381 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
with high scholastic aptitudes should have relatively more academic potential and would be less likely to exit
before graduation see Spady, 1970. It is also possible, however, that there are differences in what the ACT
exam score and high school rank percentile typically used as ability proxies are measuring. ACT scores mea-
sure ability within the pool of all entrance exam test tak- ers and if students with high ACT scores have more
schooling options, they may be prone to leave insti- tutions if they perceive it to be a bad academic fit. High
school rank percentile reflects variation within one’s high school and after controlling for other ability
measures may also be thought of as a proxy for stud- ent effort.
Also included is a variable indicating the number of transfer credits of University matriculants. Students who
have had some prior college experience they could have taken college course work while in high school should
be better able to adjust to college life, be more likely to become academically and socially integrated Tinto,
1975, and, therefore, be more likely to persist and graduate than students entering college for the first time.
There is at least one alternative hypothesis though: stu- dents who enter with previous college course work may
be “movers” who are searching for the right institutional fit and are therefore more likely to leave.
Institution-related variables are included to examine the effects of student interactions with the institution.
The initial collegiate unit of enrollment of a student is included to examine whether there are college specific
environmental factors that help to explain student depar- ture from college. Cross-sectional designs have found
that students in the Institute of Technology IT are less likely to drop out and more likely to graduate than Col-
lege of Liberal Arts CLA students Matross DesJard- ins, 1994. General College GC students,
3
on the other hand, appear to have lower chances of graduating and
higher chances of dropping out than students enrolled in other collegiate units. It is not clear, however, that these
subgroup results garnered from aggregate graduation and retention rate data will hold after accounting for other
factors usually found to be related to student departure. Also, even though students may change collegiate units
during their academic careers, we were only interested in their initial college of enrollment because most student
departure at this institution takes place from these units. In future studies we will examine how transferring
among colleges allowing collegiate unit to vary by term affects student departure decisions, especially at the
upper division.
3
General College enrolls underprepared and other special needs students and prepares them for transfer to schools and
colleges of the University and other higher education insti- tutions. General College does not grant degrees.
A student’s grade point average for each term of enrollment is calculated and included to control for vari-
ations in academic performance. One’s grade point aver- age is also hypothesized to be the reward for successful
academic achievement. Financial aid offered is included for each term and dissagregated into its component parts:
loans, scholarships, grants, workstudy earnings, and earnings as a student employee other than workstudy
on campus. Typically, financial circumstances are con- sidered environmental variables because they are out of
the control of the institution Bean, 1981. Since state and institutional policymakers do have some direct con-
trol over the way aid is distributed, aid variables are con- sidered organizational in this model. For instance, grants
are included separately from scholarships in order to examine whether there are differences in how these
sources of aid independently affect student departure [St John and Starkey 1995 discovered that financial sub-
sidies have differential effects]. To examine these effects in more detail we plan to disaggregate grants into federal
and state components so that we can evaluate whether these aid packages have differential effects on student
departure.
Finally, a dummy variable is included indicating whether the student is an athlete during each term of
enrollment. Athletes’ rates of dropout and graduation have been a source of much discussion nationally and at
the study institution. Therefore a variable distinguishing athletes from the general student population is included
in an effort to better understand the longitudinal nature of athletes’ academic progress Naughton, 1996.
5. The empirical results
4
When modeling each of the events of interest we began by estimating “naı¨ve” models and made them
more complex as we progressed. Initially, time-constant coefficient TCC models without unmeasured hetero-
geneity controls were estimated. Then unobserved het- erogeneity controls were added to the TCC models to
determine whether the results varied. Next, a time-vary- ing coefficient TVC model without unobserved hetero-
geneity controls was estimated to examine how the intro- duction of time-varying coefficients affect the results.
Finally, we estimated TVC models with various para- metric and “flexible” heterogeneity variables to see how
4
Each table of results includes the estimated coefficients, their asymptotic standard errors in parentheses, and the log
likelihood, which is useful in assessing the model fit. Unless otherwise noted, any discussion of the effect of a variable is
conditional on having controlled for the effects of all other vari- ables included in the model.
382 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
controlling for unobserved factors affects the robustness of the results.
5.1. Modeling time to first stopout As mentioned above, we initially estimated a single
risk model of time to first stopout. The simplest model estimated was the TCC model without a control for
unobserved heterogeneity. This model was used as a benchmark since most event history models of student
departure done to date have been similar to this specifi- cation Willett Singer, 1991; Singer Willett, 1991;
DesJardins, 1993; Ronco, 1996. We then estimated a TCC model but included a gamma distributed unob-
served heterogeneity control. We then estimated TCC models that assumed various mass point mixing distri-
butions for the unobserved heterogeneity term. The esti- mates produced by the TCC models did not vary to a
great degree. With regard to model fit, the likelihood dropped as the model specification went from time con-
stant with no control for unobserved heterogeneity L 5 2
8589 to a TCC three mass point model L 5 2 8466. These results suggest that the three mass point specifi-
cation is more robust than the TCC model with no het- erogeneity controls.
5
5.2. Adding time-varying regressors to the stopout models
It is unrealistic to think that the effects of factors that explain student departure from college are invariant with
respect to time, therefore we estimated TVC models. As was done for the TCC models, various distributional
assumptions about the sources of unmeasured heterogen- eity are specified as robustness checks.
The first TVC model estimated included the same regressors as the TCC models described above, although
some variables were now permitted to vary over time. Based on model fit, the benchmark TVC model was pre-
ferred to the TCC benchmark model P , 0.001; L
TVC
5 2 8331; L
TCC
5 2 8589 with 84 d.f.. Generally, a
comparison of the results obtained from the TCC model with those estimated by the TVC model indicates that
the regressors have effects on first stopout probability that change over time. Thus, adding a time dimension
improves our understanding of first stopout.
5.3. Including controls for unobserved heterogeneity Next we added unobserved heterogeneity controls to
the TVC model. The results displayed in Table 2 are produced by a TVC model that assumes a two mass point
5
Not all results of the numerous models we estimated are included herein but are available from the authors on request.
mixing control for unobserved heterogeneity we also estimated a gamma model but the two mass point model
was preferred based on model fit. Our discussion of the results will be based on the preferred model and major
differences between the gamma model and two mass point mixing model will be noted.
5.4. First stopout results We found that Asian students are less likely to stop
out in year one than their white counterparts. This first year effect was masked, however, in the TCC model
results. African-American students are more likely than white students to stop out in years three and four.
ChicanoHispanics, on the other hand, have stopout prob- abilities no different than those of their white counter-
parts when we control for unobservables. While Ottinger 1991 finds that males are more likely to stop out than
females, we find that females stopout risks are not stat- istically different than those of males except in year four.
The year-four effect is not apparent, however, until the control for unobserved heterogeneity is included. The
effects of being disabled also vary depending on the inclusion of a control for heterogeneity. In addition to
the year-four effect found when no unobservable control was included, a year-two disability effect appears when
unobserved heterogeneity takes a gamma or mass point mixing form. Of particular interest is that the sign of the
coefficient changes between years two and four: disabled students are less likely than the general population to
stop out in year two, but are more likely to leave for the first time in year four.
Examining our control for home location, the only sig- nificant effect is that students from tuition reciprocity
states are less likely than non-Minnesota, non-recip- rocity students to leave in year one. Ramist 1981
found that distance from campus to a student’s home is negatively associated with persistence.
Students who enter college later in life appear to be at higher risk of first stopout in years one and three than
individuals who enter the institution at a younger age. Again, the year-three effect becomes apparent only when
controls for heterogeneity are included.
Stopout probabilities also vary depending on the col- lege of initial enrollment. Compared with CLA students,
IT students are less likely to stop out in all but year one, and this effect tends to strengthen over time. Even after
controlling for included and unobserved variables, GC students are more likely to stop out in years one and
three than their CLA counterparts. The year-three GC effect may be important because it is the year in which
surviving GC students transfer to other degree granting colleges within the University. This year-three effect
suggests that GC students may be having problems mak- ing the transition to other collegiate units. If this hypoth-
383 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
Table 2 Estimates of first stopout for a time-varying coefficient model with two mass point mixing unobserved heterogeneity distribution
Variable Year 1
Year 2 Year 3
Year 4 Year 5 1
CoefficientSE Asians
2 0.4200
2 0.3209
2 0.0334
0.2116 0.1105
0.224 0.235
0.314 0.329
0.25 Blacks
2 0.2561
0.2574 0.7769
0.8060 2
0.4296 0.309
0.322 0.363
0.387 0.417
Hispanics 2
0.0554 2
0.1899 0.6951
0.1990 0.1962
0.583 0.467
0.522 0.659
0.679 Females
0.0125 0.0741
0.0328 0.2230
0.1047 0.083
0.084 0.113
0.131 0.124
Disabled 2
0.4149 2
0.5251 0.0451
0.5800 2
0.0606 0.281
0.284 0.305
0.303 0.353
ACT score 0.0202
0.0002 0.0185
0.0433 0.0562
0.01 0.011
0.015 0.017
0.017 HS rank
2 0.0026
2 0.0067
2 0.0080
2 0.0054
2 0.0065
0.002 0.003
0.004 0.004
0.004 Metro area
2 0.2373
2 0.0718
0.0146 2
0.1639 2
0.2561 0.154
0.178 0.257
0.261 0.221
Enrollment age 0.0984
0.0498 0.0723
0.0211 0.0190
0.028 0.041
0.042 0.065
0.049 Institute of Technology
2 0.1264
2 0.4511
2 0.4114
2 0.6348
2 0.6525
0.124 0.129
0.16 0.172
0.152 General College
0.4055 0.0321
0.3334 0.3633
0.1072 0.14
0.15 0.202
0.243 0.246
Transfer credits 0.0191
0.0052 0.0024
0.0099 0.0115
0.005 0.007
0.009 0.009
0.01 Out of state MN
2 0.1117
0.1507 0.0252
0.3048 0.1309
0.177 0.202
0.286 0.283
0.258 Reciprocity state
2 0.3784
0.0461 2
0.0048 0.2234
0.2539 0.185
0.199 0.29
0.29 0.247
Cum GPA 2
0.0102 2
0.0082 2
0.0055 2
0.0042 2
0.0023 0.0004
0.0004 0.0005
0.0005 0.0005
Athlete 2
0.4814 2
1.1798 2
0.2356 2
0.1187 0.9947
0.375 0.471
0.654 0.445
0.675 Loan
0.0000 2
0.0002 2
0.0004 2
0.0004 2
0.0004 0.0001
0.0001 0.0001
0.0001 0.0001
Earnings 2
0.0003 2
0.0003 2
0.0003 2
0.0003 2
0.0002 0.0002
0.0001 0.0001
0.0001 0.0001
Scholarship 2
0.0008 2
0.0006 2
0.0010 2
0.0001 2
0.0001 0.0003
0.0003 0.0004
0.0002 0.0002
Grants 0.0001
2 0.0001
0.0003 0.0000
2 0.0002
0.0001 0.0002
0.0002 0.0002
0.0002 Workstudy
2 0.0002
2 0.0002
2 0.0004
2 0.0004
0.0005 0.0001
0.0001 0.0004
0.0004 0.0004
Likelihood L 528316. P , 0.05; P , 0.01.
esis is true, it may help to explain why so few GC stu- dents eventually graduate from the University.
Students who perform better in college have been found to be more likely to persist Pascarella Teren-
zini, 1980, 1991; Cabrera et al., 1993. Our analysis also indicates that students with high grade point averages are
less likely to stop out. Our analysis, however, provides more detail about how this effect varies over time. Stu-
dents who perform well in college as indicated by higher GPAs are less likely to stop out over the seven
years observed, but the strength of this relationship tends to dissipate over time.
Contrary to popular belief, athletes at the study insti- tution tend to have lower probabilities of first stopout
than do non-athletes, but the result is only significant in year two. This finding is still important since there is so
little evidence available on the effect of athletic status on educational attainment Pascarella Terenzini, 1991.
384 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
Students who enter the institution with some college experience are more likely to stop out in year one than
students who do not have transfer credits. There may be some social or academic adjustment period for students
from other institutions which may explain this result. This result may, however, be counterintuitive if we
believe that students with some college work should already be adjusted to college life. There is at least one
alternative hypothesis though: students who enter with previous college course work may be “movers” who are
searching for the right institutional fit and are therefore more likely to leave.
Finally, the effect of the offer of financial aid appears to vary temporally and by type of aid offered. In every
year, conditional on receiving an aid offer, students who earn extra money by being employed on campus
Earnings are less likely to stop out. This result may reflect the effect of social integration on student stopout,
in that students who work on-campus have closer ties to the college community than do students who do not work
on-campus. Even after accounting for other factors, scholarships appear to decrease student stopout in years
one through three. Grants, however, do not appear to have a statistically significant independent effect on first
stopout probabilities. The effect of loans on first stopout is statistically significant and negative in all years except
year one. Workstudy apparently helps students become acclimated to the institution in year one thereby decreas-
ing the chances of stopout, but has no significant effect in later years.
There are several reasons why our use of disaggre- gated financial aid offers is an important contribution.
Many studies of student attrition use attitudinal data to capture the effects of students’ financial situations. These
data are usually collected from surveys done at a single point in time upon matriculation. It is often unclear,
however, what these attitudinal variables measure
6
and their reliability may be questionable if matriculating stu-
dents have a poor understanding of the financial conse- quences of college. Using actual levels of disaggregated
financial aid allows us to examine the longitudinal and differential effects of each type of aid. Previous studies
that used actual financial aid have typically included a dichotomous measure receive aiddid not or have
included a single continuous construct total aid paid. Dichotomization of aid into a yesno measure ignores the
substantial variability in the amount of aid paid to stu- dents and masks the impact that differential amounts of
aid have on student departure. Using a total aid measure ignores the differential effects that various types of aid
have on student decision-making. Changes in the way
6
Attitudinal measures designed to capture the financial con- siderations of matriculating students may also be contaminated
by non-pecuniary effects.
aid is being distributed by institutions the increasing use of financial aid “leveraging”, and recent proposals by
the federal government to change financial aid distri- bution, make it increasingly important for researchers to
examine how aid amounts and types change student departure behavior over time.
In order to provide a graphical description of the varia- bility in first stopout hazards we present Fig. 2. This
graph compares the longitudinal hazard rates for two hypothetical groups of students: the first with character-
istics that would indicate a high risk of a first stopout, the second for students with very low first stopout prob-
abilities.
7
Low risk students are likely to remain continu- ously enrolled though term 12 year four which implies
graduation in four years. The spikes in the hazard for low risk students in terms 15 and 18 are due to the risk
set diminishing because of the graduation of the majority of these students. Since there are very few low risk stu-
dents remaining after year four, any first stopout activity will have a relatively large impact on the hazard rate.
Conversely, the high risk group show propensities to leave early in their academic careers. For instance, in
their first year the high-risk group has over a 50 chance of having a first stopout the summation of term 1–3
hazards whereas the low risk groups’ cumulative hazard is only 0.5. Thus, the high risk group is about 100
times more likely to have a first stopout in year one than the low risk group. Also, notice the spikes in the hazards
between the spring and fall terms terms 3, 6, 9, …. Students who are likely to leave the institution are much
more likely to do so after their spring term.
Fig. 2. Comparison of the hazard of first stopout.
7
Both groups are defined as white, male, with no disabling conditions, from the Twin Cities metropolitan area, entered col-
lege without transfer credits, and are non-athletes. The low high risk group has ACT scores of 30 10, high school rank
percentile of 98 40, are 18 29 years old, matriculated in the Institute of Technology General College, have 4.00 2.00
grade point averages in each term of enrollment, and received 2000 0 in scholarship aid for each term of enrollment.
385 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
5.5. Modeling time to dropout The same model building process used to study first
stopout was also used to study dropout behavior. First, TCC models were estimated with and without controls
for unobserved heterogeneity. Then TVC models with no unobserved heterogeneity controls, and gamma and
mass point mixing distributional assumptions were speci- fied. As was demonstrated when stopouts were modeled,
the advantages of a longitudinal approach coupled with controls for unobserved characteristics are evident. Our
discussion of the dropout results will focus on the pre- ferred based on likelihood ratio tests TVC two mass
point mixing model.
African-American students have higher dropout pro- pensities than white students in year three. This result
contrasts with the conventional wisdom at the University of Minnesota that African-American students are at
much higher risk of dropout than other students through- out their academic careers. There are no statistically sig-
nificant
differences between
ChicanoHispanic Hispanic and white students, even after controlling for
unobservables. Again, cross-sectional analyses at the study institution typically indicate that ChicanoHispanic
students have relatively low rates of retention and high rates of dropout.
No gender differences are found and this result holds across all the TVC models that include unobserved het-
erogeneity controls. Based on cross-sectional data from the study institution, females appear to be less likely to
drop out early in their academic careers but more likely than males to leave later in their academic tenure. The
ChicanoHispanic and gender results noted above ques- tion the wisdom of using simple retention and graduation
statistics to make policy decisions.
Interestingly, disabled students are less likely than the general population to leave in year one but are much
more likely to exit in year four. No other regressor included in the model shows a statistically significant
sign reversal. Since there are few disabled students in the sample the result may be due to small numbers in
year four. Given the complex circumstances faced by disabled students, however, a more detailed analysis of
this year-four effect is in order.
With regard to the variables used as admissions cri- teria, the effects of high school rank percentile and ACT
test score on dropout differ greatly from the effects observed when modeling the stopout process. High
school rank percentile has no statistically significant effect on dropout once other factors are controlled for
including ACT test score and grade point average. In the stopout model, by contrast, students with relatively
high high school rankings are less likely to stop out in years two, three, and five through seven. In the dropout
model, students who score high on the ACT test are less likely to depart in year two than are students with lower
ACT scores. This result, too, is markedly different from the result suggested by the stopout model: the ACT vari-
able is positively associated with first stopout in years one and four through seven.
These results may be at odds with what one would expect based on simple correlations between ACT score
and high school rank percentile and stopout or dropout. These results may be due to the fact that multivariate
techniques like event history models allow us to examine the independent effects of explanatory variables whereas
simple correlations do not. For instance, ACT may be a proxy for ability and, as mentioned above, high school
rank percentile a proxy for effort. Or, the results we observe could be due to the difficulty in interpreting the
independent effects of ACT score and high school rank percentile after conditioning on grade point average. In
order to investigate the latter, we re-estimated the stopout model but excluded grade point average. The high school
rank percentile variable was negative and highly signifi- cant t-statistics ranging from 7.0 in year one to 4.2 in
years five through seven for each period whereas ACT score had a negative and significant coefficient in year
two only. Thus, it appears that term specific grade point averages and high school rank percentile are both proxies
for student ability.
A student’s original home location has differential effects on dropout probabilities. In years one through
three, students from the Twin Cities metropolitan area are less likely to drop out than the reference group non-
Minnesotan, non-tuition reciprocity agreement students. Students from out-state Minnesota Minnesotan’s from
outside the Twin Cities metropolitan area and from tui- tion reciprocity states are less likely than the reference
group to leave in year one.
The results presented in Table 3 indicate that com- pared with their white counterparts, Asian American stu-
dents are less likely to drop out in their first two years of enrollment only. This result is important because the
institution’s retention statistics indicate that Asian stu- dents are less likely to drop out throughout their aca-
demic careers.
Age at enrollment is positively associated with dro- pout in year one and year two in the gamma model,
suggesting that older students have a difficult time adjusting to their academic careers. This may be due to
a multitude of time constraints since older students are more likely to be married, working in full-time jobs, and
have other commitments. Students who enter an insti- tution after completing some college course work as
indicated by Transfer Credits are less likely to perma- nently exit the institution in year two than are students
who enter as “true” college freshmen i.e. with no pre- vious college work. This result seems intuitive given
that familiarity with college is an advantage, especially on a large campus.
Even after accounting for ability and other included
386 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
Table 3 Estimates of dropout for a time-varying coefficient model with two mass point mixing unobserved heterogeneity distribution
Variable Year 1
Year 2 Year 3
Year 4 Year 5 1
CoefficientSE Asians
2 0.5407
2 0.5485
0.0036 0.2109
2 0.4454
0.298 0.332
0.451 0.461
0.35 Blacks
2 0.5155
0.3391 0.8647
0.6540 2
0.5597 0.416
0.414 0.5
0.678 0.419
Hispanics 2
0.7277 2
0.0744 1.0523
0.0649 0.5551
1.09 0.589
0.717 1.173
0.715 Females
0.0746 2
0.0342 0.0441
0.2340 2
0.0057 0.11
0.122 0.179
0.198 0.148
Disabled 2
1.4567 2
0.6022 0.4283
1.1010 0.1812
0.574 0.384
0.405 0.443
0.487 ACT score
0.0104 2
0.0314 2
0.0250 0.0282
0.0228 0.014
0.015 0.024
0.026 0.02
HS rank 0.0035
0.0018 2
0.0047 0.0015
2 0.0041
0.003 0.004
0.006 0.006
0.004 Metro area
2 0.6783
2 0.6797
2 0.6502
2 0.2425
2 0.1043
0.187 0.217
0.335 0.417
0.282 Enrollment age
0.1128 0.0923
0.0830 2
0.0077 2
0.0098 0.041
0.054 0.066
0.113 0.06
Institute of Technology 2
0.1946 2
0.4382 2
0.2679 2
0.5869 2
0.4451 0.167
0.19 0.251
0.262 0.191
General College 0.6369
0.2359 0.4470
0.9448 0.1907
0.187 0.214
0.33 0.351
0.273 Transfer credits
2 0.0005
2 0.0649
2 0.0188
0.0066 0.0039
0.008 0.016
0.017 0.013
0.013 Out of state MN
2 0.3652
2 0.2821
2 0.0928
0.2109 0.2644
0.216 0.253
0.371 0.459
0.333 Reciprocity state
2 0.4116
2 0.2445
2 0.2830
0.2633 0.1240
0.215 0.249
0.381 0.456
0.3 Cum GPA
2 0.0121
2 0.0088
2 0.0051
2 0.0027
2 0.0009
0.0006 0.0007
0.0009 0.001
0.0006 Athlete
2 0.7321
2 1.6550
2 0.1799
2 2.6963
1.2603 0.615
0.674 0.94
1.756 0.941
Loan 0.0002
2 0.0001
2 0.0005
2 0.0003
2 0.0004
0.0001 0.0002
0.0002 0.0002
0.0001 Earnings
2 0.0003
2 0.0004
2 0.0002
2 0.0004
2 0.0002
0.0002 0.0001
0.0001 0.0001
0.0001 Scholarship
2 0.0005
2 0.0003
2 0.0016
2 0.0002
0.0000 0.0003
0.0003 0.0008
0.0003 0.0002
Grants 0.0002
0.0000 0.0004
2 0.0002
0.0001 0.0002
0.0002 0.0003
0.0003 0.0002
Workstudy 2
0.0003 2
0.0002 2
0.0003 2
0.0007 0.0003
0.0001 0.0002
0.0005 0.0008
0.0005 Likelihood L 524905. P , 0.05; P , 0.01.
characteristics, students who enter the Institute of Tech- nology at matriculation are less likely to drop out than
CLA students in all years but one and three. On the other hand, GC students are more likely to leave in year one
and year four than their CLA counterparts. The year- four effect suggests that GC students are having trouble
adjusting to the colleges they eventually transfer to. These results conform to other studies done within the
University indicating that there are dropout problems with GC students DesJardins Pontiff, 1996. The
institution may want to more closely examine whether this group of students is being adequately served by
being admitted to the University andor improve their efforts to help these students make a successful transition
to other colleges within or outside the University.
Grade point average has the expected negative relationship with dropout, but the effect appears to wane
as time passes i.e. the absolute value of the coefficients
387 S.L. DesJardins et al. Economics of Education Review 18 1999 375–390
get smaller from year one through year five plus. Thus, getting good grades appears to have a relatively stronger
impact on reducing the chances of dropout in year one than it does in later years of one’s academic career. This
result suggests that monitoring grades early in a student’s academic career may be an effective retention strategy.
Student-athletes are less likely to leave the institution in year two than students in general. Not found in this
study was an “eligibility effect” where student-athletes were found to have higher dropout probabilities in year
five when many of them lose their athletic eligibility event history research done on the 1984 and 1985
cohorts at the study institution displayed this effect; see DesJardins, 1993 or DesJardins et al., 1994. When ana-
lyzing more recent cohorts we will monitor how athletic status affects dropout probabilities in an effort to be able
to generalize about this important subgroup of students.
Financial factors related to dropout have very different time patterns than the financial factors related to first sto-
pout. Whereas loans, earnings, and scholarships gener- ally reduce the stopout probabilities, they do not appear
to have as profound an effect on dropout behavior. Loans are most likely to reduce dropout in year three when
many students transfer and in the later years five plus. Student employment effects are quite constant and
reduce dropout in years two and four through seven. Work-study also reduces dropout probabilities, but only
in year one. The results found for work-related variables suggest that there may be some socializing benefit con-
nected to certain types of work-related financial aid. Scholarships, in particular, are helpful in reducing dro-
pout in year three when students are most likely to trans- fer to upper division courses and programs. Although
grants may be useful in attracting students, they do not have a significant independent effect on student dropout
behavior in this sample. Given that we find differences in the effects of scholarships and grants, it may not be
appropriate to combine the two and use it as a single construct. However, more study is needed on how these
sources of aid operate.
5.6. Testing the robustness of the definition of dropout We defined dropout in two different ways in order to
determine whether the results vary depending on how much time a student was “given” to reenroll. Comparing
the results of the TVC mass point mixing dropout model to the preferred TVC mass point mixing “censored”
dropout model indicates that the results are trivially dif- ferent. The “censored” dropout results display a year-two
effect for age at enrollment but no two-year age effect was found in the initial dropout model results. This find-
ing merely strengthens our hypothesis that older students are having a difficult time early in their academic
careers. Ahlburg et al. 1997 found similarly robust findings in their study of dropout using a national data-
set. 5.7. Modeling competing risks: testing the robustness
of the stopout model The independent
risks models
presented above
assumed first stopout and dropout were uncorrelated with graduation. If the single outcome being modeled in this
study first stopout or dropout and graduation are not independent events, the likelihood separability no longer
holds and the events must be jointly estimated. In this study we estimate a competing risks model that allows
for the possibility of correlated risks. Allowing for corre- lated risks is an important contribution because it is
unlikely that included regressors capture all the co-deter- minants of first stopout and graduation behavior.
The purpose of estimating a competing risks model of first stopout and graduation is to test whether the single
risk stopout results presented above are sensitive to the model specification. It may be that the single risks sto-
pout model is a misspecification because we are inad- equately controlling for the interdependence of stopout
and graduation. The stopout estimates obtained from the preferred competing risks model two mass point mixing
distribution are virtually identical to the estimates pro- duced by a single risks specification. Thus, using a single
risks specification to estimate first stopout is appropriate for this particular sample.
6. Implications, limitations, and future research
