Quality & Quantity

, 41:869 | Cite as

Investigating the Number of Non-linear and Multi-modal Relationships Between Observed Variables Measuring Growth-oriented Atmosphere

  • P. NokelainenEmail author
  • T. Silander
  • P. Ruohotie
  • H. Tirri


This study investigates the number of non-linear and multi-modal relationships between observed variables measuring the Growth-oriented Atmosphere. The sample (N = 726) represents employees of three vocational high schools in Finland. The first stage of analysis showed that only 22% of all dependencies between variables were purely linear. In the second stage two sub samples of the data were identified as linear and non-linear. Both bivariate correlations and confirmatory factor analysis (CFA) parameter estimates were found to be higher in the linear sub sample. Results showed that some of the highest bivariate correlations in both sub samples were explained via third variable in the non-linear Bayesian dependence modeling (BDM). Finally, the results of CFA and BDM led in different substantive interpretations in two out of four research questions concerning organizational growth.


categorical data survey data non-linear modeling structural equation modeling organizational atmosphere 


  1. Arbuckle J.L. (1999). Amos for Windows. Analysis of Moment Structures. SmallWaters, Chicago, ILGoogle Scholar
  2. Argyris C. (1992). On Organizational Learning. Blackwell Publishers, Cambridge, MAGoogle Scholar
  3. Bayes T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society 53: 370–418CrossRefGoogle Scholar
  4. Bentler P.M. (1995). EQS Structural Equations Program Manual. Multivariate Software Inc., Encino, CAGoogle Scholar
  5. Bernardo J., Smith A. (2000). Bayesian Theory. Wiley, New YorkGoogle Scholar
  6. Bollen K.A. (1989). Structural Equations with Latent Variables. Wiley, New YorkGoogle Scholar
  7. Browne M.W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology 37: 1–21Google Scholar
  8. Browne M.W., Cudeck R. (1993). Alternative ways of assessing model fit. In: Bollen K.A., Long S.(eds). Testing Structural Equation. Newbury Park, CA: Sage, pp. 136–162Google Scholar
  9. Cattell R.B. (1978). The Scientific Use of Factor Analysis in Behavioral and Life Sciences. Plenum Press, New York, NYGoogle Scholar
  10. Chickering D.M. (1996). Learning Bayesian networks is NP–complete. In: Fisher D., Lenz H.J. (eds) Learning from Data: Artificial and Statistics. Springer Verlag, Berlin, pp. 121–130Google Scholar
  11. Chickering, D. M., Geiger, D. & Heckerman, D. (1995). Learning Bayesian networks: Search methods and experimental results. Proceedings of Fifth Conference on Artificial Intelligence and Statistics, Ft. Lauderdale, FL, USA, pp. 112–128.Google Scholar
  12. Congdon P. (2001). Bayesian Statistical Modelling. Wiley, LondonGoogle Scholar
  13. Congdon P. (2003). Applied Bayesian Modelling. Wiley, LondonGoogle Scholar
  14. Cormen T.H., Leiserson C.E., Rivest R.L. (1996). Introduction to Algorithms, 16th edn. Cambridge, MA, MIT PressGoogle Scholar
  15. Cronbach L.J. (1970). Essentials of Psychological Testing, 3rd edn. Harper & Row, New York, NYGoogle Scholar
  16. DeVellis R.F. (2003). Scale Development, Theory and Applications, 2nd edn. Sage, Thousand Oaks, CAGoogle Scholar
  17. Dubin S. (1990). Maintaining competence through updating. In: Willis S., Dubin S. (eds) Maintaining Professional Competence. Jossey-Bass, San Francisco, pp. 9–43Google Scholar
  18. Edwards J.R., Rothbard N.P. (1999). Work and family stress and well-being: an examination of person–environment fit in the work and family domains. Organizational Behavior and Human Decision Processes 77(2): 85–129CrossRefGoogle Scholar
  19. Fishbein M., Stasson M. (1990). The role of desires, self–predictions, and perceived control in the prediction of training session attendance. Journal of Applied Social Psychology 20: 173–198CrossRefGoogle Scholar
  20. Gorusch R. (1983). Factor Analysis, 2nd edn. Lawrence Erlbaum Associates, Hillsdale, NJGoogle Scholar
  21. Grilli, L. & Rampichini, C. (2004). Multilevel factor models for ordinal variables. (for publication).Google Scholar
  22. Hair J.F., Anderson R.E., Tatham R.L., Black W.C. (1995). Multivariate Data Analysis, 4th edn. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  23. Hall D. (1990). Career development theory in organizations. In: Brown D., Brooks L. (eds). Career Choice and Development. San Francisco, Jossey–Bass, pp. 422–454Google Scholar
  24. Heckerman D., Geiger D., Chickering D.M. (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning 20: 197–243Google Scholar
  25. Hofmann R., Tresp V. (1996). Discovering structure in continuous variables using Bayesian networks. In: Touretzky D.S., Mozer M.C., Hasselmo M.E. (eds). Advances in Neural Information Processing Systems, vol. 8. Cambridge, MA: MITPress, pp. 500–506Google Scholar
  26. Hofmann R., Tresp V. (1998). Non–linear Markov networks for continuous variables. In: Jordan M.I., Kearns M.S., Solla S.A.(eds). Advances in Neural Information Processing Systems, Vol 10. Cambridge, MA: MITPress, pp. 521–527Google Scholar
  27. Hu L., Bentler P. (1999). Cut–off criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternatives. Structural Equation Modeling 6(1): 1–55CrossRefGoogle Scholar
  28. Johnson D.R., Creech J.C. (1983). Ordinal measures in multiple indicator models: a simulation study of categorization error. American Sociological Review 48: 398–407CrossRefGoogle Scholar
  29. Jöreskog, K. G. (2003). Structural Equation Modeling with Ordinal Variables using LISREL, Retrieved 13.2.2005 from: Scholar
  30. Jöreskog K.G., Sörbom D. (1998). LISREL 8 Program Reference Guide. Chicago, IL: Scientific Software InternationalGoogle Scholar
  31. Kaplan D. (2000). Structural Equation Modeling Foundations and Extensions. Thousand Oaks, SageGoogle Scholar
  32. Kaufman H. (1990). Management techniques for maintaining a competent professional work force. In: Willis S., Dubin S.(eds). Maintaining Professional Competence. San Francisco, Jossey–Bass, pp. 249–261Google Scholar
  33. Lawler E.E. (1994). From job–based to competence–based organizations. Journal of Organizational Behaviour 15: 3–15CrossRefGoogle Scholar
  34. Loehlin J.C. (2004). Latent Variable Models, 4th edn. Mahwah, NJ: Lawrence Erlbaum AssociatesGoogle Scholar
  35. MacCallum R.C., Widaman K.F., Zhang S., Hong S. (1999). Sample size in factor analysis. Psychological Methods 4: 84–99CrossRefGoogle Scholar
  36. Moore D.S., McCabe G.P. (1993). Introduction to the Practice of Statistics, 2nd edn. New York, FreemanGoogle Scholar
  37. Muthén B.O. (1983). Latent variable structural equation modeling with categorical data. Journal of Econometrics 22: 48–65CrossRefGoogle Scholar
  38. Muthén B.O. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika 49: 115–132CrossRefGoogle Scholar
  39. Muthén B.O. (1989). Latent variable modeling in heterogeneous populations. Psychometrika 54: 557–585CrossRefGoogle Scholar
  40. Muthén B.O. (1993). Goodness of fit with categorical and other non– normal variables. In: Bollen K.A., Long J.S.(eds). Testing Equation Models. Newbury Park, CA: Sage, pp. 205–243Google Scholar
  41. Muthén B.O., Kaplan D. (1985). A comparison of some methodologies for the factor analysis of non–normal Likert variables. British Journal of Mathematical and Statistical Psychology 38: 171–189Google Scholar
  42. Muthén L.K., Muthén B.O. (2001). Mplus User’s Guide, 2nd edn. Los Angeles, CA: Muthén & MuthénGoogle Scholar
  43. Myllymäki P., Silander T., Tirri H., Uronen P. (2002). B–course: a web–based tool for Bayesian and causal data analysis. International Journal on Artificial Intelligence Tools 11(3): 369–387CrossRefGoogle Scholar
  44. Nokelainen P., Ruohotie P. (2003). Modeling the prerequisites of empowerment. In: Beairsto B., Klein M., Ruohotie P.(eds). Professional Learning and Leadership. Hämeenlinna, FI: RCVE, pp. 147–176Google Scholar
  45. Nokelainen P., Ruohotie P., Tirri H. (2002). Visualization of Growth–oriented Atmosphere. Paper presented at the Annual Meeting of the Educational Research Association, New OrleansGoogle Scholar
  46. Olsson U.H., Foss T., Troye S.V., Howell R.D. (2000). The performance of ML, GLS, and WLS estimation in structural equation under conditions of misspecification and nonnormality. Structural Equation Modeling 7(4): 557–595CrossRefGoogle Scholar
  47. Pearl J. (1988). Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan KaufmannGoogle Scholar
  48. Ruohotie P. (1996). Professional growth and development. In: Leithwood K., Chapman S., Carson D., Hollinger P., Hart A.(eds). Handbook of Educational Leadership and Administration. Dordrecht, Kluwer Academic Publishers, pp. 419–445Google Scholar
  49. Ruohotie P., Nokelainen P. (2000). Beyond the Growth–oriented Atmosphere. In: Beairsto B., Ruohotie P.(eds). Empowering Teachers as Lifelong Learners. Hämeenlinna, FI: RCVE, pp. 147–167Google Scholar
  50. Silander T., Tirri H. (2000). Model Selection for Bayesian Networks. Paper presented at the Annual Meeting of American Educational Research Association. New Orleans, USAGoogle Scholar
  51. Tucker T.L., Lewis C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrica 38: 1–10CrossRefGoogle Scholar
  52. Yung Y.F., Bentler P.M. (1994). Bootstrap corrected ADF test statistics in covariance structure analysis. British Journal of Mathematical and Statistical Psychology 47: 63–84Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • P. Nokelainen
    • 1
    Email author
  • T. Silander
    • 2
  • P. Ruohotie
    • 1
  • H. Tirri
    • 3
  1. 1.Research Centre for Vocational EducationUniversity of TampereHämeenlinnaFinland
  2. 2.Helsinki Institute for Information TechnologyComplex Systems Computation GroupHUTFinland
  3. 3.Nokia Group, Nokia Research CenterNokia GroupFinland

Personalised recommendations