3. Analyze the latent variable panel model of locus of control and achievement. The data are in the file “sc locus ach matrix n12k.xls,” and more information about the variables is shown in the related codebook file. Estimate the model as shown in the figure; make sure your results match those presented in the chapter.

a. Given the nature of the measured variables, are there any correlated errors you might add a priori to improve model fit? Consider, in particular, if some of the Locus items measure something in common other than general locus of control.

b. Examine the modification indexes and standardized residuals to determine if there are other model modifications you might make to improve fit. Do you have a theoretical justification for doing so? How can the modification indexes be so large in a model that generally fits well?

c. Using the concepts of setting parameters to be the same from the multigroup section of the chapter, constrain the factor loadings of the Locus factor to be the same over time.

That is, constrain the loadings for luck8, luck10, and luck12 to be the same, constrain the loadings for stops8, stops10, and stops12 to be the same, and so on. Do the same for the Ach factor loadings. Using a criterion of ΔCFI larger than an absolute value of

.01, decide whether these model modifications are reasonable. This is a type of factor invariance; it and the ΔCFI criterion will be discussed in more detail in Chapter 20.

d. Specify two alternative models to determine, based on fit, whether Ach affects Locus, and whether Locus affects Ach. Why is Δχ2 not a good choice for these comparisons?

What might you examine instead?

e. Specify an alternative model to answer the question of whether SES has any direct effects on 10th-grade locus of control and achievement. Next test for direct effects on 12th-grade Locus and Achievement. Are the effects statistically significant? Are they meaningful? How did you decide?

f. Specify an alternative model in which Locus8 is allowed to affect Locus12 and Ach8 is allowed to affect Ach12. Are the effects statistically significant? Are they meaningful?

How did you decide?