Q-Assessor Now Supports Specifying Number of Extracted Factors
Posted by Stan Kaufman on 29 September 2014 - 16:39 | Permalink
One feature some Q-Assessor users have requested has been the ability to specify how many centroid factors are extracted from the initial correlation matrix. We resisted adding this step, as there is no support for it in Brown’s book (cf the Factor Analysis section of chapter 4) and from a mathematical viewpoint, we can’t understand why this “feature” was added to PQMethod. Nevertheless, because this is a request that doesn’t seem to go away, we have added this capability.
The default number of extracted factors when you first analyze your data is the nominal seven, which is the “magic number” (per Brown) that is the maximum number of plausibly significant factors in a data set. A single popup menu option then lets you recalculate your results restricting the analysis to 1-7 factors. Thus you can restrict the search to a smaller number of factors and then rotate them as you like. Some users find significant value in this flexibility.
We remain skeptical of the value of this step, however, for this reason. The basic idea behind Q is that the cross-correlations amongst the participants’ sorts encode patterns of opinion/belief/understanding that the factor analysis process reveals. The number of statistically-significant factors thus relies within the data — not the sieve used to examine the data. If there are five significant factors, looking for seven will identify the five and show that there are two additional factors that are insignificant and can be ignored. If however the algorithms are restricted arbitrarily to look only for, say, three factors, then important information is lost. This is not part of how Brown explains this should be done, so we can only speculate why the FORTRAN code underlying PQMethod included it.
Regardless, Q-Assessor now supports both approaches to analysis.