Exam #3 Laboratory #2 Factoring Exercise Walk-ThroughUsing the file fact1.sav factor the items SES, locus of control, self concept, motivation, reading, writing, math,science and civics.Anticipating the Factor Structure How many factors do you expect to find when you factor the set of “personality” variables and "performance" variables together? Tell what variables do you expect to load on each below.Component AnalysisAnalyze  Data Reductio n Factor• Enter the variables to be factored by highlighting each and clicking the arrow• Click "Descriptives" and be sure "Initial solution" is checked • Click "Extraction" and be sure "Principal Components" is in the Method box and that only "Correlation Matrix" and "Eigenvalues Over" are checked and "1" is in the box beside "Eigenvalues over:" • Click "rotation" and be sure "Direct Oblimin" is checked 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 _________ What kind of variance is this? ______________f. Pick one of the solutions (all pick the same one – argue if you have to!) Using all the words and a cutoff of .4 applied to the rotated structure matrix, interpret each of the factors(be sure to both tell the variables that "load" on each factor,if that factor is uni- or bi-polar, and to try to give it a "name").g. How would the interpretation of the factors change if you used a cutoff of .3?h. Which cutoff do you prefer? Why?i. Obtain a solution with 3 factors. Using all the words and a cutoff of .4 applied to the rotated structure matrix, interpret each of the factorsj. Do you prefer the 2-factor or the 3-factor solution? Why might someone prefer whichever you don’t like?Common Factor Analysis - be sure to click "Principal Axis Factoring" in the “Extraction” windowa. How many factors were “kept”? ________ b. How much variance is accounted for by these factors ? ________ What kind of variance is this? _______________c. Using all the words and a cutoff of .4 applied to the rotated structure matrix, interpret each of the factors (be sure to both tell the variables that "load" on each factor, if that factor is uni- or bi-polar, and to try to give it a "name").d. How would the interpretation of the factors change if you used a cutoff of .3?e. Which cutoff do you prefer? Why?f. What are the similarities and differences between the pc and paf solution of the same variables?g. What is the “conceptual” difference between the results/interpretation/use of this analysis and the previous analysis using a component solution?Your Turn #1Using the file fact3.sav, factor the following items: sepfam findep ruls soss frss fass stanx tranx dep stress.a. The purpose of this analysis is to help determine how many different kinds of information are obtained from these variables. Which type of “factor analysis” would you use for this purpose? Why?Obtain a default solution with an oblimin rotation and answer each of the following questions.b. How many factors pass the λ > 1.00 criterion ? ________ c. How much variance is accounted for by these factors ? ________ What kind of variance is this? ______________d. Any interest in considering a 1-more-factor solution? Why or why not?e. Any interest in considering a 1-fewer-factor solution? Why or why not?f. Pick a # factors solution & look at the structure matrix. Decide if you prefer a .3 or a .4 cutoff for interpreting the factorsolution and explain your preference.g. Using the cutoff of your choice, interpret the factors (using all the words).Your Turn #2Using the file personalsuccess..sav, factor the following items from “scs” to “debil” a. The purpose of this analysis is to help determine how many different kinds of information are obtained from these variables. Which type of “factor analysis” would you use for this purpose? Why?Obtain a default solution with an oblimin rotation and answer each of the following questions.b. How many factors pass the λ > 1.00 criterion ? ________ c. How much variance is accounted for by these factors ? ________ What kind of variance is this? ______________d. Any interest in considering a 1-more-factor solution? Why or why not?e. Any interest in considering a 1-fewer-factor solution? Why or why not?f. Look at the structure matrix. Decide if you prefer a .3 or a .4 cutoff for interpreting the factor solution and explain your preference.g. Using the cutoff of your choice, interpret the factors (using all the words).Your Turn #3Sometimes factor analysis is used to understand a set of scale/questionnaire items, to help decide how many and what should be the subscales. Generally this is not a great idea – much better to test a priori hypotheses about scale structures using confirmatory factoring. But, I wanted you to get a taste of the exploratory principal components used in this way…a. Using the file fact2.sav, factori1-i40. These are the 40 items of the Teenage Inventory of Social Skills b. Run an initial PC analysis with Promax rotation of the items, and respond to the questions below.How many factors pass the - > 1.00 criterion ? _____________How much variance is accounted for by these factors ? _____________Well, that got ugly quickly, didn't it?!? Factoring individual items often leads to "messy" solutions such as this -- the whole reason we build scales is that individual items are pretty unreliable, and individually do a poor job of "tapping" the construct of interest -- so we shouldn't be too surprised with they give us unattractive factor solutions such as this. One common solution is to look at the first ?-many factors, to see if we get at least a hint of the structure we were hoping for, even though there many be additional factors in the solution.Remember, the TISS was designed to do was to provide separate measurements of "positive" and "negative" social behaviors. So, let's look to see what the first 2 PCs look like!c. Re-factor the items requesting specifically 2 principal components and a Promax rotation (remember the idea had been to construct 2 scales – one for