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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The data met multivariate normality (Mardia's coefficient 294.28 < 1443).
“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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“The Mardia's coefficient (Mardia, 1970) for the data in this study was 402.35, which is lower than the value of 440 computed based on the formula p(p+2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialKnekta, E., Runyon, C., & Eddy, S. L. (2019) · CBE—Life Sciences Education · doi:10.1187/cbe.18-04-0064 · Cited by 694 · see citing works
“…the participant’s responses on different subsets of items relate more closely to one another than to other subsets, that is, it is an analysis of the dimensionality among the items (Raykov and Marcoulides, 2008; Leandre et al., 2012; Tabachnick and Fidell, 2013; Kline, 2016; Bandalos, 2018).”
BackgroundMethodInfluentialMartínez Steele, E., Popkin, B. M., Swinburn, B., & Monteiro, C. A. (2017) · Population Health Metrics · doi:10.1186/s12963-017-0119-3 · Cited by 585 · see citing works
Plonsky (2013) · doi:10.1017/s0272263113000399 · Cited by 347 · see citing works
“For example, MANOVA preserves statistical power and better refl ects the multivariate nature of the reality we attempt to measure (Fish, 1988 ; Raykov & Marcoulides, 2008 , chapter 1; see Gelman, Hill, & Yajima, 2012, for an alternate, Bayesian perspective on multiple comparisons).”
BackgroundA questionnaire-based validation of multidimensional models of self-regulated learning strategies
TENG, L. S., & ZHANG, L. J. (2016) · The Modern Language Journal · doi:10.1111/modl.12339 · Cited by 345 · see citing works
Promoting students' well-being by developing their readiness for the artificial intelligence age
Dai, Y., Chai, C.-S., Lin, P.-Y., Jong, M. S.-Y., Guo, Y., & Qin, J. (2020) · Sustainability · doi:10.3390/su12166597 · Cited by 330 · see citing works
“Mardia’s coefficient was measured to ensure that the multivariate normality was acceptable [54].”
MethodSeparate but correlated: The latent structure of space and mathematics across development.
Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C., Hambrick, D. Z., Ping, R. M., & Konstantopoulos, S. (2016) · Journal of Experimental Psychology General · doi:10.1037/xge0000182 · Cited by 306 · see citing works
Reis, D., Xanthopoulou, D., & Tsaousis, I. (2015) · Burnout Research · doi:10.1016/j.burn.2014.11.001 · Cited by 271 · see citing works
Dai, H. M., Teo, T. P., Rappa, N. A., & Huang, F. (2020) · Computers & Education · doi:10.1016/j.compedu.2020.103850 · Cited by 284 · see citing works
Teo, T. P., & Zhou, M. (2014) · Journal of Computing in Higher Education · doi:10.1007/s12528-014-9080-3 · Cited by 241 · see citing works
“68, 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 and Marcoulides 2008).”
BackgroundGottfried, A. E., Marcoulides, G. A., Gottfried, A. W., & Oliver, P. H. (2009) · Journal of Educational Psychology · doi:10.1037/a0015084 · Cited by 241 · see citing works
Self-citationMethodological Advances in Educational Effectiveness Research
Creemers, B., Kyriakides, L. E., & Sammons, P. (2010) · Routledge eBooks · doi:10.4324/9780203851005 · Cited by 242 · see citing works
Teo, T. P., & Noyes, J. (2012) · Interactive Learning Environments · doi:10.1080/10494820.2011.641674 · Cited by 237 · see citing works
“The Mardia’s coefficient for the data in this study was 77.18, indicating multivariate normality of the data as the value was lower than the value of 224 computed based on the formula p(p þ 2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialSaçkes, M., Trundle, K. C., Bell, R. L., et al. (2010) · Journal of Research in Science Teaching · doi:10.1002/tea.20395 · Cited by 235 · see citing works
Application of Structural Equation Modeling in Educational Research and Practice
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Chai, C. S., Wang, X., & Xu, C. (2020) · Mathematics · doi:10.3390/math8112089 · Cited by 226 · see citing works
“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].”
BackgroundStudents’ perceptions of school climate as determinants of wellbeing, resilience and identity
Aldridge, J. M., Fraser, B. J., Fozdar, F., Ala’i, K. G., Earnest, J., & Afari, E. (2015) · Improving Schools · doi:10.1177/1365480215612616 · Cited by 235 · see citing works
“Mardia’s coefficient (a measure of multivariate normality) was 2527.965, which is less than the recommended value (Raykov & Marcoulides, 2008).”
BackgroundInfluentialHuang, F., Teo, T. P., Sánchez‐Prieto, J. C., García‐Peñalvo, F. J., & Migueláñéz, S. O. (2019) · Computers & Education · doi:10.1016/j.compedu.2019.01.012 · Cited by 203 · see citing works
Factors that influence university students’ intention to use Moodle: a study in Macau
Teo, T. P., Zhou, M., Fan, A. C. W., & Huang, F. (2019) · Educational Technology Research and Development · doi:10.1007/s11423-019-09650-x · Cited by 184 · see citing works
“Consequently multivariate normality was assumed and the data were considered to be adequate for CFA (Raykov and Marcoulides 2008).”
MethodInfluentialStrassnig, M., Raykov, T., O’Gorman, C., Bowie, C. R., Sabbag, S. A., Durand, D., Patterson, T. L., Pinkham, A. E., Penn, D. L., & Harvey, P. D. (2015) · Schizophrenia Research · doi:10.1016/j.schres.2015.03.033 · Cited by 178 · see citing works
“All of the factor analyses performed used the robust full information maximum likelihoodmethod ofmodelfitting and parameter estimation (Raykov and Marcoulides, 2008).”
MethodSelf-citationZeedyk, S. M., Rodriguez, G., Tipton, L. A., Baker, B. L., & Blacher, J. (2014) · Research in Autism · doi:10.1016/j.rasd.2014.06.001 · Cited by 177 · see citing works
“The LSD test was utilized because it takes into account the unequal sample size (Raykov & Marcoulides, 2008).”
BackgroundMethodAn initial development and validation of a Digital Natives Assessment Scale (DNAS)
Teo, T. P. (2013) · Computers & Education · doi:10.1016/j.compedu.2013.02.012 · Cited by 175 · see citing works
Lin, P.-Y., Chai, C.-S., Jong, M. S.-Y., Dai, Y., Guo, Y., & Qin, J. (2021) · Computers and Education: Artificial Intelligence · doi:10.1016/j.caeai.2020.100006 · Cited by 171 · see citing works
Plonsky, L., & Gönülal, T. (2015) · Language Learning · doi:10.1111/lang.12111 · Cited by 158 · see citing works
Working memory components as predictors of children's mathematical word problem solving.
Zheng, X.-H., Swanson, H. L., & Marcoulides, G. (2011) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2011.06.001 · Cited by 161 · see citing works
Self-citationGould, D. R., Flett, R., & Lauer, L. (2011) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2011.07.005 · Cited by 152 · see citing works
Marcoulides, K. M., & Yuan, K. (2016) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2016.1225260 · Cited by 151 · see citing works
“…believe that there can still be a place for model fit indexes, as long as no decision concerning goodness of fit is based on just a single index, no matter how favorable for the model that index might appear (Hu & Bentler, 1999; Raykov & Marcoulides, 2006, 2008; Tomarken & Waller, 2005; Yu, 2002).”
BackgroundTeng, L. S. (2021) · Language Teaching Research · doi:10.1177/13621688211006881 · Cited by 179 · see citing works
“Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables (predictors) (Raykov & Marcoulides, 2008).”
MethodChinese students’ intentions to use the Internet-based technology for learning
Huang, F., Teo, T. P., & Zhou, M. (2019) · Educational Technology Research and Development · doi:10.1007/s11423-019-09695-y · Cited by 168 · see citing works
“Mardia’s coefficient was 559.81, which is less than 812 [ p ( p + 2)]; thus, the requirement of multivariate normality was satisfied, as recommended by Raykov and Marcoulides (2012).”
MethodInfluentialTeo, T. P., & van Schaik, P. (2011) · International Journal of Human-Computer Interaction · doi:10.1080/10447318.2011.581892 · Cited by 143 · see citing works
“This figure was less than the recommended value (( p ( p + 2), where p = total number of observed indicators) by Raykov and Marcoulides (2008); hence, the requirement of multivariate normality was satisfied.”
BackgroundTeachers and technology: development of an extended theory of planned behavior
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“89, which is lower than the value of 899 computed based on the formula, p(p ? 2) where p equals the number of observed variables in the model (Raykov and Marcoulides 2008).”
BackgroundShaping Professional Development to Promote the Diffusion of Instructional Expertise Among Teachers
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“Moreover, controlling for prior reduces the potential of residuals’ nonnormality and therefore increases the consistency of estimates (Raykov & Marcoulides, 2008).”
BackgroundServant leadership, organisational trust, and bank employee outcomes
Karatepe, O. M., Ozturk, A., & Kim, T. T. (2019) · The Service Industries Journal · doi:10.1080/02642069.2018.1464559 · Cited by 137 · see citing works
“Multivariate normality can be assumed when the Mardia’s coefficient is less than p (p + 2), where p equals the number of observed variables in the model (Bollen, 1989; Raykov & Marcoulides, 2008).”
Understanding continuance intention among MOOC participants: The role of habit and MOOC performance
Dai, H. M., Teo, T. P., & Rappa, N. A. (2020) · Computers in Human Behavior · doi:10.1016/j.chb.2020.106455 · Cited by 135 · see citing works
Régnier, J., Cadet, H., Bonilla, L. F., et al. (2013) · Bulletin of the Seismological Society of America · doi:10.1785/0120120240 · Cited by 134 · see citing works
Bećirović, S., Polz, E., & Tinkel, I. (2025) · Smart Learning Environments · doi:10.1186/s40561-025-00384-3 · Cited by 133 · see citing works
“The data in this investigation were presumed to follow a multivariate normal distribution (Raykov & Marcoulides, 2008).”
Teo, T. P., Chee, T. S., Lee, C. B., Sing, C. C., Koh, J. H. L., Chen, W., & Cheah, H. M. (2010) · Computers & Education · doi:10.1016/j.compedu.2010.08.001 · Cited by 132 · see citing works
Lau, W. W. F., & Yuen, A. H. K. (2014) · Computers & Education · doi:10.1016/j.compedu.2014.04.016 · Cited by 132 · see citing works
Teng, M. F., Wang, C., & Zhang, L. J. (2022) · Assessing Writing · doi:10.1016/j.asw.2021.100573 · Cited by 124 · see citing works
Teo, T. P. (2014) · Computers & Education · doi:10.1016/j.compedu.2014.11.015 · Cited by 122 · see citing works
Teo, T. P. (2014) · Computers & Education · doi:10.1016/j.compedu.2014.01.014 · Cited by 133 · see citing works
Aboramadan, M., Turkmenoglu, M. A., Dahleez, K. A., & Cicek, B. (2021) · International Journal of Contemporary Hospitality Management · doi:10.1108/ijchm-04-2020-0348 · Cited by 118 · see citing works
Creating College Opportunity: School Counselors and Their Influence on Postsecondary Enrollment
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“While inclusive analysis strategies (IAS)—in particular, checking for consistency between estimates in my final model and an alternative model including additional, auxiliary variables that were ‘‘predictive’’ of missing values [see Panter and Sterba (2011) for more detail about IAS]—improved the likelihood that my da…”
BackgroundMethodTeo, T. P., & Milutinović, V. (2015) · Australasian Journal of Educational Technology · doi:10.14742/ajet.1668 · Cited by 108 · see citing works
“Mardia’s (1970) coefficient for the data in this study was 157.49, which is lower than the value of 575 computed based on the formula p(p + 2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialFormative Constructs Implemented via Common Factors
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“These are commonly referred to as loadings and can be interpreted as ordinary factor or component loadings (e.g., Raykov & Marcoulides, 2008).”
BackgroundMethodModelling Serbian pre-service teachers' attitudes towards computer use: A SEM and MIMIC approach
Teo, T. P., Milutinović, V., & Zhou, M. (2015) · Computers & Education · doi:10.1016/j.compedu.2015.10.022 · Cited by 106 · see citing works
“M A The Mardia’s coefficient (Mardia, 1970) for the data in this study was 139.147, which is lower than the value of 528 computed based on the formula p ( p +2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
MethodInfluentialHeck, R. H., & Moriyama, K. I. (2010) · School Effectiveness and School Improvement · doi:10.1080/09243453.2010.500097 · Cited by 103 · see citing works
“One of the advantages of the SEM approach for analyzing multilevel data structures is that missing data can be incorporated directly into the analysis, which reduces parameter bias that can result from eliminating these cases (Raykov & Marcoulides, 2008).”
BackgroundUrsavaş, Ö. F., Yalçın, Y., & Bakır-Yalçın, E. (2019) · British Journal of Educational Technology · doi:10.1111/bjet.12834 · Cited by 103 · see citing works
Huang, F., & Teo, T. P. (2019) · Educational Technology Research and Development · doi:10.1007/s11423-019-09722-y · Cited by 103 · see citing works
Teng, M. F., Qin, C., & Wang, C. (2021) · Metacognition and Learning · doi:10.1007/s11409-021-09278-4 · Cited by 146 · see citing works
“The CFA results revealed that the standardized estimate loadings from observed variables to the unobserved variables were all higher than 0.50, which is a benchmark value that indicates an acceptable effect size (Raykov & Marcoulides, 2008).”
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The influence of teachers’ conceptions of teaching and learning on their technology acceptance
Teo, T. P., & Zhou, M. (2016) · Interactive Learning Environments · doi:10.1080/10494820.2016.1143844 · Cited by 100 · see citing works
“Mardia ’ s coef fi cient for the data inthis study was 526.74, which islowerthanthe value of1023computed based on the formula p ( p + 2), where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
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Applying Structural Equation Modeling (SEM) in Educational Research
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Zhan, E. S., Molina, M. D., Rheu, M., & Peng, W. (2023) · International Journal of Human-Computer Interaction · doi:10.1080/10447318.2023.2261731 · Cited by 100 · see citing works
“…univariate tests reveal that the seven types of fear of AI variables are not statistically affected by the assigned AI technology according to Raykov and Marcoulides’ (2008) recommendation that a significance level at .007 (.05/number of dependent variables) should be used to interpret if…”
Teo, T. P. (2014) · Interactive Learning Environments · doi:10.1080/10494820.2014.917110 · Cited by 92 · see citing works
“The Mardia ’ s coef fi cient for the data in this study was 154.44, which is lower than the value of 399 computed based on the formula p ( p + 2) where p equals the number of observed variables in the model (Raykov & Marcoulides, 2008).”
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Liu, Y., Cheng, Q., Zhou, K., Xia, Q., & Wang, X. (2016) · GEOCHEMICAL JOURNAL · doi:10.2343/geochemj.2.0415 · Cited by 92 · see citing works
Salar, R., Arıcı, F., Çaliklar, Ş., & Yılmaz, R. M. (2020) · Journal of Science Education and Technology · doi:10.1007/s10956-019-09810-x · Cited by 90 · see citing works
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“An RMSEA below .05 with the left endpoint of its 90% confidence interval (CI) that is markedly smaller than .05 represents an excellent fit (e.g., Raykov & Marcoulides, 2008).”
Gottfried, A. E., Marcoulides, G. A., Gottfried, A. W., & Oliver, P. H. (2013) · Journal of Research on Educational Effectiveness · doi:10.1080/19345747.2012.698376 · Cited by 89 · see citing works
“…is needed: a nonsignificant chi-square goodness-of-fit value; a CFI > .90; an RMSEA below 0.05 and the left endpoint of its 90% confidence interval is markedly smaller than 0.05 (with this interval not excessively wide; for further details, see Hu & Bentler, 1999; Raykov & Marcoulides, 2008).”
BackgroundInfluentialSelf-citationChai, C. S., Chiu, T. K. F., Wang, X., Jiang, F., & Lin, X. (2022) · Sustainability · doi:10.3390/su15010605 · Cited by 101 · see citing works
“Based on Raykov and Marcoulide’s [59] recommendation, the multivariate coefficient value was 73.957, which was less than the required maximum of 32 × 34 = 1088 (32 was the number of items used for confirmatory factor analysis (CFA)).”
InfluentialUnderstanding English teachers’ non-volitional use of online teaching: A Chinese study
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Paravantis, J. A., Stigka, E. K., Mihalakakou, G. K., Μichalena, E., Hills, J. M., & Dourmas, V. (2018) · Renewable Energy · doi:10.1016/j.renene.2018.02.068 · Cited by 87 · see citing works
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Uzun, S. U., & Zencir, M. (2021) · Current Psychology · doi:10.1007/s12144-018-0001-x · Cited by 85 · see citing works
Kim, T., Kim, W., Majeed, S., & Haldorai, K. (2023) · International Journal of Hospitality Management · doi:10.1016/j.ijhm.2023.103486 · Cited by 85 · see citing works
Assessing student-writers’ self-efficacy beliefs about text revision in EFL writing
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Marshall, J. A., Muhlack, R. A., Morton, B. J., Dunnigan, L., Chittleborough, D. J., & Kwong, P. C. W. (2019) · Soil Systems · doi:10.3390/soilsystems3020027 · Cited by 80 · see citing works
“Principal omponent analysis is a f m of factor a alysis, wh ch tr nsforms original sets of variables into a smaller set of line r co binations that account for most of the variance of th original set [35].”
BackgroundInfluentialModeling Key Drivers of E-Learning Satisfaction among Student Teachers
Teo, T., & Wong, S. L. (2013) · Journal of Educational Computing Research · doi:10.2190/ec.48.1.d · Cited by 77 · see citing works
“This figure is less than the recommended value (p(p+2), where p = total number of observed indicators; 28(30) = 840) by Raykov and Marcoulides (2008), hence the requirement of multivariate normality was met.”
BackgroundAssessing users satisfaction with web digital library: the case of Universiti Teknologi MARA
Masrek, M. N., & Gaskin, J. (2016) · International Journal of Information and Learning Technology · doi:10.1108/ijilt-06-2015-0019 · Cited by 64 · see citing works
Teng, L. S., & Zhang, L. J. (2015) · The Asia-Pacific Education Researcher · doi:10.1007/s40299-015-0243-4 · Cited by 72 · see citing works
“78, which was much less than the recommended value 323 calculated from the formula p(p ? 2), where p = total number of observed indicators (Raykov and Marcoulides 2008).”
BackgroundDigital literacy scale: Validity and reliability study with the rasch model
Avinç, E., & Doğan, F. (2024) · Education and Information Technologies · doi:10.1007/s10639-024-12662-7 · Cited by 115 · see citing works
“As delineated by Raykov and Marcoulides (2008), EFA serves as a potent analytical approach that offers profound insights into the psychometric properties of a measurement instrument, shedding light on the latent variables within the data-set.”
Teo, T. P., Yurdakul, I. K., & Ursavaş, Ö. F. (2014) · Interactive Learning Environments · doi:10.1080/10494820.2014.980275 · Cited by 70 · see citing works
“Mardia ’ s coef fi - cient (Mardia, 1970) for the data in this study was 178.19, 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).”
MethodInfluentialTeo, T. P., & Huang, F. (2018) · Interactive Learning Environments · doi:10.1080/10494820.2018.1489856 · Cited by 71 · see citing works
“The value obtained in this study, 119.725, was less than Raykov and Marcoulides (2008) recommended value ( p ( p + 2), where p stands for the total number of observed items (49 (51) = 2499).”
ResultInfluentialA Comparison of Alternative Models of Individual Quality of Life for Social Service Recipients
Gómez, L. E., Alonso, M. Á. V., Martínez, B. A., et al. (2010) · Social Indicators Research · doi:10.1007/s11205-010-9639-y · Cited by 68 · see citing works
Firms’ Intentions to Use Nonownership Services
Wittkowski, K., Benoit, S., & Wirtz, J. (2013) · Journal of Service Research · doi:10.1177/1094670512471997 · Cited by 68 · see citing works
Estimated effects of in utero cocaine exposure on language development through early adolescence
Bandstra, E. S., Morrow, C. E., Accornero, V. H., et al. (2011) · Neurotoxicology and Teratology · doi:10.1016/j.ntt.2010.07.001 · Cited by 66 · see citing works
Williamson, A. A., Zendarski, N. J., Lange, K., Quach, J., Molloy, C. S., Clifford, S. A., & Mulraney, M. (2020) · SLEEP · doi:10.1093/sleep/zsaa139 · Cited by 66 · see citing works
“90 across items and waves, see Supplementary Tables 1–4) [32].”
BackgroundInfluentialModeling the determinants of pre‐service teachers' perceived usefulness of e‐learning
Teo, T. P. (2011) · Campus-Wide Information Systems · doi:10.1108/10650741111117824 · Cited by 65 · see citing works
Do digital natives differ by computer self-efficacy and experience? An empirical study
Teo, T. P. (2015) · Interactive Learning Environments · doi:10.1080/10494820.2015.1041408 · Cited by 65 · see citing works
“Mardia ’ s coef fi cient obtained in this study is 150.532, which is less than the recommended value of 462 (computed by [ p [ p + 2]] where p = total number of observed indicators; 21[22]) by Raykov and Marcoulides (2008).”
MethodInfluentialTeng, M. F., & Wang, C. (2022) · Foreign Language Annals · doi:10.1111/flan.12638 · Cited by 91 · see citing works
The Heterogeneous Nature of Number–Space Interactions
van Dijck, J., Gevers, W., Lafosse, C., et al. (2012) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2011.00182 · Cited by 64 · see citing works
“Therefore, scrutinous evaluation of the normality assumption is needed (Raykov and Marcoulides, 2008).”
BackgroundMethodInfluentialExploring Colleagues’ Professional Influence on Mathematics Teachers’ Learning
Sun, M., Wilhelm, A. G., Larson, C. J., & Frank, K. A. (2014) · Teachers College Record The Voice of Scholarship in Education · doi:10.1177/016146811411600604 · Cited by 64 · see citing works
“Moreover, controlling for prior knowledge or practice reduces the potential of residuals’ non-normality and, therefore, increases the consistency of estimates (Raykov & Marcoulides, 2008).”
BackgroundWorking memory components and problem-solving accuracy: are there multiple pathways?
Swanson, H. L., & Fung, W. W. (2016) · Journal of Educational Psychology · doi:10.1037/edu0000116 · Cited by 63 · see citing works
Aldridge, J. M., McChesney, K., & Afari, E. (2019) · Learning Environments Research · doi:10.1007/s10984-019-09296-9 · Cited by 63 · see citing works
Internet ethics of adolescents: Understanding demographic differences
Lau, W. W. F., & Yuen, A. H. K. (2013) · Computers & Education · doi:10.1016/j.compedu.2013.12.006 · Cited by 62 · see citing works
Exploring relationships among TPACK constructs and ICT achievement among trainee teachers
Khine, M. S., Ali, N., & Afari, E. (2016) · Education and Information Technologies · doi:10.1007/s10639-016-9507-8 · Cited by 63 · see citing works
“The value of the Mardia’s coefficient obtained in this study, using AMOS 22, was 44.79, which is less than the recommended value (Raykov and Marcoulides 2008).”
BackgroundMethodInfluentialCalano, B. J. D., Cacal, M. J. B., Cal, C. B., Calletor, K. P., Guce, F. I. C. C., Bongar, M. V. V., & Macindo, J. R. B. (2019) · Journal of Clinical Nursing · doi:10.1111/jocn.14787 · Cited by 62 · see citing works
Kyndt, E., Govaerts, N., Verbeek, E., & Dochy, F. J. R. C. (2013) · The British Journal of Social Work · doi:10.1093/bjsw/bct056 · Cited by 64 · see citing works
Measuring Attitudes toward Computer and Internet Usage among Postgraduate Students in Malaysia
Abedalaziz, N., Jamaluddin, S., & Leng, C. H. (2013) · The Turkish Online Journal of Educational Technology · Cited by 61 · see citing works
Ursavaş, Ö. F., Yalçın, Y., İslamoğlu, H., Bakır-Yalçın, E., & Cukurova, M. (2025) · International Journal of Educational Technology in Higher Education · doi:10.1186/s41239-025-00535-z · Cited by 69 · see citing works
“Furthermore, multivariate normality was assessed using Mardia’s (1970) normalized multivariate kurtosis and the p × ( p + 2) formula provided by Raykov and Marcoulides (2008).”
Zeedyk, S. M., Cohen, S. R., Eisenhower, A., & Blacher, J. (2015) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-015-2575-6 · Cited by 60 · see citing works
“, direct oblimin) was employed, as the factors were assumed to correlate with one another; this is the method that has been recommended when utilizing maximum likelihood estimation (Raykov and Marcoulides 2008).”
BackgroundMethodInfluentialMothers of children with developmental disabilities: Stress in early and middle childhood
Azad, G. F., Blacher, J., & Marcoulides, G. A. (2013) · Research in Developmental Disabilities · doi:10.1016/j.ridd.2013.07.009 · Cited by 59 · see citing works
Self-citationEksail, F. A. A., & Afari, E. (2019) · Education and Information Technologies · doi:10.1007/s10639-019-10086-2 · Cited by 56 · see citing works
Rodriguez, G., Drastal, K. C., & Hartley, S. L. (2020) · Autism · doi:10.1177/1362361320947513 · Cited by 56 · see citing works
“The LSD post hoc test was used to examine significant differences between categories and is recommended in the presence of unequal sample sizes (Raykov & Marcoulides, 2008).”
MethodNgollo, M., Lebert, A., Dagdemir, A., Judes, G., Karslı-Çeppioğlu, S., Daures, M., Kémény, J., Penault-Llorca, F. M., Boiteux, J., Bignon, Y., et al. (2014) · BMC Cancer · doi:10.1186/1471-2407-14-994 · Cited by 55 · see citing works
“To a large extent, the interpretation of principal components is generally guided by the degree to which each variable is associated with a particular component [47].”
Breslau, N., Breslau, J. A., Miller, E. P., & Raykov, T. (2010) · Psychiatry Research · doi:10.1016/j.psychres.2010.07.027 · Cited by 53 · see citing works
“The LVM method offers important advantages over standard regression approaches.”
MethodInfluentialSelf-citationThe Integration of Work and Learning: Tackling the Complexity with Structural Equation Modelling
Kyndt, E., & Onghena, P. (2014) · Professional and practice-based learning · doi:10.1007/978-94-007-7012-6_14 · Cited by 44 · see citing works
Dietary patterns associated with overweight among Brazilian adolescents
Borges, C. A., Marchioni, D. M. L., Levy, R. B., & Slater, B. (2018) · Appetite · doi:10.1016/j.appet.2018.01.001 · Cited by 53 · see citing works
- 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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