225
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Factor Analysis with Ordered Categorical Indicators and Measurement of Self-Efficacy in Physical Activity Contexts: A Substantive-Methodological Synergy

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon

References

  • Ainsworth, B. E., Bassett, D. R., Strath, S. J., Swartz, A. M., O’brien, W. L., Thompson, R. W., Jones, D. A., Macera, C. D., & Kimsey, D. C. (2000). Comparison of three methods for measuring the time spent in physical activity. Medicine & Science in Sports & Exercise, 32(Supplement), S457–464. https://doi.org/10.1097/00005768-200009001-00004
  • American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for educational and psychological testing. American Educational Research Association.
  • Asparouhov, T., & Muthén, B. (2010). Simple second order chi-square correction. Mplus Technical Appendix. https://www.statmodel.com/download/WLSMVnewchi21.pdf
  • Babakus, E., Ferguson, C. E., Jr., & Jöreskog, K. G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 24(2), 222–228. https://doi.org/10.1177/002224378702400209
  • Bandalos, D. L. (2014). Relative performance of categorical diagonally weighted least squares and robust maximum likelihood estimation. Structural Equation Modeling, 21(1), 102–116. https://doi.org/10.1080/10705511.2014.859510
  • Bandura, A. (1977). Self-efficacy: Towards a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295x.84.2.191
  • Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Prentice-Hall.
  • Bandura, A. (1997). Self-efficacy: The exercise of control. Freeman.
  • Bandura, A. (2001). Social cognitive theory: An agentic perspective. Annual Review of Psychology, 52(1), 1–26. https://doi.org/10.1146/annurev.psych.52.1.1
  • Bandura, A. (2006). Guide for constructing self-efficacy scales. In F. Pajares & T. C. Urdan (Eds.), Self-efficacy beliefs of adolescents (pp. 307–337). Information Age Publishing.
  • Bateman, A. G., Myers, N. D., Chen, S., & Lee, S. (2022). Measurement of physical activity self-efficacy in physical activity interventions for adults: A systematic review.Measurement in. Physical Education and Exercise Science, 26(2), 141–154. https://doi.org/10.1080/1091367X.2021.1962324
  • Bauman, A. E., Reis, R. S., Sallis, J. F., Wells, J. C., Loos, R. J. F., & Martin, B. W. (2012). Correlates of physical activity: Why are some people physically active and others not? The Lancet, 380, 258–271. https://doi.org/10.1016/S0140-6736(12)60735-1
  • Baumgartner, T. A. (1997). Editor’s note. Measurement in Physical Education and Exercise Science, 1(2), 103–104. https://doi.org/10.1207/s15327841mpee0102_1
  • Baumgartner, T. A., & Safrit. (2003). A genealogy of measurement specialists in physical education and exercise science. Measurement in Physical Education and Exercise Science, 7(2), 121–127. https://doi.org/10.1207/S15327841MPEE0702_5
  • Beauchamp, M. R., Crawford, K. L., & Jackson, B. (2019). Social cognitive theory and physical activity: Mechanisms of behavior change, critique, and legacy. Psychology of Sport & Exercise, 42, 110–117. https://doi.org/10.1016/j.psychsport.2018.11.009
  • Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13(2), 186–203. https://doi.org/10.1207/s15328007sem1302_2
  • Bollen, K. A. (1989). Structural equation modeling with latent variables. Wiley.
  • Bollen, K. A., & Barb, K. H. (1981). Pearson’s r and coarsely categorized measures. American Sociological Review, 46(2), 232–239. https://doi.org/10.2307/2094981
  • Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. The British Journal of Mathematical and Statistical Psychology, 37(1), 62–83. https://doi.org/10.1111/j.2044-8317.1984.tb00789.x
  • Craig, C. L., Marshall, A. L., Sjöström, M., Bauman, A. E., Booth, M. L., Ainsworth, B. E., Oja, P. (2003). International physical activity questionnaire: 12-country reliability and validity. Medicine and Science in Sports and Exercise, 35(8), 1381–1395. https://doi.org/10.1249/01.MSS.0000078924.61453.FB
  • DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling, 9(3), 327–346. https://doi.org/10.1207/s15328007sem0903_2
  • DiStefano, C., & Morgan, G. B. (2014). A comparison of diagonal weighted least squares robust estimation techniques for ordinal data. Structural Equation Modeling, 21(3), 425–438. https://doi.org/10.1080/10705511.2014.915373
  • Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 response categories: A comparison of categorical variable estimators using simulated data. The British Journal of Mathematical and Statistical Psychology, 47(2), 309–326. https://doi.org/10.1111/j.2044-8317.1994.tb01039.x
  • Feltz, D. L., & Chase, M. A. (1988). The measurement of self-efficacy and confidence in sport. In J. Duda (Ed.), Advancement in sport and exercise psychology measurement (pp. 63–78). Fitness Information Technology.
  • Feltz, D. L., Short, S. E., & Sullivan, P. J. (2008). Self-efficacy in sport: Research and strategies for working with athletes, teams, and coaches. Human Kinetics.
  • Finney, S. J., & DiStefano, C. (2013). Nonnormal and categorical data in structural equation modelingStructural equation modeling: A second course Series. 2nd ed., R. C. Serlin & G. R. Hancock & R. O. Mueller Eds.Eds., Information Age.
  • Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491. https://doi.org/10.1037/1082-989x.9.4.466
  • Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling, 16(4), 625–641. https://doi.org/10.1080/10705510903203573
  • Gentle, J. E. (2003). Random number generation and Monte Carlo methods (2nd ed.). Springer.
  • Gill, D. L. (1997). Measurement, statistics, and research design issues in sport and exercise psychology. Measurement in Physical Education and Exercise Science, 1(1), 39–53. https://doi.org/10.1207/s15327841mpee0101_3
  • Graham, J. M., Guthrie, A. C., & Thompson, B. (2003). Consequences of not interpreting structure coefficients in published CFA research: A reminder. Structural Equation Modeling, 10(1), 142–153. https://doi.org/10.1207/S15328007SEM1001_7
  • Green, S. B., Akey, T. M., Fleming, K. K., Hershberger, S. L., & Marquis, J. G. (1997). Effect of the number of scale points on chi-square fit indices in confirmatory factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 4(2), 108–120. https://doi.org/10.1080/10705519709540064
  • Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In R. Cudeck, S. H. C. du Toit, & D. Sörbom (Eds.), Structural equation modeling: Past and present. A festschrift in honor of Karl G. Jöreskog (pp. 195–261). Scientific Software International, Inc.
  • Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
  • Hutchinson, S. R., & Olmos, A. (1998). Behavior of descriptive fit indexes in confirmatory factor analysis using ordered categorical data. Structural Equation Modeling: A Multidisciplinary Journal, 5(4), 344–364. https://doi.org/10.1080/10705519809540111
  • Jackson, B., Beauchamp, M. R., & Dimmock, J. A. (2020). Efficacy beliefs in physical activity settings: Contemporary debate and unanswered questions. In G. Tenenbaum & R. C. Eklund (Eds.), Handbook of Sport Psychology (4th ed., pp. 57–80). Wiley.
  • Jensen, B., Martin, K., & Arthur, D. (2000). Mentoring students in the process of writing a research journal manuscript. Measurement in Physical Education and Exercise Science, 4(2), 117–122. https://doi.org/10.1207/S15327841Mpee0402_6
  • Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34(2), 183–202. https://doi.org/10.1007/bf02289343
  • Jöreskog, K. G., & Sörbom, D. (1996). PRELIS 2. User’s reference guide. Scientific Software International.
  • Jöreskog, K. G., Sörbom, D., du Toit, S., & du Toit, M. (1999). LISREL 8: New statistical features. Scientific Software International.
  • Kamata, A., & Bauer, D. J. (2008). A note on the relation between factor analytic and item response theory models. Structural Equation Modeling: A Multidisciplinary Journal, 15(1), 136–153. https://doi.org/10.1080/10705510701758406
  • Looney, M. A. (1997). ‘Home’ improvement: The task for measurement specialists. Measurement in Physical Education and Exercise Science, 1(2), 105–116. https://doi.org/10.1207/s15327841mpee0102_2
  • MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51(1), 201–206. https://doi.org/10.1146/annurev.psych.51.1.201
  • McAuley, E. (1992). The role of efficacy cognitions in the prediction of exercise behavior in middle-aged adults. Journal of Behavioral Medicine, 15(1), 65–88. https://doi.org/10.1007/bf00848378
  • McAuley, E. (1993). Self-efficacy and the maintenance of exercise participation in older adults. Journal of Behavioral Medicine, 16(1), 103–113. https://doi.org/10.1007/BF00844757
  • McAuley, E., & Mihalko, S. L. (1988). Measuring exercise related self-efficacy. In J. Duda (Ed.), Advancement in sport and exercise psychology measurement (pp. 371–390). Fitness Information Technology.
  • Millsap, R. E., & Yun-Tien, J. (2004). Assessing factorial invariance in ordered-categorical measures. Multivariate Behavioral Research, 39(3), 479–515. https://doi.org/10.1207/S15327906MBR3903_4
  • Morin, A. J. S., Myers, N. D., & Lee, S. (2020). Modern factor analytic techniques: Bifactor models, exploratory structural equation modeling (ESEM) and bifactor-ESEM. In G. Tenenbaum & R. C. Eklund (Eds.), The Handbook of Sport Psychology (4th ed., pp. 1044–1073). Wiley.
  • Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43(4), 551–560. https://doi.org/10.1007/bf02293813
  • Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49(1), 115–132. https://doi.org/10.1007/bf02294210
  • Muthén, B. O. (1993). Goodness of fit with categorical and other nonnormal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–243). Sage.
  • Muthén, B., du Toit, S. H. C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Retrieved from https://www.statmodel.com/download/Article_075.pdf
  • Muthén, B., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. The British Journal of Mathematical and Statistical Psychology, 38(2), 171–189. https://doi.org/10.1111/j.2044-8317.1985.tb00832.x
  • Muthén, L. K., & Muthén, B. O. (1998-2017). Mplus User’s Guide (8th ed.). Muthén & Muthén.
  • Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9(4), 599–620. https://doi.org/10.1207/s15328007sem0904_8
  • Myers, N. D., Ahn, S., & Jin, Y. (2011). Sample size and power estimates for a confirmatory factor analytic model in exercise and sport: A Monte Carlo approach. Research Quarterly for Exercise and Sport, 82(3), 412–423. https://doi.org/10.5641/027013611X13275191443621
  • Myers, N. D., Bateman, A., Lee, S., & Silverman, S. (2020). Measurement in physical education and exercise science (MPEES): A brief report on 2019. Measurement in Physical Education and Exercise Science, 24(2), 93–102. https://doi.org/10.1080/1091367X.2020.1739690
  • Myers, N. D., Bateman, A. G., McMahon, A., Prilleltensky, I., Lee, S., Prilleltensky, O., Pfeiffer, K. A., & Brincks, A. M. (2021). Measurement of physical activity self-efficacy in adults with obesity: A latent variable approach to explore dimensionality, temporal invariance, and external validity. Journal of Sport & Exercise Psychology, 43(6), 497–513. https://doi.org/10.1123/jsep.2021-0040
  • Myers, N. D., & Feltz, D. L. (2007). From self-efficacy to collective efficacy in sport: Transitional methodological issues. In G. Tenenbaum & R. C. Eklund, Eds., The Handbook of Sport Psychology (3rd, pp. 799–819). Wiley. https://doi.org/10.1002/9781118270011.ch36
  • Myers, N. D., Feltz, D. L., & Wolfe, E. W. (2008). A confirmatory study of rating scale category effectiveness for the coaching efficacy scale. Research Quarterly for Exercise and Sport, 79(3), 300–311. https://doi.org/10.5641/193250308X13086832905752
  • Myers, N. D., McMahon, A., Prilleltensky, I., Lee, S., Dietz, S., Prilleltensky, O., Pfeiffer, K. A., Bateman, A. G., & Brincks, A. M. (2020). Effectiveness of the fun for wellness online behavioral intervention to promote physical activity in adults with obesity (or overweight): A randomized controlled trial. Journal of Medical Internet Research Formative Research, 4(2), e15919. https://doi.org/10.2196/15919
  • Myers, N. D., Ntoumanis, N., Gunnell, K. E., Gucciardi, D. F., & Lee, S. (2018). A review of some emergent quantitative analyses in sport and exercise psychology. International Review of Sport and Exercise Psychology, 11(1), 70–100. https://doi.org/10.1080/1750984X.2017.1317356
  • Myers, N. D., Paiement, C. A., & Feltz, D. L. (2007). Regressing team performance on collective efficacy: Considerations of temporal proximity and concordance. Measurement in Physical Education and Exercise Science, 11, 1–24. https://doi.org/10.1080/10913670709337009
  • Myers, N. D., Prilleltensky, I., Hill, C. R., & Feltz, D. L. (2017). Well-being self-efficacy and complier average causal effect modeling: A substantive-methodological synergy. Psychology of Sport & Exercise, 30, 135–144. https://doi.org/10.1016/j.psychsport.2017.02.010
  • Myers, N. D., Prilleltensky, I., Lee, S., Dietz, S., Prilleltensky, O., McMahon, A., Pfeiffer, K. A., Ellithorpe, M. E., & Brincks, A. M. (2019). Effectiveness of the fun for wellness online behavioral intervention to promote well-being and physical activity: Protocol for a randomized controlled trial. BMC Public Health, 19, 737. https://doi.org/10.1186/s12889-019-7089-2
  • Myers, N. D., Prilleltensky, I., Prilleltensky, O., McMahon, A., Dietz, S., & Rubenstein, C. L. (2017). Efficacy of the fun for wellness online intervention to promote multidimensional well-being: A randomized controlled trial. Prevention Science, 18(8), 984–994. https://doi.org/10.1007/s11121-017-0779-z
  • Myers, N. D., Wolfe, E. W., & Feltz, D. L. (2005). An evaluation of the psychometric properties of the coaching efficacy scale for coaches from United States of America. Measurement in Physical Education and Exercise Science, 9(3), 135–160. https://doi.org/10.1207/s15327841mpee0903_1
  • Ntoumanis, N., & Myers, N. D. (Eds.). (2016). An introduction to intermediate and advanced statistical analyses for sport and exercise scientists. John Wiley & Sons.
  • Olsson, U. H. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44(4), 443–460. https://doi.org/10.1007/bf02296207
  • Olsson, U. H., Foss, T., Troye, S. V., & Howell, R. D. (2000). The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality. Structural Equation Modeling, 7(4), 557–595. https://doi.org/10.1207/s15328007sem0704_3
  • Olsson, U. H., Troye, S. V., & Howell, R. D. (1999). Theoretic fit and empirical fit: The performance of maximum likelihood versus generalized least squares estimation in structural equation models. Multivariate Behavioral Research, 34(1), 31–58. https://doi.org/10.1207/s15327906mbr3401_2
  • Pajares, F., Hartley, J., & Valiante, G. (2001). Response format in writing self-efficacy assessment: Greater discrimination increases prediction. Measurement and Evaluation in Counseling and Development, 33(4), 214–221. https://doi.org/10.1080/07481756.2001.12069012
  • Potthast, M. J. (1993). Confirmatory factor analysis of ordered categorical variables with large models. The British Journal of Mathematical and Statistical Psychology, 46(2), 273–286. https://doi.org/10.1111/j.2044-8317.1993.tb01016.x
  • Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354. https://doi.org/10.1037/a0029315
  • Rhodes, R. E., & Courneya, K. S. (2003). Self-efficacy, controllability and intention in the theory of planned behavior: Measurement redundancy or causal independence? Psychology & Health, 18(1), 79–91. https://doi.org/10.1080/0887044031000080665
  • Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02
  • Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clog (Eds.), Latent variable analysis: Applications for developmental research (pp. 399–419). Sage.
  • Savalei, V. (2021). Improving fit indices in structural equation modeling with categorical data. Multivariate Behavioral Research, 56(3), 390–407. https://doi.org/10.1080/00273171.2020.1717922
  • Scarpa, M. P., Prilleltensky, I., McMahon, A., Myers, N. D., Prilleltensky, O., Lee, S., Pfeiffer, K. A., Bateman, A. G., & Brincks, A. M. (2021). Is fun for wellness engaging? Evaluation of user experience of an online intervention to promote well-being and physical activity. Frontiers in Computer Science, 3, Article 690389. https://doi.org/10.3389/fcomp.2021.690389
  • Steiger, J. H. (2001). Driving fast in reverse: The relationship between software development, theory, and education in structural equation modeling. Journal of the American Statistical Association, 96(453), 331–338. https://doi.org/10.1198/016214501750332893
  • Takane, Y., & De Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52(3), 393–408. https://doi.org/10.1007/bf02294363
  • Tran, L., Tran, P., & Tran, L. (2020). A cross-sectional examination of sociodemographic factors associated with meeting physical activity recommendations in overweight and obese US adults. Obesity Research & Clinical Practice, 14(1), 91–98. https://doi.org/10.1016/j.orcp.2020.01.002
  • Tudor-Locke, C., Brashear, M. M., Johnson, W. D., & Katzmarzyk, P. T. (2010). Accelerometer profiles of physical activity and inactivity in normal weight, overweight, and obese U.S. men and women. The International Journal of Behavioral Nutrition and Physical Activity, 7, 60. https://doi.org/10.1186/1479-5868-7-60
  • United States Department of Health and Human Services. (2013). Managing overweight and obesity in adults: Systematic evidence review from the obesity expert panel. https://www.nhlbi.nih.gov/sites/default/files/media/docs/obesity-evidence-review.pdf
  • United States Department of Health and Human Services: 2018 Physical activity guidelines advisory committee. (2018). 2018 Physical activity guidelines advisory committee scientific report. https://health.gov/paguidelines/second-edition/report/
  • World Health Organization. (2018). Obesity and overweight fact sheet. Retrieved from http://www.who.int/mediacentre/factsheets/fs311/en/
  • Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17(3), 392–423. https://doi.org/10.1080/10705511.2010.489003
  • Yu, C., & Muthén, B. O. (2002, April). Evaluation of model fit indices for latent variable models with categorical and continuous outcomes [ Paper presentation]. American Educational Research Association 70th Annual Meeting, New Orleans, LA, United States.
  • Zhu, W., & Kang, S. J. (1998). Cross-cultural stability of the optimal categorization of a self-efficacy scale: A Rasch analysis. Measurement in Physical Education and Exercise Science, 2(4), 225–241. https://doi.org/10.1207/s15327841mpee0204_3

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.