Anirban, you might also want to look at what Robert Moss (he is on RG) has to say about the model you refer to. Robert has a different theory where there are fewer factors. See Robert's Dimensional Systems Model, Clinical Biopsychology Model, and Emotional Restructuring. It might be useful to you. John
Cattell utilized oblique rotation to construct the 16PF, and found 5 second-order factors that closely resemble the Big Five. Oblique rotation allows the factors to correlate with each other and hence, does not necessarily impose an orthogonal structure on the data. Thus, if you read some more literature in the area, you may be able to conclude that although the five factors are related to some degree, they are relatively independent dimensions that can be studied orthogonally or obliquely. Hope this helps :)
To add information from my own background reading and data, the 5 factor model holds up better when the 5 dimensions are considered to not be completely orthogonal.
These are not related because high score on any one of these do not guarantee the same on another trait. in many cases it happens that a person is agreeable but he is not open to experience,because does'nt want to annoy anybody, cannot become devil's adovcate and again neuroticism interferes with healthy functioning of other traits.
For a genetic prove of the big five read DeYoung, C. G., Quilty, L. C., & Peterson, J. B. (2007). Between facets and domains: 10 Aspects of the Big Five, Journal of Personality and Social Psychology, 93, 880-896.The basic question is, from a cross-cultural point of view, if you can replicate the normative American factor structure. Best way to do so is the use of procrustean factor rotation http://culturemindspace.blogspot.co.nz/2012/03/how-to-do-procrustean-factor-rotation.html . In Tartu we use statistica program, so I am not sure if the Fischer syntax allows for 5 orthogonal factors. If not you can send me your factor scores and I calculate the Tucker similarity correlations for you within minutes.
The manual for NEO-FFI for example state that all 5 factors are orthogonal because of low interscale correlations. There are some articles which confirm that but there were always some results suggesting the opposite, even manual for the revised version of NEO-PI.
Here is one article which discuss the problem thoroughly, it's not new but I think you might find the answer here:
It is a mistake to think of the Big Five factors as orthogonal despite the initial research that identified them. There are several references already listed that will be very useful in determining their overlap. In our research we find consistently strong relationships between agreeableness, conscientiousness, and emotional stability. It is from this pattern that many have argued that there is a smaller subset of factors representing the Big Five. Given this pattern our lab has begun focusing more on the AB5C. Rather than taking a hierarchical approach to identifying personality facets, it focuses on traits that exist at the intersection between the Big Five.
I have mentioned the work of Robert Moss in an earlier post - but will do so again. Robert Moss (on RG) argues that the five factor model is not derived from a neuroscientific theory, and that neither volumetric nor functional neuroimaging of brain areas explains the manner in which those areas operate to produce any given behaviour. Bob suggests that there are two different, but basic, patterns by which individuals have learned to activate positive feelings and deactivate negative ones within relationships. These two patterns involve either the giving (Type-G) or the taking (Type-T) of power, control, attention, and other things. At the simplest level this is consistent with the basic motivational rule and refers to both the sensory and emotional memories (i.e. how one feels) and action (i.e. how one behaves) in relationship interactions. See his "Clinical Biopsychological Perspectives on Relationship Behavior Patterns: Givers and Takers" and also his other papers on RG. Bob would like it if researchers could look at his model and prove or disprove it.