SEPATH

  • Introductory Example - Confirmatory Factor Analysis
  • Example 1: Stability of Alienation
    This example, from a paper on stability of alienation by Wheaton, Múthen, Alwin, and Summers (1977), is one of the classic examples of a full structural equation model discussed in many textbooks and program manuals.  
  • Example 2: A Confirmatory Factor Analysis
    Lawley and Maxwell (1971, chapter 7) present techniques for confirmatory factor analysis. These authors are careful to point out that estimation of standard errors must be adjusted when a correlation matrix is analyzed instead of a covariance matrix. They give formulae for computing standard errors when a covariance matrix is analyzed, and provide an alternative method for computing standard errors when the sample correlation matrix is analyzed. The formulae are illustrated with a numerical example, the results of which are presented in their Tables 7.9  (page 99) and 7.10 (page 102).  
  • Example 3: Confirmatory Factor Analysis with Identifying Constraints
    Everitt (1984, pages 45-52) discusses in considerable detail a confirmatory factor analysis of a data set in Child (1970). This factor model is similar in some ways to the Lawley-Maxwell example. However, in this case one factor loads on only two manifest variables. This pattern, unfortunately, leads to a model that is not identified, unless some identifying constraints are applied. In this model, two factor loadings are constrained to be equal to each other, and two factor covariances are constrained to be zero. Data for this example are in the Child.sta data file.
  • Example 4: Effect of Peer Influence on Ambition
    Duncan, Haller, and Portes (1968) analyzed the effect of peer influences on ambition. The correlation matrix from their study, based on 329 subjects, is in the Dhp.sta data file. A portion of that file is shown below.
  • Example 5: Standardized Solutions for the Effect of Peer Influence on Ambition
    In a standardized solution, the latent variables all have unit variance. Setting the variances of exogenous latent variables to unity is trivial, because (a) these variances can be specified directly as part of a model, and (b) they are essentially arbitrary. Endogenous latent variable variances are a different matter. In some structural modeling programs, there is no convenient way to constrain the endogenous latent variables. For such programs to produce a standardized solution, a two stage procedure is employed. First, model parameters are estimated with the variances of the endogenous variables identified (at some unspecified value). After iteration is complete, the standardized coefficients are computed, using well known results from the algebra of multiple linear regression to transform the variances of endogenous latent variables to unity.  
  • Example 6: Factor Analysis with an Intercept Variable
    This example, discussed in the textbook by Bollen (1989, pages 308-311), shows, in a very simple context, the general technique for estimating factor means.
  • Example 7: Comparing Factor Structure in Two Groups
    This example, discussed in the textbook by Bollen (1989, pages 355-365), shows how to compare two groups for equivalence of factor structure. It provides a basic introduction to the techniques involved in fitting and comparing factor models in two or more populations. The textbook contains an extensive discussion of the example.
  • Example 8: Testing for Circumplex Structure
    The data matrix, from Guttman (1954), is in the Guttman.sta data file.
  • Example 9: Testing for Stability of a Correlation Matrix over Time
    Suppose you measure a set of variables twice, and want to test the hypothesis that the correlation coefficient has not changed from time 1 to time 2. For example, suppose 120 individuals are measured twice on verbal, quantitative, and analytical ability. In this case, the covariance matrix would be 6x6.
  • Example 10: A Multiple Regression Model for Home Environment and Math Achievement
  • Example 11: Structural Models for Home Environment and Mathematics Achievement
  • Example 12: Test Theory Models for Sets of Congeneric Tests
    A variety of interesting test theory models can be tested and estimated using structural equations modeling. These models are all special cases of the common factor model, and are discussed in Jöreskog (1974) on pages 49-56.
  • Example 13: Comparing Dependent Variances
  • Example 14: A Multi-Trait, Multi-Method Model
    When personality traits or characteristics are measured, variation among people can occur for several reasons. Two obvious contributing factors are variation in the traits themselves, and variations in the way people react to a particular method.
  • Example 15: A Longitudinal Factor Model
    Corballis and Traub (1970) presented a longitudinal factor analysis model, which stipulates that factorial structure underlying a set of tests remains constant over two or more administrations of the tests. An example of such a model is given by Everitt (1984, pages 52-55). The data were from a study by Meyer and Bendig (1961), who administered the 5 Thurstone Primary Mental Abilities tests to 49 boys and 61 girls in grades 8 and 11. The tests are Verbal Meaning (V), Space (S), Reasoning (R), Numerical (N), and Word Fluency (W). The correlation matrix for these data is in the Meyer.sta data file.
  • Example 16: A Structural Model for 10 Personality and Drug Use Variables
    Huba and Harlow (1987) present a structural model relating personality characteristics to alcohol and marijuana consumption in adolescents. The correlation matrix (to the two-digit level of precision given in their printed article) for their data, based on 257 observations, is given in the Hh.sta data file.
  • Example 17: A Test for Compound Symmetry
    A test for compound symmetry (i.e., equal variances and correlations for all pairs of variables) of the covariance matrix is sometimes performed in the context of repeated measures analysis of variance (see, e.g., Winer, 1971, pages 596-598). This hypothesis states that the covariance matrix has equal diagonal elements, and equal off-diagonal elements. The Winer.sta data file contains the pooled covariance matrix analyzed by Winer.
  • Example 18: Testing the Equality of Correlation Matrices from Different Populations