Procedural Aspects of Replicability Analysis
For those familiar with
shrinkage analyses and cross validation of prediction equations in
multiple regression, these procedures and suggestions will perhaps
feel familiar. Replicability analyses in EFA (e.g., Thompson, 2004)
can be conducted in two different ways: via internal or external replication.
In internal replication, the researcher splits a single data set into
two samples via random assignment. In external replication, the researcher
uses two separately gathered data sets. In brief, replicability analysis
occurs as follows:
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EFA is conducted on each sample by extracting a fixed number of factors using a chosen extraction method (i.e., maximum likelihood or PAF) and rotation method (i.e., oblimin or varimax).
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Standardized factor loadings are extracted from the appropriate results for each sample (e.g., pattern matrix if using an oblique rotation), creating a table listing each item’s loading on each factor within each sample.
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Factor loadings and structures are then compared.
The first two steps
in this process are fairly straightforward and clear. You conduct
identical EFAs on your samples, and then you extract your standardized
loadings for comparison. The final step, comparison of factor loadings
and structures, is not as straightforward. As we will discuss in the
next section, most references on this topic do not go into detail
as to how researchers should perform this comparison, what the criteria
are for strong vs weak replication, and how to summarize or quantify
the results of the replication.
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