PCing Around

Use the fact1.sav data set

Anticipating the Factor Structure:

Let’s start with an analysis using everything from SES to hsprog (not subn or college performance).

How many factors do you expect to find when you factor this collection of “personality” variables and "performance" variables together?

Tell what variables do you expect to load on each below.

Getting the “λ > 1.00” solution

a.How many factors pass the λ > 1.00 criterion ? ______

b.How much variance is accounted for by these factors ? ______What kind of variance is this? ______

c.Any interest in considering a 1-more-factor solution? Why or why not?

d.Any interest in considering a 1-fewer-factor solution? Why or why not?

e.How much variance is accounted for by these factors ? 1-more______1-less ______

Interpreting the “λ > 1.00” solution

f.Get one orthogonal and one oblique rotation. Using a .3 cutoff, what variables load on each factor? Be sure to note any differences between the orthog and oblique & tell which you prefer.

Factor #1

Factor #2

Factor #3

g.Any surprises? How do you interpret the surprises??

Using the “λ > 1.00” solution

h.Run a multiple regression with these variables as predictors and college performance as the criterion.

i.Obtain the proper PC scores and use them as the predictors of college performance

j.Based on your answer to “f” obtain the improper pc scores and use them as the predictors of college perfomance

R-square? Full-variable? Proper PCs Improper PCs

Which variables “are related to college performance”?

Full-variable?

Proper PCs

Improper PCs

So, what did you learn about how variables are related to each other? How they are related to college performance>

Please note – if we were doing a full-fledged exploratory search, we’d repeat steps a-j with the -1 and +2 numbers of factors and use the similarities and differences among the interpretations and predictions of the different factoring versions to decide which we would pronounce our “best solution”.
Using independent models to explore dependent models.

You are going to run a PC with all the variables from before, plus college performance.What do you expect?

Will the number of factors change or stay the same?

Will college performance be univocal? On which PC will it load?

Will it be multi-vocal? On which PCs will it load?

Getting the “λ > 1.00” solution

  1. How many factors pass the λ > 1.00 criterion ? ______
  1. How much variance is accounted for by these factors ? ______What kind of variance is this? ______
  1. Any interest in considering a 1-more-factor solution? Why or why not?
  1. Any interest in considering a 1-fewer-factor solution? Why or why not?
  1. How much variance is accounted for by these factors ? 1-more______1-less ______

Interpreting the “λ > 1.00” solution

  1. Get one orthogonal and one oblique rotation. Using a .3 cutoff, what variables load on each factor? Be sure to note any differences between the orthog and oblique & tell which you prefer.

Factor #1

Factor #2

Factor #3

  1. Compare “the story” from the full-variable multiple regression and this factoring. Did we learn anything new about how these variables are related to college performance