The Fixed-Links Model for Investigating the Effects of General and Specific Processes on Intelligence
Abstract
This article presents a model for investigating the effects of general and specific processes on intelligence as criterion variable. The model enables the representation of the processes as exogenous latent variables that predict the criterion, that is, the endogenous latent variable. The representation of these processes is achieved by the decomposition of the variances of the manifest variables. The decomposition presupposes the constraint of the loadings of the manifest variables on the latent variables. Smooth functions obtained on the basis of mean scores aid the attainment of constraints for the specific processes. Several alternative types of constraints for the general process are considered. The results of an empirical investigation demonstrate that constraints according to weighted uniformity are most appropriate. An example is provided.
References
Bollen, K. A. (1989). Structural equations with latent variables. New York: WileyCampbell, D. T. , Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological Bulletin, 56, 81– 105Carroll, J. B. (1993). Human cognitive abilities. New York: Cambridge University PressDuncan, T. E. , Duncan, S. C. (1995). Modeling the processes of development via latent variable growth curve methodology. Structural Equation Modeling, 2, 187– 213Duncan, T. E. , Duncan, S. C. (2004). An introduction to latent growth curve modeling. Behavior Therapy, 35, 333– 363Eid, M. (2000). A multitrait-multimethod model with minimal assumptions. Psychometrika, 65, 241– 261Jensen, A. R. (1987). Individual differences in the Hick paradigm. In P. A. Vernon (Ed.), Speed of information processing and intelligence (pp. 103-175). Norwood, NJ: AblexJensen, A. R. (1998). The g factor: The science of mental ability. Westport, CT: PraegerJöreskog, K. G. (1973). A general method for estimating the linear structural equation system. In A. S. Goldberg & O. D. Duncan (Eds.), Structural equation models in the social sciences. (pp. 85-112). New York: Seminar PressJöreskog, K. , Sörbom, D. (1996). LISREL 8: User's reference guide. Chicago: Scientific Software InternationalKeesling, W. (1972). Maximum likelihood approaches to causal flow analysis. Unpublished doctoral dissertation, University of ChicagoKenny, D. A. , Kashy, D. A. (1992). Analysis of the multitrait-multimethod matrix by confirmatory factor analysis. Psychological Bulletin, 112, 165– 172Marsh, H. W. (1989). Confirmatory factor analysis of multitrait-multimethod data: Many problems and a few solutions. Applied Psychological Measurement, 13, 335– 361McArdle, J. J. (1986). Latent variable growth within behavior genetic models. Behavior Genetics, 16, 163– 200McArdle, J. J. (1988). Growth curve analysis in contemporary psychological research. In J. R. Nesselroade & R. B. Cattell (eds.), Handbook of multivariate experimental psychology (2nd ed.), (pp. 561-614). New York: PlenumMcArdle, J. J. , Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110– 133Meredith, W. , Tisak, J. (1984, June). Tuckerizing curves. Paper presented at the annual meeting of the Psychometric Society, Santa Barbara, CAMeredith, W. , Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107– 122Mulaik, S. (1972). The foundations of factor analysis. New York: McGraw-HillNeubauer, A. C. (1997). The mental speed approach to the assessment of intelligence. Advances in Cognition and Educational Practice, 4, 149– 173Oberauer, K. , Wilhelm, O. , Schmiedek, F. (2005). Experimental strategies in multivariate research. In A. Beauducel, B. Biehl, M. Bosniak, W. Conrad, G. Schönberger, D. Wagener (Eds.), Multivariate research strategies. Festschrift in Honor of Werner W. Wittmann (pp. 119-149). Aachen: ShakerPinheiro, J. C. , Bates, D. M. (2000). Mixed-effects models in S and S-Plus. New York: SpringerRao, C. R. (1958). Some statistical methods for comparisons of growth curves. Biometrics, 14, 1– 17Scher, A. M. , Young, A. C. , Meredith, W. M. (1960). Factor analysis of the electrocardiograph. Circulation Research, 8, 519– 526Schmid, J. , Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53– 61Schulze, R. (2005). Modeling structures of intelligence. In O. Wilhelm & R. W. Engle (Eds.), Handbook of understanding und measuring intelligence (pp. 241-263). Thousand Oaks, CA: SageSchweizer, K. (2005). An overview of research into the cognitive basis of intelligence. Journal of Differential Psychology, 26, 43– 51Schweizer, K. (2006). The fixed-links model in combination with the polynomial function as a tool for investigating choice reaction time data. Structural Equation Modeling, 13, 403– 419Schweizer, K. , Klieme, E. (2005). Kompetenzstufen der Lehrerkooperation: Ein empirisches Beispiel für das Latent-Growth-Curve-Modell [Competency steps in teacher cooperation: An empirical example of the latent growth curve model]. Psychologie in Erziehung und Bildung, 52, 66– 79Schweizer, K. , Moosbrugger, H. , Schermelleh-Engel, K. (2003). Models for investigating hierarchical structures in differential psychology. Methods of Psychological Research Online, 8, 159– 180Snijders, T. , Bosker, R. (1999). Multilevel analysis. London: SageSpearman, C. (1904). “General intelligence,” objectively determined and measured. American Journal of Psychology, 9, 209– 293Spearman, C. (1927). The ability of man. London: MacmillanStankov, L. (2000). Complexity, metacognition and fluid intelligence. Intelligence, 28, 121– 143Steyer, R. (1989). Models of classical psychometric test theory as stochastic measurement models: Representation, uniqueness, meaningfulness, identifiability, and testability. Methodika, 3, 25– 60Steyer, R. , Ferring, D. , Schmitt, M. J. (1992). States and traits in psychological assessment. European Journal of Psychological Assessment, 8, 79– 98Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19– 23Wagenmakers, E.-J. , Grasman, R. P. P. P. , Molenaar, P. C. M. (2005). On the relation between the mean and the variance of a diffusion model response time distribution. Journal of Mathematical Psychology, 49, 195– 204Weisberg, S. (1985). Applied linear regression (2nd ed.). New York: WileyWidaman, K. F. (1985). Hierarchially nested covariance structure models for multitrait-multimethod data. Applied Psychological Measurement, 9, 1– 26Wiley, D. E. (1973). The identification problem for structural equation models with unmeasured variables. In A. S. Goldberg & O. D. Duncan (Eds.), Structural equation models in the social sciences (pp. 69-83). New York: Seminar Press
