I think your question is too broad. What kinds of personal qualities are you interested in predicting? Traits? Behavior? Here are some citations that might suggest narrower focus:
Wolfradt, U., & Pretz, J. E. (2001). Individual differences in creativity: Personality, story writing, and hobbies. European journal of personality, 15(4), 297-310.
Küfner, A. C., Back, M. D., Nestler, S., & Egloff, B. (2010). Tell me a story and I will tell you who you are! Lens model analyses of personality and creative writing. Journal of Research in Personality, 44(4), 427-435.
Argamon, S., Dhawle, S., Koppel, M., & Pennebaker, J. W. (2005, June). Lexical predictors of personality type. In Proceedings of the 2005 Joint Annual Meeting of the Interface and the Classification Society of North America.
Robinson, J. M. (1985). Style and personality in the literary work. The Philosophical Review, 94(2), 227-247.
Li, J., & Chignell, M. (2010). Birds of a feather: How personality influences blog writing and reading. International Journal of Human-Computer Studies, 68(9), 589-602.
Historically, one approach was using short writing samples, through sentence completion tests, to diagnose thought disorder and other symptoms You can find a history on The Sentence Completion Method by Robert I. Watson Jr. in Clinical Diagnosis of Mental Disorders (Springer, 1978), pp 255-279
[Abstract] The sentence completion method of projective testing encompasses a wide variety of tests, all of which share a common format. In each instance, individuals being studied by this method are required to complete a number of sentence stems which are presented to them. Since the origination of this testing technique, a great many stems have been used, various methods of administration have been attempted, and a good deal of diversity has developed in the interpretation of the resulting material. The ease with which a sentence completion test can be constructed has proven to be both one of the strengths and one of the weaknesses of this method. Since the generation of the stems is not complicated, a great many sentence completion tests have been authored. While this often leads to the valid use of a test for the particular question it has been designed to answer, the number of such instruments has precluded the development of an extensive body of literature on a single sentence completion test. Without one dominant test on which to focus, it has been deemed expedient to deal with the method in general for the first part of this chapter. This is then followed by the specifics of a number of the most popular sentence completion tests in clinical use.
In the field of diagnosing thought disorder there have historically been various attempts of this sort to diagnose various forms of thought disorder. You might find illuminating examples in Irving Weiner's Psychodiagnosis in Schizophrenia and Silvano Arieti's Interpretation of Schizophrenia. These examples may be less about "writing" than about the relationship between language and thought, but certainly a piece of writing can give many clues to psychological functioning. I've never forgotten, for example, Weiner's description of "peculiar verbalizations." This may not be the track you're on, but there certainly are interesting possible directions to take.