Peck claims that he arrived at this theory through experience, although he footnotes the fact that there have been many theories on psychological development prior to his, the most recent being a six-stage faith developmental model (see "Stages of Faith" by James W. Fowler)
Although Peck's elucidation of his theory is informal and sketchy, I find his model of psychospiritual development idiosyncratic enough to be regarded as a separate theory by itself.
Peck aptly calls it psychospiritual since it has both psychological and spiritual/religious dimensions. It is much akin to the developmental theories in psychology, yet it has a very strong religious flavor--Stage 1 being the lack of spirituality/ethical behavior, Stage 2 as orthodoxly religious, Stage 3 as a time of religious skepticism or atheism, and Stage 4 the mystical level.
Yet I believe Peck's theory tends to be ethically judgmental in character, i.e., it explicitly holds the higher stages as undeniably better than the lower ones, and tends to describe people in ethical terms--'chaotic/unprincipled' (Stage 1), or dogmatic (Stage 2), or principled (Stage 3)
Nevertheless, I see the veracity of such categories, albeit demanding much care and caution. Pigeonholing, specially in ethical terms, is dangerous business and can easily be misused and abused. However, I believe that Dr. Peck has realized the limitations of his theory and has provided caveats and exceptions in his later books, such as in "Further Along the Road Less Travelled"