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Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning – Journal of Educational and Behavioral Statistics, 2012
The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…
Descriptors: Structural Equation Models, Goodness of Fit, Geometric Concepts, Algebra
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Mischo, Christoph; Maaß, Katja – Journal of Education and Training Studies, 2013
This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…
Descriptors: Mathematical Models, Teacher Attitudes, Beliefs, Intervention
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Kshirsagar, Anant M.; Radhakrishnan, R. – International Journal of Mathematical Education in Science and Technology, 2009
In a balanced design (i.e. a design in which all cells have the same number of observations), if the effects in the linear model are random and normally distributed, the distribution of the ratio of any sum of squares (s.s.) in the ANOVA to the expected value of its mean square (m.s.) has a [chi][superscript 2]-distribution. In this note, we…
Descriptors: Statistical Analysis, Geometric Concepts, Mathematical Models, Structural Equation Models
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Mooijaart, Ab; Satorra, Albert – Psychometrika, 2009
In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…
Descriptors: Structural Equation Models, Geometric Concepts, Goodness of Fit, Models
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Curran, Patrick J.; Bauer, Daniel J. – Psychological Methods, 2007
Multilevel models have come to play an increasingly important role in many areas of social science research. However, in contrast to other modeling strategies, there is currently no widely used approach for graphically diagramming multilevel models. Ideally, such diagrams would serve two functions: to provide a formal structure for deriving the…
Descriptors: Equations (Mathematics), Social Science Research, Social Sciences, Mathematical Models
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Sobel, Michael E. – Psychometrika, 1990
Total, direct, and indirect effects in linear structural equation models are examined. Formulas currently given for direct and total effects are reported, and causation is considered. It is concluded that in many instances the effects do not support the interpretations given in the literature. (SLD)
Descriptors: Effect Size, Equations (Mathematics), Mathematical Models, Statistical Analysis
Thompson, Bruce – 1998
This paper provides an introduction to basic issues concerning structural equation modeling (SEM), a research methodology increasingly being used in social science research. First, seven key issues that must be considered in any SEM analysis are explained. These include matrix of associations to analyze, model identification, parameter estimation…
Descriptors: Mathematical Models, Research Methodology, Social Science Research, Statistical Analysis
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Mueller, Ralph O. – Structural Equation Modeling, 1997
Basic philosophical and statistical issues in structural equation modeling (SEM) are reviewed, including model conceptualization, identification, and parameter estimation and data-model-fit assessment and model modification. These issues should be addressed before the researcher uses any of the new generation of SEM software. (SLD)
Descriptors: Computer Software, Estimation (Mathematics), Goodness of Fit, Identification
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Bechger, Timo M.; Maris, Gunter – Psicologica: International Journal of Methodology and Experimental Psychology, 2004
This paper is about the structural equation modelling of quantitative measures that are obtained from a multiple facet design. A facet is simply a set consisting of a finite number of elements. It is assumed that measures are obtained by combining each element of each facet. Methods and traits are two such facets, and a multitrait-multimethod…
Descriptors: Structural Equation Models, Multitrait Multimethod Techniques, Schematic Studies, Correlation