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Educational Attainment as Process: Using Hierarchical Discrete-Time Event History Analysis to Model Rate of Progress

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Abstract

Variables that address student enrollment patterns (e.g., persistence, enrollment inconsistency, completed credit hours, course credit load, course completion rate, procrastination) constitute a longstanding fixture of analytical strategies in educational research, particularly research that focuses on explaining variation in academic outcomes. However, nearly all measures of enrollment patterns are handicapped by untested assumptions about a more fundamental measure, namely students’ rate of progress. In this paper, I first explain how a variety of widely used measures of enrollment patterns are inextricably linked to students’ rate of progress. I then describe a method of modeling mathematically students’ rate of progress that employs hierarchical (multilevel) discrete-time event history analysis of repeated events. I conclude with an empirical example of the application of this method in which I test several hypotheses concerning students’ rate of progress through the remedial math sequence toward the outcome of college-level math competency. In addition to the utility of the method that is proposed here, the issues discussed in this paper have important practical implications for institutional research, particularly with respect to the use of the various measures of enrollment patterns to explain variation in students’ attainment.

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Notes

  1. The term persistence sometimes is treated as an abbreviation for persistence to degree attainment (e.g., Baker and Velez 1996). Although persistence and attainment are conceptually interrelated (Horn and Berger 2004), they are operationally distinct (American Council on Education 2003). Thus, I differentiate between students’ persistence and the result of persistence, which may or may not include the completion of a credential.

  2. The terms retention, attrition, departure, and dropout can be ambiguous because they often are measured with respect to a single institution (e.g., Murtaugh et al. 1999). Yet, many students persist in their postsecondary pursuits while moving from one college to another (Adelman 1999; Bach et al. 2000; Bahr 2009; Pascarella and Terenzini 2005; Porter 2003; Rab 2004).

  3. Explaining variation in academic attainment is the principal objective underlying research on, and the use of, measures of enrollment patterns, but it is not the only objective. Among the other objectives is managing/predicting institutional enrollment (Cabrera et al. 1993).

  4. Explanatory value refers to the extent to which variation in a given outcome may be “explained” by its covariation with a given predictor.

  5. The complementary log–log function sometimes is recommended in place of the logit for discrete-time event history analysis (Allison 1982, 1995; Jenkins 2005), but the logit is discussed here due to wider familiarity, use, and availability in software packages.

  6. In terms of the language that typically is used to describe every history analysis, the completion of these hypothetical steps may be conceptualized as a series of nonreversible (one-way) transitions in the direction of some academic outcome of interest to the researcher. For example, the transition from freshman to sophomore is a step toward the outcome of completing a postsecondary degree. Note, however, that the method of modeling rate of progress that is described here does not require that the multiple steps (or transitions) be ordered with respect to one another, so long as these steps are essentially equivalent to one another.

  7. Note that, at the beginning of the observation period defined for this study, there were 107 distinct community colleges in California, of which 104 were semester-based. There are now 109 community colleges, of which 106 are semester-based.

  8. Of the original cohort of 167,982 students, 47.42% did not enroll in any substantive math coursework at any time during the six-year observation period, 1.11% enrolled exclusively in vocational math coursework, and 51.47% enrolled in at least one nonvocational math course.

  9. A “missing” first math grade is one that a college failed to report or reported as “in progress”.

References

  • Adelman, C. (1999). Answers in the tool box: Academic intensity, attendance patterns, and bachelor’s degree attainment. Washington, DC: Office of Educational Research and Improvement. ERIC ED431363.

    Google Scholar 

  • Agresti, A., & Finlay, B. (1997). Statistical methods for the social sciences. Upper Saddle River, New Jersey: Prentice Hall.

    Google Scholar 

  • Allison, P. D. (1982). Discrete-time methods for the analysis of event histories. Sociological Methodology, 13, 61–98.

    Article  Google Scholar 

  • Allison, P. D. (1984). Event history analysis: Regression for longitudinal event data. Thousand Oaks, California: Sage.

    Google Scholar 

  • Allison, P. D. (1995). Survival analysis using the SAS system: A practical guide. Cary, North Carolina: SAS Institute Inc.

    Google Scholar 

  • American Council on Education. (2003). Issue brief: Student success: Understanding graduation and persistence rates. Washington, DC: American Council on Education.

    Google Scholar 

  • Arulampalam, W., Naylor, R. A., & Smith, J. P. (2004). A hazard model of the probability of medical school dropout in the UK. Journal of the Royal Statistical Society, Series A, 167, 157–178.

    Google Scholar 

  • Bach, S. K., Banks, M. T., Kinnick, M. K., Ricks, M. F., Stoering, J. M., & Walleri, R. D. (2000). Student attendance patterns and performance in an urban postsecondary environment. Research in Higher Education, 41, 315–330.

    Article  Google Scholar 

  • Bahr, P. R. (2007). Double jeopardy: Testing the effects of multiple basic skill deficiencies on successful remediation. Research in Higher Education, 48, 695–725.

    Article  Google Scholar 

  • Bahr, P. R. (2008a). Does mathematics remediation work?: A comparative analysis of academic attainment among community college students. Research in Higher Education, 49, 420–450.

    Article  Google Scholar 

  • Bahr, P. R. (2008b). Cooling Out in the community college: What is the effect of academic advising on students’ chances of success? Research in Higher Education, 49, 704–732.

    Article  Google Scholar 

  • Bahr, P. R. (2009). College hopping: Exploring the occurrence, frequency, and consequences of lateral transfer. Community College Review, 36, 271–298.

    Article  Google Scholar 

  • Bahr, P. R. (forthcoming). Preparing the underprepared: An analysis of racial disparities in postsecondary mathematics remediation. Journal of Higher Education.

  • Baker, T. L., & Velez, W. (1996). Access to and opportunity in postsecondary education in the United States: A review. Sociology of Education, 69(extra issue), 82–101.

    Google Scholar 

  • Barber, J. S., Murphy, S. A., Axinn, W. G., & Maples, J. (2000). Discrete-time multilevel hazard analysis. Sociological Methodology, 30, 201–235.

    Google Scholar 

  • Beekhoven, S., De Jong, U., & Van Hout, H. (2002). Explaining academic progress via combining concepts of integration theory and rational choice theory. Research in Higher Education, 43, 577–600.

    Article  Google Scholar 

  • Beekhoven, S., De Jong, U., & Van Hout, H. (2003). Different courses, different students, same results?: An examination of differences in study progress of students in different courses. Higher Education, 46, 37–59.

    Article  Google Scholar 

  • Berger, J. B., & Milem, J. F. (1999). The role of student involvement and perceptions of integration in a causal model of student persistence. Research in Higher Education, 40, 641–664.

    Article  Google Scholar 

  • Burley, H., Butner, B., & Cejda, B. (2001). Dropout and stopout patterns among developmental education students in Texas community colleges. Community College Journal of Research and Practice, 25, 767–782.

    Article  Google Scholar 

  • Cabrera, A. F., Burkum, K. R., & La Nasa, S. M. (2003). Pathways to a four-year degree: Determinants of degree completion among socioeconomically disadvantaged students. Paper presented at the annual meeting of the Association for the Study of Higher Education, Portland, Oregon. ERIC ED482160.

  • Cabrera, A. F., Nora, A., & Castaneda, M. B. (1993). College persistence: Structural equations modeling test of an integrated model of student retention. Journal of Higher Education, 64, 123–139.

    Article  Google Scholar 

  • Calcagno, J. C., Crosta, P., Bailey, T., & Jenkins, D. (2007). Stepping stones to a degree: The impact of enrollment pathways and milestones on community college students outcomes. Research in Higher Education, 48, 775–801.

    Article  Google Scholar 

  • Cofer, J., & Somers, P. (2001). What influences student persistence at two-year colleges? Community College Review, 29, 56–76.

    Article  Google Scholar 

  • DesJardins, S. L., Ahlburg, D. A., & McCall, B. P. (2002). A temporal investigation of factors related to timely degree completion. Journal of Higher Education, 73, 555–581.

    Article  Google Scholar 

  • Fenske, R. H., Porter, J. D., & DuBrock, C. P. (2000). Tracking financial aid and persistence of women, minority, and needy students in science, engineering, and mathematics. Research in Higher Education, 41, 67–94.

    Article  Google Scholar 

  • Glynn, J. G., & Miller, T. E. (2002). A simplified approach to monitoring and reporting student transitions with a focus on retention and graduation rates. College & University, 78, 17–23.

    Google Scholar 

  • Goldstein, H. (2003). Multilevel statistical models. London: Hodder Arnold.

    Google Scholar 

  • Hagedorn, L. S., & Lester, J. (2006). Hispanic community college students and the transfer game: Strikes, misses, and grand slam experiences. Community College Journal of Research and Practice, 30, 827–853.

    Article  Google Scholar 

  • Hagedorn, L. S., Maxwell, W. E., Cypers, S., Moon, H. S., & Lester, J. (2007). Course shopping in urban community colleges: An analysis of student drop and add activities. Journal of Higher Education, 78, 464–485.

    Article  Google Scholar 

  • Horn, L., & Berger, R. (2004). College persistence on the rise?: Changes in 5-year degree completion and postsecondary persistence rates between 1994 and 2000 (NCES 2005-156). Washington, DC: National Center for Education Statistics.

    Google Scholar 

  • Hoyt, J. E. (1999). Remedial education and student attrition. Community College Review, 27, 51–73.

    Article  Google Scholar 

  • Hu, S., & St. John, E. P. (2001). Student persistence in a public higher education system: Understanding racial and ethnic differences. Journal of Higher Education, 72, 265–286.

    Article  Google Scholar 

  • Ishitani, T. T. (2003). A longitudinal approach to assessing attrition behavior among first-generation students: Time-varying effect of pre-college characteristics. Research in Higher Education, 44, 433–449.

    Article  Google Scholar 

  • Jenkins, S. P. (2005). Survival analysis. Unpublished manuscript, Institute for Social and Economic Research, University of Essex, Colchester, UK. http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/pdfs/ec968lnotesv6.pdf

  • Jensen, E. L. (1981). Student financial aid and persistence in college. Journal of Higher Education, 52, 280–294.

    Article  Google Scholar 

  • Johnson, I. Y. (2006). Analysis of stopout behavior at a public research university: The multi-spell discrete-time approach. Research in Higher Education, 47, 905–934.

    Article  Google Scholar 

  • Johnson, M., & Kuennen, E. (2004). Delaying developmental mathematics: The characteristics and costs. Journal of Developmental Education, 28, 24–29.

    Google Scholar 

  • Kahn, J. H., & Nauta, M. M. (2001). Social-cognitive predictors of first-year college persistence: The importance of proximal assessment”. Research in Higher Education, 42, 633–652.

    Article  Google Scholar 

  • Kalamatianou, A. G., & McClean, S. (2003). The perpetual student: Modeling duration of undergraduate studies based on lifetime-type educational data. Lifetime Data Analysis, 9, 311–330.

    Article  Google Scholar 

  • Kreft, I., & De Leeuw, J. (1998). Introducing multilevel modeling. Thousand Oaks, California: Sage.

    Google Scholar 

  • Leinbach, D. T., & Jenkins, D. (2008). Using longitudinal data to increase community college student success: A guide to measuring milestone and momentum point attainment. New York: Community College Research Center.

    Google Scholar 

  • Leppel, K. (2002). Similarities and differences between the college persistence of men and women. Review of Higher Education, 25, 433–450.

    Article  Google Scholar 

  • Lesik, S. A. (2007). Do developmental mathematics programs have a causal impact on student retention?: An application of discrete-time survival and regression discontinuity analysis. Research in Higher Education, 48, 583–608.

    Article  Google Scholar 

  • Long, J. S. (1997). Regression models for categorical and limited dependent variables. Thousand Oaks, California: Sage.

    Google Scholar 

  • Maxwell, W., Hagedorn, L. S., Cypers, S., & Moon, H. S. (2003). Course dropping and course completion: A new direction for community college student research. Paper presented at the annual meeting of the American Educational Research Association, Chicago, Illinois.

  • Milem, J. F., & Berger, J. B. (1997). A modified model of college student persistence: Exploring the relationship between Astin’s theory of involvement and Tinto’s theory of student departure. Journal of College Student Development, 38, 387–400.

    Google Scholar 

  • Murtaugh, P. A., Burns, L. D., & Schuster, J. (1999). Predicting the retention of university students. Research in Higher Education, 40, 355–371.

    Article  Google Scholar 

  • Napoli, A. R., & Wortman, P. M. (1998). Psychosocial factors related to retention and early departure of two-year community college students. Research in Higher Education, 39, 419–455.

    Article  Google Scholar 

  • Okun, M. A., Benin, M., & Brandt-Williams, A. (1996). Staying in college: Moderators of the relation between intention and institutional departure. Journal of Higher Education, 67, 577–596.

    Article  Google Scholar 

  • O’Toole, D. M., Stratton, L. S., & Wetzel, J. N. (2003). A longitudinal analysis of the frequency of part-time enrollment and the persistence of students who enroll part-time. Research in Higher Education, 44, 519–537.

    Article  Google Scholar 

  • Pascarella, E. T., & Terenzini, P. T. (2005). How college affects students, volume 2: A third decade of research. San Francisco, California: Jossey-Bass.

    Google Scholar 

  • Paulsen, M. B., & St. John, E. P. (2002). Social class and college costs: Examining the financial nexus between college choice and persistence. Journal of Higher Education, 73, 189–236.

    Article  Google Scholar 

  • Porter, S. R. (2003). Understanding retention outcomes: Using multiple data sources to distinguish between dropouts, stopouts, and transfer-outs. Journal of College Student Retention, 5, 53–70.

    Article  Google Scholar 

  • Powers, D. A., & Xie, Y. (2000). Statistical methods for categorical data analysis. San Diego, California: Academic Press.

    Google Scholar 

  • Rab, S. Y. (2004). Swirling students: Putting a new spin on college attrition. Doctoral dissertation manuscript, University of Pennsylvania. UMI # 3125888.

  • Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis and methods. Thousand Oaks, California: Sage.

    Google Scholar 

  • Robinson, R. (2004). Pathways to completion: Patterns of progression through a university degree. Higher Education, 47, 1–20.

    Article  Google Scholar 

  • Sandler, M. E. (2000). Career decision-making self-efficacy, perceived stress, and an integrated model of student persistence: A structural model of finances, attitudes, behavior, and career development. Research in Higher Education, 41, 537–580.

    Article  Google Scholar 

  • Scott, M. A., & Kennedy, B. B. (2005). Pitfalls in pathways: Some perspectives on competing risks event history analysis in education research. Journal of Educational and Behavioral Statistics, 30, 413–442.

    Article  Google Scholar 

  • Singer, J. D., & Willett, J. B. (1993). It’s about time: Using discrete-time survival analysis to study duration and timing of events. Journal of Educational Statistics, 18, 155–195.

    Article  Google Scholar 

  • Smith, D. B., & Tonidandel, S. (2003). Taking account of time: The application of event history analysis to leadership research. The Leadership Quarterly, 14, 241–256.

    Article  Google Scholar 

  • Stratton, L. S., O’Toole, D. M., & Wetzel, J. N. (2007). Are the factors affecting dropout behavior related to initial enrollment intensity for college undergraduates? Research in Higher Education, 48, 453–485.

    Article  Google Scholar 

  • Summers, M. D. (2003). ERIC review: Attrition research at community colleges. Community College Review, 30, 64–84.

    Article  Google Scholar 

  • Szafran, R. F. (2001). The effect of academic load on success for new college students: Is lighter better? Research in Higher Education, 42, 27–50.

    Article  Google Scholar 

  • Taniguchi, H., & Kaufman, G. (2005). Degree completion among nontraditional college students. Social Science Quarterly, 86, 912–927.

    Article  Google Scholar 

  • Titus, M. A. (2004). An examination of the influence of institutional context on student persistence at 4-year colleges and universities: A multilevel approach. Research in Higher Education, 45, 673–699.

    Article  Google Scholar 

  • Van Der Hulst, M., & Jansen, E. (2002). Effects of curriculum organisation on study progress in engineering studies. Higher Education, 43, 489–506.

    Article  Google Scholar 

  • Wang, W. (2001). Succeeding in transferable level math: The effects of procrastination and other variables. Paper presented at the annual meeting of the California Association for Institutional Research, Sacramento, California.

  • Willett, J. B., & Singer, J. D. (1991). From whether to when: New methods for studying student dropout and teacher attrition. Review of Educational Research, 61, 407–450.

    Google Scholar 

  • World Almanac and Book of Facts. (2007). New York, NY: Primedia Reference, Inc.

  • Yamaguchi, K. (1991). Event history analysis. Thousand Oaks, California: Sage.

    Google Scholar 

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Acknowledgments

I am indebted to Tim Brown, Willard Hom, Myrna Huffman, Tom Nobert, Mary Kay Patton, and Patrick Perry of the California Community College Chancellor’s Office for their assistance with the data employed in this study. I thank Elisabeth Bahr for her assistance with the editing of this manuscript. Finally, I am grateful to John C. Smart and the anonymous referees of Research in Higher Education for their respective recommendations concerning improving this work. An earlier version of this paper was presented at the 2008 Forum of the Association for Institutional Research.

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  1. Department of Sociology, Wayne State University, Detroit, MI, 48202, USA

    Peter Riley Bahr

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Bahr, P.R. Educational Attainment as Process: Using Hierarchical Discrete-Time Event History Analysis to Model Rate of Progress. Res High Educ 50, 691–714 (2009). https://doi.org/10.1007/s11162-009-9135-x

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