Chapter Questions
Define confirmatory models, alternative models, and modelgenerating approaches.
Define model fit, model comparison, and model parsimony.
Calculate the following fit indices for the model output in Figure 5.1:$$\begin{aligned}& \mathrm{GFI}=1-\left(\chi_{\text {model }}^2 / \chi_{\text {null }}^2\right) \\& \mathrm{NFI}=\left(\chi_{\text {null }}^2-\chi_{\text {model }}^2\right) / \chi_{\text {null }}^2 \\& \left.\mathrm{RFI}=1-\left[\chi_{\text {model }}^2 / d f_{\text {model }}\right) /\left(\chi_{\text {null }}^2 / d f_{\text {null }}\right)\right] \\& \mathrm{IFI}=\left(\chi_{\text {null }}^2-\chi_{\text {mode }}^2\right) /\left(\chi^2 \text { null }-d f_{\text {model }}\right) \\& \mathrm{TLI}=\left[\left(\chi_{\text {null }}^2 / d f_{\text {null }}\right)-\left(\chi_{\text {model }}^2 / d f_{\text {model }}\right)\right] /\left[\left(\chi_{\chi_{\text {null }}^2}^2 / d f_{\text {null }}\right)-1\right] \\& \mathrm{CFI}=1-\left[\chi_{\text {model }}^2-d f_{\text {model }} /\left(\chi^2 \text { null }-d f_{\text {null }}\right]\right. \\& \text { Model AIC }=\chi^2 \text { model }+2 q(q \text { is the number of free parameters }) \\& \text { Null AIC }=\chi_{\text {null }}^2+2 q(q \text { is the number of free parameters })\end{aligned}$$$$R M S E A=\sqrt{\left[\chi_{\text {Model }}^2-d f_{\text {Model }}\right] /\left[(N-1) d f_{\text {Model }}\right]}$$or$$R M S E A=\sqrt{(N C P / N-1) / d f}$$
How are modification indices in LISREL--SIMPLIS used?
What steps should a researcher take in examining parameter estimates in a model?
How should a researcher test for the difference between two alternative models?
How are structural equation models affected by sample size and power considerations?
Describe the four-step approach for modeling in SEM.
What new approaches are available to help a researcher identify the best model?
Use $G^*$ Power 3 to calculate power for modified model with $\mathrm{NCP}=6.3496$ at $p=.05, p=.01$, and $p=.001$ levels of significance. What happens to power when alpha increases?
Use G*Power 3 to calculate power for modified model with alpha $=.05$ and $\mathrm{NCP}=6.3496$ at $d f=1, d f=2$, and $d f=3$ levels of model complexity. What happens to power when degrees of freedom increases?