Parceling Items in Factor Analysis

First of all, what are parcels? Not the little packages your grandma left on the table in the hall when she came back from shopping. Well, not only that.

In factor analysis, parcels are simply the sum of a small number of items. I prefer using parcels when possible because both basic psychometric theory and common sense tells me that a combination of items will have greater variance and, c.p., greater reliability than a single item.

Just so you know that I learned my share of useless things in graduate school, c.p. is Latin for ceteris paribus which translates to “other things being equal”. The word “etcetera”  meaning other things, has the same root.

Know you know. But I digress. Even more than usual. Back to parcels.

As parcels can be expected to have greater variance and greater reliability, harking back to our deep knowledge of both correlation and test theory we can assume that parcels would tend to have higher correlations than individual items. As factor loadings are simply correlations of a variable (be it item or parcel) with the factor, we would assume that  – there’s that c.p. again – factor loadings of parcels would be higher.

Jeremy Anglim, in a post written several years ago, talks a bit about parceling and concludes that it is less of a problem in a case, like today, where one is trying to determine the number of factors. Actually, he was talking about confirmatory factor analysis but I just wanted you to see that I read other people’s blogs.

The very best article on parceling was called To Parcel or Not to Parcel and I don’t say that just because I took several statistics courses from one of the authors.

 

To recap this post and the last one:

I have a small sample size and due to the unique nature of a very small population it is not feasible to increase it by much.I need to reduce the number of items to an acceptable subject to variables ratio. The communality estimates are quite high (over .6) for the parcels. My primary interest is in the number of factors in the measure and finding an interpretable factor.

So… here we go. The person who provided me the data set went in and helpfully renamed the items that were supposed to measure socializing with people of the same culture ‘social1’, ‘social2’ etc, and renamed the items on language, spirituality, etc. similarly. I also had the original measure that gave me the actual text of each item.

Step 1: Correlation analysis

This was super-simple. All you need is a LIBNAME statement that references the location of your data and then:

PROC CORR DATA = mydataset ;

VAR  firstvar — lastvar ;

In my case, it looked like this

PROC CORR DATA = in.culture ;

VAR social1 — art ;

The double dashes are interpreted as ‘all of the variables in the data set located from var1 to var2 ‘ . This saves you typing if you know all of your variables of interest are in sequence. I could have just used a single dash if they were named the same, like item1 – item17 , and  then it would have used all of the variables named that regardless of their location in the data set. The problem I run into there is knowing what exactly item12 is supposed to measure. We could discuss this, but we won’t. Back to parcels.

Since you want to put together items that are both conceptually related and empirically – that is, the things you think should correlate do- you first want to look at the correlations.

Step 2: Create parcels

The items that were expected to assess similar factors tended to correlate from .42 to .67 with one another. I put these together in a ver simple data step.

data parcels ;
set out.factors ;
socialp1 = social1 + social5 ;
socialp2 = social4 + social3 ;
socialp3 = social2 + social6 + social7 ;
languagep = language2 + language1 ;
spiritualp = spiritual1 + spiritual4 ;
culturep1 = social2 + dance + total;
culturep2 = language3 + art ;

There was one item that asked how often the respondent ate food from the culture, and that didn’t seem to have a justifiable reason for putting with any other item in the measure.

Step 3: Conduct factor analysis

This was also super-simple to code. It is simply

proc factor data= parcels rotate= varimax scree ;
Var socialp1 – socialp3 languagep spiritualp spiritual2 culturep1 culturep2  ;

I actually did this twice, once with and once without the food item. Since it loaded by itself on a separate factor, I did not include it in the second analysis. Both factor analyses yielded two factors that every item but the food item loaded on. It was a very nice simple structure.

Since I have to get back to work at my day job making video games, though, that will have to wait until the next post, probably on Monday.

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Be more than ordinary. Take a break. Play Forgotten Trail. I bet you have a computer!

Learn and have fun. More productive than fruit crush, candy ninja or whatever the heck else it is you or your kids are playing.