoulides, 2008).”
BackgroundInfluentialTeng, M. F., & Teng, L. S. (2024) · Research Methods in Applied Linguistics · doi:10.1016/j.rmal.2024.100136 · Cited by 20
Automatic detection of acne scars: Preliminary results
Dey, B. C., Nirmal, B., & Galigekere, R. R. (2013) · doi:10.1109/pht.2013.6461325 · Cited by 16
Afari, E. (2013) · International Review of Contemporary Learning Research · doi:10.12785/irclr/020102 · Cited by 16
“This value is less than the recommended value [p (p + 2); where p = total number of observed indicators; 40(42) = 1,680] by Raykov and Marcoulides (2008), hence the requirement of multivariate normality was satisfied.”
BackgroundPorras, C. V., Roa‐Díaz, Z. M., Barnes, C. R., Adamson-Macedo, E. N., Ferré‐Grau, C., & Fernández, I. D. M. (2020) · Maternal and Child Health Journal · doi:10.1007/s10995-019-02860-y · Cited by 16
Sathler, D. (2021) · Environmental Science & Policy · doi:10.1016/j.envsci.2021.09.004 · Cited by 17
Singhaputtangkul, N., Low, S. P., Teo, A. L., et al. (2013) · Architectural Science Review · doi:10.1080/00038628.2013.783458 · Cited by 16
Does Brain Reserve Protect Older Women from Vascular Depression?
Paulson, D. L., Bowen, M. E., & Lichtenberg, P. A. (2013) · The Journals of Gerontology Series B · doi:10.1093/geronb/gbt007 · Cited by 21
Human Development and National Culture: A Multivariate Exploration
Gamlath, S. (2016) · Social Indicators Research · doi:10.1007/s11205-016-1396-0 · Cited by 15
Dobia, B., Bodkin‐Andrews, G., Parada, R. H., O’Rourke, V., Gilbert, S., Daley, A., & Roffey, S. (2013) · Cited by 16
Technology Acceptance Model: History, Theory, and Application
Ursavaş, Ö. F. (2022) · Springer texts in education · doi:10.1007/978-3-031-10846-4_4 · Cited by 28
Teng, M. F. (2023) · Language Learning Journal · doi:10.1080/09571736.2023.2267575 · Cited by 19
“The standardised estimate loadings from the factors on the observed variables were all higher than .50, a benchmark value indicating an acceptable effect size (Raykov and Marcoulides 2008).”
Validez de constructo y confiabilidad del instrumento calidad de vida versión familiar en español
Barrera Ortiz, L., Carrillo González, G. M., Chaparro Díaz, L., Sánchez Herrera, B., Vargas Rosero, E., & Carreño, S. P. (2015) · Enfermería Global · doi:10.6018/eglobal.14.1.185111 · Cited by 16
Kaba, Y., & Şengül, S. (2018) · Pegem Journal of Education and Instruction · doi:10.14527/pegegog.2018.023 · Cited by 15
“RMSEA value that is equal to or less than .06 represents a good fit (Raykov & Marcoulides, 2008).”
MethodNumber space is made by response space: Evidence from left spatial neglect
Pinto, M., PELLEGRINO, M. A., Lasaponara, S., Scozia, G., D'Onofrio, M., Raffa, G., Nigro, S. L., Rossi‐Arnaud, C., Tomaiuolo, F., & Doricchi, F. (2021) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2021.107773 · Cited by 15
Influence of achievement goal on technology use among undergraduates in Malaysia
Teo, T. P., Moses, P., Cheah, P. K., Huang, F., & Tey, T. C. Y. (2023) · Interactive Learning Environments · doi:10.1080/10494820.2023.2197957 · Cited by 15
“The formula, ( p ( p + 2)), where p refers to the total number of observed items was used to calculate Mardia ’ s coe ffi cient to test for multivariate normality (Raykov & Marcoulides, 2008).”
Joachim, K. C., Wilk, P., Ryan, B. L., & Speechley, K. N. (2016) · Epilepsia · doi:10.1111/epi.13494 · Cited by 15
“Additional caution was taken when applying MIs in the third step due to limitations in their ability to be interpreted and theoretically justified.(24) MIs are data-driven suggestions for improving a model’s fit.”
BackgroundMethodInfluentialAssessing Music Perception in Young Children: Evidence for and Psychometric Features of the M-Factor
Barros, C. G., Swardfager, W., Moreno, S., Bortz, G., Ilari, B. S., Jackowski, A. P., Ploubidis, G. B., Little, T. D., Lamont, A. M., & Cogo‐Moreira, H. (2017) · Frontiers in Neuroscience · doi:10.3389/fnins.2017.00018 · Cited by 14
Revisiting the Bi-Factor Model: Can Mixture Modeling Help Assess Its Applicability?
Raykov, T., Marcoulides, G. A., Menold, N., & Harrison, M. (2018) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2018.1436441 · Cited by 15
Self-citationConceptualising and interpreting reliability
Johnson, S., & Johnson, R. (2010) · Digital Education Resource Archive (University College London) · Cited by 15
The Development of the Turkish Craving for Internet Gaming Scale (CIGS): A Validation Study
Savcı, M., & Griffiths, M. D. (2019) · International Journal of Mental Health and Addiction · doi:10.1007/s11469-019-00114-0 · Cited by 15
“Table 2 Goodness of fit indices and acceptable limits Indices Acceptable limits χ2/df ≤ 5 acceptable fit, ≤ 3 perfect fit RMSEA ≤ 0.10 weak fit, ≤ 0.08 good fit, ≤ 0.05 perfect fit GFI .85–.89 acceptable fit, ≥ .90 good fit AGFI .85–.89 acceptable fit, ≥ .90 good fit CFI ≥ .90 acceptable fit, ≥ .95 good fit, ≥ .97 per…”
BackgroundInfluentialUrsavaş, Ö. F. (2022) · Springer texts in education · doi:10.1007/978-3-031-10846-4_2 · Cited by 14
Early Childhood Educators Pay Equity: A Dream Deferred
Liu, L., Joseph, G. E., Taylor, J. M., Hassairi, N., & Soderberg, J. S. (2023) · Early Childhood Education Journal · doi:10.1007/s10643-023-01600-w · Cited by 25
“…model allows for simultaneously examining the relationships between multiple independent variables (e.g., professional and demographic characteristics) and a single dependent variable (e.g., hourly wages) while controlling for other potentially confounding variables (Raykov & Marcoulides, 2008 ).”
Multicultural Education Policy in the Global Institutional Context
Cha, Y., Ham, S., & Yang, K.-E. (2016) · Springer eBooks · doi:10.1007/978-981-10-2222-7_2 · Cited by 14
“Bartlett’s weighted least squares method was used for factor score estimation (see Raykov and Marcoulides 2008) linkages to global civil society (std. beta = 0.650, p 0.10).”
MethodInfluentialBurnout Syndrome in Middle and Senior Management in the Industrial Manufacturing Sector of Mexico
Macias-Velasquez, S., Baez-Lopez, Y. A., Maldonado-Macías, A. A., Limón-Romero, J., & Tlapa, D. (2019) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph16081467 · Cited by 14
“The evaluation of this type of normality considers the normalized value of multivariate Mardia kurtosis, with the procedure carried out by comparing the Mardia coefficient for the data under study with a calculated value based on the formula p(p + 2), where p is the number of variables observed in the model [52].”
MethodThe role of gender and employment status in MOOC learning: An exploratory study
Dai, H. M., Teo, T. P., & Rappa, N. A. (2022) · Journal of Computer Assisted Learning · doi:10.1111/jcal.12681 · Cited by 14
Turkish Adaptation of Utley Geometry Attitude Scale: A Validity and Reliability Study
Avcu, R. (2015) · Eurasian Journal of Educational Research · doi:10.14689/ejer.2015.58.1 · Cited by 14
“On the other hand, RMSEA, RMR, and SRMR values less than .05 suggest perfect model fit and values less than .08 suggest good model fit (Brown, 2006; Byrne, 1994; Hooper, Coughlan & Mullen, 2008; Hu & Bentler, 1999; Raykov & Marcoulides, 2008).”
MethodKabasakal, Z., Sağkal, A. S., & Türnüklü, A. (2016) · TED EĞİTİM VE BİLİM · doi:10.15390/eb.2015.4704 · Cited by 22
Dhammic Technology Acceptance Model (DTAM)
Teo, T. P., & Jarupunphol, P. (2015) · Journal of Educational Computing Research · doi:10.1177/0735633114568859 · Cited by 14
“The Mardia’s coefficient for the data in this study was 192.57, which is lower than the value of 483 computed based on the formula p(p+2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialMeta-Analysis of Scale Reliability Using Latent Variable Modeling
Raykov, T., & Marcoulides, G. A. (2013) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2013.769396 · Cited by 15
“An examination of whether MI holds or not can be carried out using the LVM methodology, and a detailed discussion of this process can be found, for example, in Raykov and Marcoulides (2008).”
MethodSelf-citationKhan, Z. R. (2014) · Research Online (University of Wollongong) · Cited by 14
Brillinger, M., Scheuer, S., & Albert, C. (2022) · Journal of Environmental Management · doi:10.1016/j.jenvman.2022.115350 · Cited by 14
Pekmezci, F. B., & Ertaş, B. D. (2024) · Teaching and Teacher Education · doi:10.1016/j.tate.2024.104514 · Cited by 23
Milutinović, V. (2024) · International Journal of Human-Computer Interaction · doi:10.1080/10447318.2024.2331877 · Cited by 14
“As calculated using the formula p (p þ 2), where p (20) is the model’s number of observed items, the Mardia’s coefficient should be lower than 440, and for the current sample data it was 54.77 (Raykov & Marcoulides, 2008).”
InfluentialKhine, M. S., & Afari, E. (2017) · Psychology Society & Education · doi:10.25115/psye.v6i1.504 · Cited by 13
“This value, as required, was less than [p (p + 2)] where p = the number of observed variables in the model; 40(42) = 1680 (Raykov & Marcoulides, 2008).”
BackgroundFang, G., & Teo, T. P. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.626271 · Cited by 14
Tu, C. C., Yang, D., Pan, L., & Dai, X. (2022) · Psychology in the Schools · doi:10.1002/pits.22693 · Cited by 13
“For multivariate normality, Mardia's coefficient was 155.46 (i.e., lower than p(p + 2) = 483) (Raykov & Marcoulides, 2008).”
InfluentialInfluences of contextual variables on the intention to use technology in education
Teo, T. P. (2013) · Campus-Wide Information Systems · doi:10.1108/10650741311306282 · Cited by 13
“18, which is much lower than the computed value of 675 based on the formula p(pþ 2) where p equals the number of observed variables in the model (Raykov and Marcoulides, 2008).”
BackgroundViviescas, J. C., Osorio, J. P., & Griffiths, D. V. (2019) · Bulletin of Engineering Geology and the Environment · doi:10.1007/s10064-019-01472-8 · Cited by 13
Reading Self-Efficacy in Early Adolescence: Which Measure Works Best?
Piercey, R. R. (2013) · UKnowledge (University of Kentucky) · Cited by 13
Modelling the Influences of Beliefs on Preservice Teachers' Attitudes towards Computer Use
Teo, T. P. (2012) · European Journal of Educational Research · doi:10.12973/eu-jer.1.1.13 · Cited by 13
“The Mardia’s coefficient for the data in this study was 109.771, which is much lower than the computed value of 440 based on the formula p ( p +2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialShadowen, N. L., Chieffo, L. P., & Guerra, N. G. (2015) · Frontiers The Interdisciplinary Journal of Study Abroad · doi:10.36366/frontiers.v26i1.368 · Cited by 13
“References Ashwill, M. A., & Hoang Oanh, D. T. (2009).”
BackgroundMethodInfluentialSuffering a Loss Is Good Fortune: Myth or Reality?
Zhao, C., Shen, S., Rao, L., Zheng, R., Liu, H., & Li, S. (2017) · Journal of Behavioral Decision Making · doi:10.1002/bdm.2056 · Cited by 12
“The Mardia's coefficient for the data in this study was 31.55, which is lower than the value of 168 computed based on the formula p (p + 2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008) .”
MethodInfluentialTowards robust cross-domain domain adaptation for part-of-speech tagging
Schnabel, T. (2013) · OPUS Publication Server of the University of Stuttgart (University of Stuttgart) · doi:10.18419/opus-3064 · Cited by 12
Mukherjee, A., & Banerji, H. (2025) · npj Heritage Science · doi:10.1038/s40494-025-01561-w · Cited by 12
“Communality represents shared variances 106 that can be explained by the common factors and anextractionvalue greater than 0.3 isacceptable 107 .”
InfluentialRudolph, C. W. (2021) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2021.103560 · Cited by 15
Lin, Y. H., Lee, T. H., & Wang, C.-K. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph182212223 · Cited by 12
“The multivariate normality assumption was evaluated using Mardia’s index test [75].”
MethodSalele, N., & Khan, M. S. H. (2022) · SAGE Open · doi:10.1177/21582440221102436 · Cited by 12
“Having Mardia’s coefficient lower than the computed result from the formula indicates that multivariate normality was also achieved (Mardia, 1970; Raykov & Marcoulides, 2008).”
BackgroundAplin-Houtz, M. J., Leahy, S., Willey, S., Lane, E. K., Sharma, S., & Meriac, J. P. (2023) · Employee Responsibilities and Rights Journal · doi:10.1007/s10672-023-09453-6 · Cited by 14
Ziviani, C. R., Féres‐Carneiro, T., & Magalhães, A. S. (2011) · Psicologia Reflexão e Crítica · doi:10.1590/s0102-79722011000100005 · Cited by 12
“In effect, according to Raykov and Marcoulides (2008), performing a PCA precludes the need for rotation of resulting principal components.”
MethodOn the Fallibility of Principal Components in Research
Raykov, T., Marcoulides, G. A., & Li, T. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416629714 · Cited by 12
Self-citationÇevrimiçi Sosyal Ağların Öğretim Amaçlı Kabul ve Kullanımı Ölçeğinin Geliştirilmesi
Kuzu, E. B., & Akbulut, Y. (2017) · Türk bilgisayar ve matematik eğitimi dergisi · doi:10.16949/turkbilmat.298120 · Cited by 12
Teaching Principal Components Using Correlations
Westfall, P. H., Arias, A. L., & Fulton, L. V. (2017) · Multivariate Behavioral Research · doi:10.1080/00273171.2017.1340824 · Cited by 12
“Similarly, it is common to calculate correlations between the individual Yi variables comprising a component score, with the component score itself, to identify which variables are most related to the component (Raykov & Marcoulides, 2012 ch.7; Rencher, 1992; Trendafilov & Adachi, 2015).”
BackgroundADENAIKE, A. S., PETERS, S. O., Adeleke, M. A., et al. (2018) · Tropical Animal Health and Production · doi:10.1007/s11250-018-1547-1 · Cited by 12
Kouadra, R., Demdoum, A., Chabour, N., et al. (2018) · Acta Geochimica · doi:10.1007/s11631-018-0298-z · Cited by 12
Bigirimana, J., Uzayisenga, B., & Gut, L. J. (2019) · Crop Protection · doi:10.1016/j.cropro.2019.04.029 · Cited by 12
Zhao, C., & Huang, F. (2024) · Learning and Motivation · doi:10.1016/j.lmot.2024.101984 · Cited by 11
Salehi, P., Ba, Y., Kim, N., Mosallanezhad, A., Pan, A., Cohen, M. C., Wang, Y., Zhao, J. L., Bhatti, S. A., Sung, J., et al. (2024) · Journal of Artificial Intelligence Research · doi:10.1613/jair.1.14990 · Cited by 16
“Approaches for evaluating construct validity include multivariate analytical tools, such as Factor Analysis (Raykov & Marcoulides, 2008; Tabachnick et al., 2013), Principal Components Analysis (PCA; Bandalos, 2018), and Structural Equation Modeling (Kline, 2023).”
MethodMultidimensional Assessment of Internet Addiction: Scale Development and Validation
Sondhi, N., & Joshi, H. (2021) · Global Business Review · doi:10.1177/0972150921989876 · Cited by 11
Latent Growth Curve Model Selection: The Potential of Individual Case Residuals
Raykov, T., & Penev, S. I. (2014) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2014.856693 · Cited by 11
“…of this article, to obtain the pertinent ICRs after fitting each of these models to data, let us denote as usual by a hat an estimator— in particular the factor score estimators for the intercept, slope, quadratic, and cubic coefficients (if present in the model; e.g., Raykov & Marcoulides, 2008).”
BackgroundSelf-citationUrsavaş, Ö. F., Yurdakul, I. K., Türk, M., & McIlroy, D. (2016) · Journal of Educational Computing Research · doi:10.1177/0735633115622959 · Cited by 11
“Mardia’s (1970) coefficient for the data in this study was 173.219, which is lower than the value of 483 computed based on the formula p(p+p) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluential
Metadata
- Authors
- Raykov, T., & Marcoulides, G. A.
- ORCID
- Raykov, Tenko
- Venue
- Routledge eBooks
- Publisher
- Routledge
- Published
- 2008-03-10
- OpenAlex
- W619790032
- Cited by
- 716
- References
- 0
- Citations by year
- 2026: 30 · 2025: 54 · 2024: 48 · 2023: 52 · 2022: 55 · 2021: 51 · 2020: 52 · 2019: 57 · 2018: 34 · 2017: 38 · 2016: 42 · 2015: 52 · 2014: 36 · 2013: 50 · 2012: 19
- FWCI
- 5.12
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Routledge eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Routledge eBooks
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- multivariate analysis, multivariate techniques, behavioral science, social sciences, educational sciences, statistical analysis
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