1. Latent variable path analysis Combination of CFA and observed variable path analysis More parameters estimated, so need to have a larger sample size Chief advantage is that you are determining how latent constructs are related to each other, leaving aside error, which may distort correlations/covariances State-of-the-art!! Is there one “right answer” to a given dataset?

2. What will we do today? First, I will show you the observed variable path analysis (like last week) Then I will show you an alternative model for the observed variable path analysis Talk about how to compare them Then I will show you a latent variable path analysis, and the same with the alternative model Hopefully, you will see how these tools can be used to usefully describe a dataset

3. Maruyama & McGarvey’s (1980) dataset concerning peer acceptance 249 subjects (child, teacher and parent data) Interested in seeing how exogenous variables (like socio-economic status) and parent evaluations predict peer acceptance of children Five major potential latent variables: –Socio-economic status –Academic abilities –Academic achievement –Adult evaluation of child –Peer evaluation of child

4. Vocab Verbal ach Popular in class          Educ of head Mother eval     Original model: observed variables

5. Vocab Verbal ach Popular in class.35**.12~.26*    Educ of head Mother eval.22*   Original model: obtained results R 2 =.03 R 2 =.21

6. Vocab Verbal ach Popular in class          Educ of head Mother eval    Alternative model: observed variables   

7. Vocab Verbal ach Popular in class.35**.26*.13*    Educ of head Mother eval.22*  Alternative model: obtained results .12~ R 2 =.21 R 2 =.02 R 2 =.09

8. Comparison of two models Original model  2 (6) = 9.83 RMSEA =.05 NFI =.90 PNFI =.54 CFI =.96 RFI =.84 Crit. N = 424.98 GFI =.98 AGFI =.96 PGFI =.39 Alternative model  2 (6) = 6.83 RMSEA =.023 NFI =.93 PNFI =.56 CFI =.99 RFI =.89 Crit. N = 611.33 GFI =.99 AGFI =.97 PGFI =.40

9. Now, on to latent variable path analysis! Two-step process: 1) CFA on the potential latent variables; and 2) path analysis on the latent variables Need to achieve good fit with the CFA before can proceed; may need to drop indicators and/or latent variables May make sense to do the observed variable path analysis first (as we did here), except that you assume that you’re using the best indicators (which may not be true)