EFA versus PCA
In a previous question on the differences between EFA and PCA, I state:
- Principal components analysis involves extracting linear composites of observed variables.
- Factor analysis is based on a formal model predicting observed variables from theoretical latent factors.
I find that typically within the context of developing psychological scales factor analysis is more theoretically appropriate. Latent factors are often assumed to cause the observed variables.
Assessing Scale Dimensionality
Determining the dimensionality underlying a set of likert items is not just a question of EFA versus PCA. There are multiple techniques. William Revelle has some software in R for implementing several techniques (see this discussion).
In general there is rarely a definitive answer as to how many factors are required to model a set of items. If you extract more factors, you can explain more variance in the items. Of course, just by chance you might explain some variance, so some approaches try to rule out chance (e.g., the parallel test). However, even with very large samples, where chance becomes less of an explanation, I'd expect to see systematic but small increases in variance explained by extracting more factors. Thus, you are left with the issue of how much variance must be explained by the first factor relative to others in order to conclude that the scale is sufficiently unidimensional for your purpose. Such issues are closely tied to application and broader issues of validity.
You might find the following article useful to read, for a broader discussion of definitions and approaches at quantifying unidimensionality:
Hattie, J. (1985).
Methodology review: Assessing unidimensionality of tests and ltems.
Applied Psychological Measurement, 9(2):139.
Here's a web presentation examining a few different decision rules for defining unidimensionality
Cronbach alpha and its versions are measures of inter-item homogeneity. By definition, a scale should be homogeneous enough to be able to measure one construct. Reliability approach poses that items in a scale are all the "same" except for some biases that are treated as "random error", unrelated to the measured construct, and that cancel each other in the end. So, alpha is not suitable for battery of constructs: it is unidimentional. Another pair of shoes, though, is that truly unidimensional construct is somewhat unrealistic concept. In factor analysis of a scale it often splits into main factor which is the construct of interest and few minor factors which interfere. Still, reliability approach treat these systematic factors as noise. See more.
Best Answer
First yes it does, see http://www.personality-project.org/r/psych/help/omega.html and second there is a package
sirthttp://www.inside-r.org/packages/cran/sirt/docs/stratified.cronbach.alpha that you can use for stratified alpha.