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Below are the major theories/models/concepts over the years which attempt to explain college student retention/attrition.

Astin's (1977, 1985) Theory of Involvement

The more involved a student is with the college, the higher likelihood of student retention.

Bean's (1980, 1983) Model of Work Turnover to Student Attrition

Used concepts from organizational studies of worker turnover. Examines how organizational attributes and reward structures affect student satisfaction and persistence.

Bean and Metzner's (1985) Nontraditional Student Attrition

Environmental factors have a greater impact on departure decisions of adult students than academic variables.

Kamens (1971, 1974)

Used multi-institutional data to demonstrate how colleges of greater size and complexity had lower attrition rates.

McNeely (1937) "College Student Mortality"

Examined many factors in college student retention including time to degree, when attrition was most prevalent in a student's education, impact of college size etc.

Spady Model (1971)

Interaction between student characteristics and campus environment 

Summerskill (1962)

Personality attributes of students is the main reasons for persistence and leaving.

Tinto Model (1975, 1993)

Academic and social integration with the formal and informal academic and social systems of a college.

* Most of these theories have been taken from:

Berger, J. B., & Lyons, S. (2005). Past to present: A historical look at retention. In Seidman, A.  (Ed.). College student retention: Formula for student success. Praeger Press. 

Braxton, J. M. & Hirschy, A. S. (2005). Theoretical Developments in the study of college student departure. In Seidman, A. (Ed.). College student retention: Formula for student success. Praeger Press.

Other References

Astin, A. W. (1977). Four critical years. San Francisco: Jossey-Bass.

Astin, A. W. (1985). Achieving academic excellence. San Francisco: Jossey-Bass. 

Bean, J. (1980). Dropouts and turnover: The synthesis and test of a casual model of student attrition. Research in Higher Education, 12, 155-187.

Bean, J. (1983). The application of a model of turnover in work organizations to the student attrition process. The Review of Higher Education, 6, 129-148.

Bean, J. P. & Metzner, B. S. (1985). A conceptual model of nontraditional student attrition. Review of Educational Research, 55, 485-540.

Kamens, D. H. (1971). The college "charter" and college size: Effects on occupational choice and college attrition. Sociology of Education, 44(summer), 270-296.

Kamens, D. H. (1974). Colleges and elite formation: The case of prestigious American colleges. Sociology of Education, 47(summer), 354-378.

McNeely, J. H. (1937). College student mortality. U.S. Office of Education, Bulletin 1937, no. 11. Washington, D.C.: U.S. Government Printing Office.

Spady, W. (1971). Dropouts from higher education: An interdisciplinary review and synthesis. Interchange, 1, 64-85.

Summerskill, J. (1962). In N. Sanford (Ed.), The American College. New York: Wiley.

Tinto, V. (1975). Dropouts from higher education: a theoretical synthesis of recent research. Review of Educational Research, 45, 89-125.

Tinto, V. (1993). Leaving college: Rethinking the causes and cures of student attrition. Chicago: The University of Chicago Press.