1. Introduction to Path Analysis

21. We could follow similar steps to compute the correlation between X1 and X6: r16 = p61 + p41p64 + p51p65 + p41p54p65 + (r16 – [p61 + p41p64 + p51p65 + p41p54p65]) where the highlighted terms are the direct and indirect effects. The last term, in parentheses, on the right is the residual, or spurious, correlation between X1 and X6 The direct and indirect effects are shown on the next slide.

23. Direct and indirect effects are highlighted.
Similarly, we could show the decomposition of direct and indirect effects foe X1, X2, X3, X4 and X5 on X6:
r26 = p62 + p42p64 + p52p65 + p42p54p65 + (r26 – [p62 + p42p64 + p52p65 + p42p54p65])
r36 = p63 + p43p64 + p53p65 + p43p54p65 + (r26 – [p63 + p43p64 + p53p65 + p43p54p65])
r46 = p64 + p54p65 + (r26 – [p64 + p54p65])
r56 = p65 + (r26 –p65)
Direct and indirect effects are highlighted.

25. A model similar to Pajares & Miller

26. To test this model, estimate the following regression equations:

27. Computing the regressions yields the standardized regression coefficients (βs), which are the desired path coefficients. The following slide incorporates the path coefficients.

29. The reduce model (after removing non-significant paths)

30. The next step in the analysis would be to compute a new set of regression equations to obtain the path coefficients for the remaining paths. Perhaps we will have time to do this in class.