# Jeromy Anglim's Blog: Psychology and Statistics

## Saturday, September 26, 2009

### Item Parcelling in Confirmatory Factor Analysis

This post discusses item parcelling in the context of Confirmatory Factor Analysis. What is parcelling? How do you parcel? Should you parcel?
What is parcelling?
Item parcelling is one of several procedures for combining individual items and using these combined items as the observed variables, typically as the observed variables in Confirmatory Factor Analysis (CFA) or Structural Equation Modelling (SEM). Parels are an alternative to using the individual items.

How do you parcel?
Item parcels are typically created by taking the sum or mean of a set of items within a factor.
For example, if you had six items (i1, i2, i3, i4, i5, i6) on factor 1 (f1), and you wanted three parcels (p1, p2, p3), then a simple way to create these parcels would be to calculate:
p1 = i1 + i2
p2 = i3 + i4
p3 = i5 + i6
There are many other ways of getting parcels and debate exists in the literature on the pros and cons of the different approaches. These parcelled variables are then used in your SEM software as observed variables (for info about how to run a CFA in Amos, check out Simon Moss' notes. For SEM in R, I have the following post).

Should you parcel?
This is a long debated topic. The following links provide useful reading:

My informal observations:
Over the while I've run a few CFAs and compared the results obtained with items versus parcels. My informal observations on the matter (i.e., don't quote me) are as follows:

• Problems in the assignment of items to factors (e.g., item assigned to wrong factor; items that have correlated errors) will tend to be smoothed over if you parcel. Thus, if you are wanting to test alternative models of item assignment to factors, parcelling is a bad idea. However, if you are still working out which items belong to which factors, exploratory factor analysis tends to be more useful anyway.
• If you are mainly asking questions about how many factors or if your main focus is on testing various structural models then parcelling may be less of a problem. In such a case the parcels are mainly a means of getting an estimate of the reliability of estimation of latent factors and the focus is on accurately estimating the direct and indirect effects between latent factors. In addition any model comparison will all be using the same set of parcels.
• Many scales have 50 or 100 items. Modelling this many items on moderately sized samples (e.g., n = 200) may not work. You can run into estimation problems. Thus, you are then left with the choice of reducing the number of observed variables (e.g., by parcelling) or not doing CFA.

#### 3 comments:

1. Item parceling should only be done if a clearly defined uni-dimensional factor structure has been identified for a measure. Otherwise, it masks important differences in the structure of a model, especially full structural models.

See the Bandalos and Finney Chapter 10 in Marcoulides, George A. (Ed); Schumacker, Randall E. (Ed), (2001). New developments and techniques in structural equation modeling, (pp. 269-296).

2. Dear Statistician,

Can I enter parcels in a multiple regression model as explanatory variables with other factor scores?

Thanks

3. Also how is the choice done with parcelling? I mean do the items need to be correlated significantly or have a good reliability? What are the basic, yet specific requirements?