In Beebe's model, the "shadows" are simply the first four functions with the attitudes reversed. He points out that we cannot make too much of this order. It is just to parallel the preference order of the primary four, especially in relation to the archetypal complexes which also parallel the hero/parent/child and inferior.
It is never claimed to be an order of relative strengths, or even "development".
Before Beebe's model was more known about, (and in a period where the internet was just becoming mainstream), Lenore Thomson publishes her book with an attempt at an eight function model. She places the "shadows" inbetween the dom/aux and tert/inferior. This also is not claimed to necessarily be an order of strength, but the two functions that are #7 and 8 in Beebe's model, are said to be "the first we run to for solutions" when the dominant and auxiliary can't solve a problem. They are the same brain hemisphere as the dom/aux, and thus their lateral "alternatives".
She calls them the "Crow's Nest" of a ship, with the dom. as the captain, and the aux. as the first mate. The tertiary and inferior are rebels who are off the boat, one heading the ship's direction, and the other trying to pull it the opposite way. The remaining two functions (the dom and aux. with the opposite attitudes), are called "Double Agents".
So on these forums, people take Nardi's cognitive process test, and many come out with results similar to the ship model. At least as far as #8 being strong (often third place), and the inferior being on the bottom (and for many, the tertiary right above it).
so I've been trying to sort out an explanation for all of this.
I figured the answer lies in the disparity between the functions as perspectives, and as behaviors. Many of the familiar definitions we see and use, are actually behavioral "skill", but the functions are really more like perspectives. Basically, interpretations of data; being gathered in the form of tangible or conceptual elements, and decided in terms of technical (impersonal) or humane (personal) considerations.
A few years ago, someone on INTPCentral "reverse engineered" the test, and among other things, figured out which questions corresponded to which functions. There are 48 questions. Four groups of eight, with each of the eight functions having four questions scoring in favor of them. The remaining sixteen questions were for all of the possible dom/aux pairs.
Looking at this again, the common themes of the individual function questions:
Se physical experience, action
Si storehouse of familiar experiences, regular activity
Ne new ideas, random contexts
Ni foreseeing, symbolic, etc.
Te efficiency; esp. with others, straight line of reasoning
Ti definitions, analyzing
Fe taking care of others, communicate to feel unity
Fi true to what you want for yourself, what is good
These you can pretty much see in his book, and other associates such as Berens and Hartzler.
What I find are the best representations of the functions as perspectives:
Se: emergent tangibles
Si: stored tangibles (facts)
Ne: emergent conceptualizations
Ni: stored conceptualizations
Te: set technical considerations
Ti: variable technical considerations
Fe: set humane considerations
Fi: variable humane considerations
The Nardi test "process" definitions are basically behavioral. They are not reflecting an inner cognition of a particular perspective, but rather what we DO with them. How we react to things.
This is what likely causes the difference in order between the test results and the standard order, and thus why some "shadows" might seem stronger than some primary functions.