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SOC 681 – Causal Models with Directly Observed Variables

SOC 681 – Causal Models with Directly Observed Variables. James G. Anderson, Ph.D. Purdue University. Types of SEMs. Regression Models Path Models Recursive Nonrecursive. Class Exercise: Example 7 SEMs with Directly Observed Variables.

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SOC 681 – Causal Models with Directly Observed Variables

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  1. SOC 681 – Causal Models with Directly Observed Variables James G. Anderson, Ph.D. Purdue University

  2. Types of SEMs • Regression Models • Path Models • Recursive • Nonrecursive

  3. Class Exercise: Example 7SEMs with Directly Observed Variables • Felson and Bohrnstedt’s study of 209 girls from 6th through 8th grade • Variables • Academic: Perceived academic ability • Attract: Perceived attractiveness • GPA: Grade point average • Height: Deviation of height from the mean height • Weight: Weight adjusted for height • Rating: Rating of physical attractiveness

  4. Assumptions • Relations among variables in the model are linear, additive and causal. • Curvilinear, multiplicative and interaction relations are excluded. • Variables not included in the model but subsumed under the residuals are assumed to be not correlated with the model variables.

  5. Assumptions • Variables are measured on an interval scale. • Variables are measured without error.

  6. Objectives • Estimate the effect parameters (i.e., path coefficients). These parameters indicate the direct effects of a variable hypothesized as a cause of a variable taken as an effect. • Decompose the correlations between an exogenous and endogenous or two endogenous variables into direct and indirect effects. • Determine the goodness of fit of the model to the data (i.e., how well the model reproduces the observed covariances/correlations among the observed variable).

  7. AMOS Input • ASCII • SPSS • Microsoft Excel • Microsoft Access • Microsoft FoxPro • dBase • Lotus

  8. AMOS Output • Path diagram • Structural equations effect coefficients, standard errors, t-scores, R2 values • Goodness of fit statistics • Direct and Indirect Effects • Modification Indices.

  9. Model One

  10. Decomposing the Effects of Variables on Achievement

  11. Model Two

  12. Goodness of Fit: Model 2 • Chi-Square = 29.07 df = 15 p < 0.06 • Chi-Square/df = 1.8 • RMSEA = 0.086 • GFI = 0.94 • AGFI = 0.85 • AIC = 67.82

  13. Chi Square: 2 • Best for models with N=75 to N=100 • For N>100, chi square is almost always significant since the magnitude is affected by the sample size • Chi square is also affected by the size of correlations in the model: the larger the correlations, the poorer the fit

  14. Chi Square to df Ratio: 2/df • There are no consistent standards for what is considered an acceptable model • Some authors suggest a ratio of 2 to 1 • In general, a lower chi square to df ratio indicates a better fitting model

  15. Root Mean Square Error of Approximation (RMSEA) • Value: [ (2/df-1)/(N-1) ] • If 2 < df for the model, RMSEA is set to 0 • Good models have values of < .05; values of > .10 indicate a poor fit.

  16. GFI and AGFI (LISREL measures) • Values close to .90 reflect a good fit. • These indices are affected by sample size and can be large for poorly specified models. • These are usually not the best measures to use.

  17. Akaike Information Criterion (AIC) • Value: 2 + k(k-1) - 2(df) where k= number of variables in the model • A better fit is indicated when AIC is smaller • Not standardized and not interpreted for a given model. • For two models estimated from the same data, the model with the smaller AIC is preferred.

  18. Model Building • Standardized Residuals ACH – Ethnic = 3.93 • Modification Index ACH – Ethnic = 10.05

  19. Model Three

  20. Goodness of Fit: Model 3 • Chi-Square = 16.51 df = 14 p < 0.32 • Chi-Square/df = 1.08 • RMSEA = 0.037 • GFI = 0.96 • AGFI = 0.90 • AIC = 59.87

  21. Comparing Models • Chi-Square Difference = 12.56 df Difference = 1 p < .0005 • AIC Difference = 7.95

  22. Difference in Chi Square Value: X2diff = X2model 1 -X2 model 2 DFdiff = DF model 1 –DFmodel 2

  23. Decomposing the Effects of Variables on Achievement

  24. Class Exercise: Example 7SEMs with Directly Observed Variables • Attach the data for female subjects from the Felson and Bohrnstedt study (SPSS file Fels_fem.sav) • Fit the non-recursive model • Delete the non-significant path between Attract and Academic and refit the model • Compare the chi square values and the AIC values for the two models

  25. Class Exercise: Example 7SEMs with Directly Observed Variables • Felson and Bohrnstedt’s study of 209 girls from 6th through 8th grade • Variables • Academic: Perceived academic ability • Attract: Perceived attractiveness • GPA: Grade point average • Height: Deviation of height from the mean height • Weight: Weight adjusted for height • Rating: Rating of physical attractiveness

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