MCUAAAR Workshop Structural Equation Modeling with AMOS Part I: Basic Modeling and Measurement Applications Wayne State University College of Nursing Room 117 and Advanced Computing Lab Science and Engineering Library November 30, 2001 9:00 AM to 1:00 PM Advanced Registration Required: Respond to Tom Templin by e-mail at t.templin@wayne.edu Agenda: 9:00-9:45 Cohn Building 5557 Cass, Room 117 -Coffee and bagels etc. -Introduction to SEM 10:00-1:00 Advanced Computing Lab, Science and Engineering Library, Room 73 -Hands-on Workshop Presenter: Thomas Templin PhD., is an Associate Professor of Research in the Center for Health Research, College of Nursing, Wayne State University. He is the RCMAR measurement core co-leader and has extensive experience in measurement applications of structural equation models.
Example 1. Multiple regression with default output specifications and text macros (Hamilton Data). Graphic output: Hamilton Data Chi Square =.000 df = 0 p = \p CFI = 1.000 RMSEA = \rmsea Income 2.56 2.16.13 Education.03 136.02 SAT 1 382.74 d1 Select text output: Your model contains the following variables SAT observed endogenous Income observed exogenous Education observed exogenous d1 unobserved exogenous Number of variables in your model: 4 Number of observed variables: 3 Number of unobserved variables: 1 Number of exogenous variables: 3 Number of endogenous variables: 1 Summary of Parameters Weights Covariances Variances Means Intercepts Total ------- ----------- --------- ----- ---------- ----- Fixed: 1 0 0 0 0 1 Labeled: 0 0 0 0 0 0 Unlabeled: 2 1 3 0 0 6 ------- ----------- --------- ----- ---------- ----- Total: 3 1 3 0 0 7
NOTE: The model is recursive. Sample size: 21 Model: Default model Computation of degrees of freedom Number of distinct sample moments: 6 Number of distinct parameters to be estimated: 6 ------------------------- Degrees of freedom: 0 0e 1 0.0e+000-7.6766e-002 1.00e+004 1.95374841431e+001 0 1.00e+004 1e 0 7.3e+000 0.0000e+000 7.09e-001 2.90240847735e+000 18 9.00e-001 2e 0 5.4e+000 0.0000e+000 2.43e-001 5.05431611526e-001 3 0.00e+000 3e 0 1.1e+001 0.0000e+000 1.65e-001 1.91946452118e-002 1 1.06e+000 4e 0 9.2e+000 0.0000e+000 4.89e-002 1.01991897459e-004 1 1.05e+000 5e 0 9.7e+000 0.0000e+000 4.06e-003 4.03249700298e-009 1 1.00e+000 6e 0 1.2e+001 0.0000e+000 2.58e-005 7.10542735760e-015 1 1.00e+000 Minimum was achieved Chi-square = 0.000 Degrees of freedom = 0 Probability level cannot be computed Maximum Likelihood Estimates ---------------------------- Regression Weights: Estimate S.E. C.R. Label ------------------- -------- ------- ------- ------- SAT <------------- Income 2.156 3.125 0.690 SAT <---------- Education 136.022 30.555 4.452 Covariances: Estimate S.E. C.R. Label ------------ -------- ------- ------- ------- Income <------> Education 0.127 0.065 1.952 Variances: Estimate S.E. C.R. Label ---------- -------- ------- ------- ------- Income 2.562 0.810 3.162 Education 0.027 0.008 3.162 d1 382.736 121.032 3.162
Example 2. Multiple regression with additional output specifications and text macros (Hamilton Data). Graphic Output:
Hamilton Data Chi Square =.000 df = 0 p = \p CFI = 1.000 RMSEA = \rmsea Income.11.60.49.72 SAT Education d1 Text output: Maximum Likelihood Estimates ---------------------------- Regression Weights: Estimate S.E. C.R. Label ------------------- -------- ------- ------- ------- SAT <------------- Income 2.156 3.125 0.690 SAT <---------- Education 136.022 30.555 4.452 Standardized Regression Weights: Estimate -------------------------------- -------- SAT <------------- Income 0.111 SAT <---------- Education 0.717 Covariances: Estimate S.E. C.R. Label ------------ -------- ------- ------- ------- Income <------> Education 0.127 0.065 1.952 Correlations: Estimate ------------- -------- Income <------> Education 0.485
Variances: Estimate S.E. C.R. Label ---------- -------- ------- ------- ------- Income 2.562 0.810 3.162 Education 0.027 0.008 3.162 d1 382.736 121.032 3.162 Squared Multiple Correlations: Estimate ------------------------------ -------- SAT 0.603 Implied Covariances Educatio Income SAT -------- -------- -------- Education 0.027 Income 0.127 2.562 SAT 3.920 22.809 965.075 Implied Correlations Educatio Income SAT -------- -------- -------- Education 1.000 Income 0.485 1.000 SAT 0.771 0.459 1.000 Use tracing rules to calculate implied correlation between education and SAT..771 = path coefficient between educ. and SAT + ( path coefficient between income and SAT times the path coefficient between income and education)..72 +.49*.11 =.771 Example 3. Effect of omitted path on model fit, degrees of freedom, implied correlation matrix, and fit indices (Hamilton Data). Graphic output:
Hamilton Data Chi Square = 5.364 df = 1 p =.021 CFI =.791 RMSEA =.467 Income.12.57.75 SAT Education d1 Text Output: Implied Correlations Educatio Income SAT -------- -------- -------- Education 1.000 Income 0.000 1.000 SAT 0.746 0.116 1.000 Modification Indices -------------------- Covariances: M.I. Par Change --------- ---------- Income <------> Education 4.705 0.127 Variances: M.I. Par Change --------- ---------- Regression Weights: M.I. Par Change --------- ----------
Example 4. Complete mediation path model (Hamilton Data). Hamilton Data Chi Square =.470 df = 1 p =.493 CFI = 1.000 RMSEA =.000 d2.24.59 Income.49 Education.77 SAT d1 Text Output: Implied Correlations Income Educatio SAT -------- -------- -------- Income 1.000 Education 0.485 1.000 SAT 0.374 0.771 1.000 Sample Correlations Income Educatio SAT -------- -------- -------- Income 1.000 Education 0.485 1.000 SAT 0.459 0.771 1.000
Example 5. Common cause model to illustrate equivalent models (Hamilton Data). Hamilton Data Chi Square =.470 df = 1 p =.493 CFI = 1.000 RMSEA =.000.24.59 Income.49.77 SAT d2 Education d1 Implied Correlations Educatio Income SAT -------- -------- -------- Education 1.000 Income 0.485 1.000 SAT 0.771 0.374 1.000
Exercise 1. (a) Fill in the missing specifications for the following multiple regression model (covariances, parameter constraints, and error terms). value knowledge performance satisfaction (b) Use the Warren5v data in the Excel 5 spreadsheet Userguide.xls in c:\program files\amos 4\examples to estimate this model. (c) Use the following text and macros for the title: Warren5v Data Chi Square = \cmin df = \df p = \p CFI = \cfi RMSEA = \rmsea
(d) Print out the graphic out put for both standardized and raw coefficients. (e) Annotate the graphic output (path coefficients, estimated variance, multiple R-squared, covariances, correlations).
Example 6. Confirmatory factor analysis, Holzinger & Swinford (1939) Grant-White Data (file Grant.xls in Userguide.xls). Exercise 2. (a) Fill in the missing specifications for the following confirmatory factor analysis model (covariances, parameter constraints, and error terms). VISPERC2 spatial CUBES LOZENGES PARAGRAPH Verbal SENTENCE WORDMEAN (b) Use the grnt_fem data in the Excel 5 spreadsheet Userguide.xls in c:\program files\amos 4\examples to estimate this model. This is girls data from the Grant-White school. (c) Use same text macros as before. (d) Print out and interpret the standardized solution for the graphic output.
Example 7. Latent variable SEM with only direct effects, Warren data as modified by Rock et al. (1977) (file Warren9v.xls in Userguide.xls). Exercise 3. Fill in the missing specifications for the following direct effects latent variable SEM (parameter constraints, error terms, etc.). 1knowledge 2knowledge 1value 2value 1performance 2performance 1satisfaction 2satisfaction
Example 8. Latent variable SEM with direct and indirect effects, Warren data as modified by Rock et al. (1977) (file Warren9v.xls in Userguide.xls). Exercise 4. Fill in the missing specifications for the following latent variable SEM (parameter constraints, error terms, etc). 1knowledge 2knowledge 1value 2value 2performance 1performance Example 9. MIMIC model to test for gender bias in measurement, Holzinger & Swinford (1939) Grant-White Data (file Grant.xls in Userguide.xls). Example 10. Multi-group SEM with latent means: test of measurement invariance. Holzinger & Swinford (1939) Grant- White Data (file Grant.xls in Userguide.xls).
References Arbuckle, J. L. and W. Wothke (1999). AMOS 4.0 Users Guide. Chicago, SmallWaters. Loehlin, J. C. (1998). Latent Variable Models. Mahwah, New Jersey, Lawrence Erlbaum Associates. Kline, R. B. (1998). Principles and practice of structural equation modeling. New York, Guilford Press.