Confirmatory factor analysis

[Art Kendall]

My opinion of some uses CFA is that they are a formalization of what we used to do to confirm a scoring key.
Background.
This is in the context of using factor analysis to create summative scale where items are used with unit weights.
The items are taken to be imperfect measurements of an underlying factor.  The sum(average) of several repeated measures was considered a better representation of the construct.  Using all items in e.g., a regression would require huge numbers of cases. Each item has some variance due to the construct one is trying to achieve a measure of, some variance specific (unique) to the item, and some noise variance.
For example, a construct of spelling ability would have a list of words.  An item would have some variability due to spelling ability, some variability due to some other linguistic aspects, and some due to chance.

A scoring key contains a list of of constructs that the factors are taken to represent, which items go into a particular factor, and something to say which items need to be reflected. Reflection was needed for constructs other than achievement,  because good practice called for balancing demand characteristics of the items.

Care is taken to use only items that load cleanly on a single factor.  This is to achieve divergent validity.
The confirmation might be done for different reasons.
** Does a translation to another language show the same kind of structure?
** Does the same structure appear in different groups of respondents? (Sometimes groups were random halves of the original group.)
**How do new potential items fit in with the items measuring the construct.
For example, the Lorr liberalism- conservatism scale was found to have three consistently separable dimensions:
general liberalism-conservatism
egalitarianism
sexual freedom.
Several new items were tried out to keep the instrument up to date.
a stem "equal right for gay people" was rejected as a candidate item because it turned out to have loadings on both egalitarianism and on sexual freedom. Even though is is somehow related to lib-can, it is omitted because it is "double barreled", it reflected more than one construct.

What we did.
A principal axes factoring with varimax rotation was done on the new data.
The eigenvalues were plotted on the same graph.
Solutions were found using the original number of factors retained as the ballpark.
Lists were made of the items loading non-trivially and cleanly on each factor. (the sign of the loading was noted).
These lists were a scoring key based the new data.
The keys were then compared to see if they had the same groupings of items.


On 10/29/2013 4:08 AM, Marta García-Granero-2 [via SPSSX Discussion] wrote:

(PD: Can anybody recommend a GOOOOD book on CFA, besides the one I
already have (Tabacknich&Fidell)?