Completing the Three Stages of Doctoral Education: An Event History Analysis

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1 Res High Educ (2012) 53: DOI /s Completing the Three Stages of Doctoral Education: An Event History Analysis Frim D. Ampaw Audrey J. Jaeger Received: 9 February 2011 / Published online: 17 December 2011 Ó Springer Science+Business Media, LLC 2011 Abstract Doctoral programs have high dropout rates of 43% representing the highest among all post-baccalaureate programs. Cross sectional studies of doctoral students retention have showed the importance of financial aid in predicting degree completion. These studies however, do not estimate the labor market s effect on doctoral student retention and neglect the longitudinal nature of doctoral study and the multiple requirements that make doctoral education a three-stage process. This research study examines the effect of various factors, including financial aid and labor market conditions, on the likelihood that doctoral students will complete the three stages of doctoral education: transition, development, and research. The results show that although financial aid as a whole is important, the type of financial aid received is even more significant and has differential impacts on doctoral students retention at each stage. The study concludes that research assistantships have the highest likelihood of degree completion compared to students with other forms of financial support. Labor market conditions are also an important factor affecting doctoral student retention with higher expected earnings motivating doctoral students in the later part of their programs to complete their degrees. Keywords Doctoral students Retention Degree completion Event history analysis Only 41% of students enrolled in doctoral programs successfully complete their degree within 7 years and 57% within a 10-year period (Council of Graduate Schools (CGS) 2008). These completion rates vary by the field of study, gender, nationality, and the race/ ethnic background of the student. International students in engineering have the highest 10-year completion rates 70% (CGS 2008). Completion rates in masters and professional F. D. Ampaw (&) Department of Educational Leadership, Central Michigan University, 332 EHS Building, Mount Pleasant, MI 48858, USA A. J. Jaeger Department of Leadership, Policy and Adult & Higher Education, North Carolina State University, Raleigh, NC, USA

2 Res High Educ (2012) 53: degree programs, such as law and business, are over 80% (Ehrenberg and Mavros 1995). Medical education, which is somewhat comparable to doctoral education in terms of the length of study and the multiple requirements needed, has the highest graduation rates for post baccalaureate programs. In a medical degree program, 96% of students complete within 10 years (Association of American Medical Colleges (AAMC) 2007), and medical residency programs have completion rates between 83 and 94%, depending on the specialization (Dodson and Webb 2004; Van Zanten et al. 2002). Doctoral students are valuable to the research and teaching missions of many institutions. Doctoral students support faculty as research assistants and often carry a significant responsibility in seeing a research project to completion. In addition, doctoral students lead numerous sections of introductory and advanced courses. As undergraduate student enrollments increase, doctoral students are often called on to teach more courses and more students (Williams June 2011). High attrition rates imply that departments must recruit more students each year, and thus lose the experience and knowledge that continuing doctoral students bring to the classroom and research projects. Doctoral students who leave before completing their respective programs also lose their investment of time and money as well as suffer the emotional cost of non-completion (Ampaw and Jaeger 2010; Bowen and Rudenstine 1992; Lovitts 2001). Over the last few decades, retention and persistence research has focused mainly on undergraduate students (Pascarella and Terenzini 1991). However, as the above numbers indicate, doctoral retention and persistence is also a major problem, even more so if we consider that these are the students that have successfully navigated the challenges of undergraduate education. Several models (Girves and Wemmerus 1988; Nerad and Cerny 1991; Pascarella and Terenzini 1991; Pyke and Sheridan 1993; Tinto 1975, 1993) have been developed to analyze undergraduate retention and persistence; nonetheless, these approaches may not be as effective when applied to graduate students based on various issues. Undergraduate and graduate students differ in the respective goals for their degree as well as the tasks to complete that degree. To complete an undergraduate degree the primary task is course completion. On the other hand, to obtain a doctoral degree students complete courses, develop and propose research topics, conduct research, and report findings. This progression for doctoral students creates a systematic process that can be best described by different stages (Ampaw 2010; Tinto 1993). Factors affecting students ability to move through the completion of coursework into the proposal development stage will differ from the factors that are important in the completion and presentation of research (Tinto 1993). Previous studies on doctoral retention have generally ignored these stages of doctoral education due to a reliance on cross-sectional data (Berg and Ferber 1983; Girves and Wemmerus 1988; Nerad and Cerny 1991; Pyke and Sheridan 1993; Tinto 1993). Presenting only a snapshot of doctoral education, these studies do not consider how the variables within the study are affected by time. The few longitudinal studies available have either focused on descriptive statistics (Bowen and Rudenstine 1992) or limited the fields of study (Ehrenberg and Mavros 1995; Lott et al. 2009; Stiles 2003). Another limitation of existing literature is the narrow and restrictive focus on effects related to institutional and student characteristics on retention and persistence. Graduate education does not occur in isolation within institutions. Changes in the economy affect graduate students, particularly since the opportunity costs of attending graduate school are higher than pursuing an undergraduate degree. Thus, it is necessary to include labor market conditions in a persistence model. Ehrenberg (1991) theorized that the labor market factors that affect the decision to undertake and complete doctoral study are the forgone earnings

3 642 Res High Educ (2012) 53: that students will lose during the study period and the expected earnings they hope to obtain with their completed degree. Studies analyzed by Ehrenberg show that post-graduation earnings of doctorates in a particular field influence the supply of new doctorates into that field. Research has not addressed how changes in other labor market conditions, such as forgone earnings and unemployment rates, affect the persistence of doctoral students (Ampaw 2010). The purpose of this study was to examine the effects of labor market conditions and other student characteristics on retention and persistence of students at different stages of doctoral education. The framework for this study included factors that took into account the effect of changes in the students lifetime earnings, forgone earnings, and financial aid on three stages of doctoral education. The following research questions guided this study: (1) What factors affect the retention and persistence of doctoral students beyond 18 credits (typically 1 year of coursework)? (2) What factors affect the advancement to candidacy of doctoral students? (3) What factors affect on the completion of a doctoral degree? Theoretical Framework The framework for this research was based on a model of institutional doctoral persistence mapped across three stages as advocated by Tinto (1993) and Bowen and Rudenstine (1992). The model asserts that individual attributes, such as demographics and prior educational experiences, shape goals, commitments, and financial assistance of entering students (Tinto). External commitments (e.g., work and family) and financial resources also affect the parameters of the student s participation in graduate school, which is often discussed in terms of full-time or part-time enrollment. For example, students with family responsibilities and/or limited financial resources may choose to enroll part-time. These attributes and early orientations affect the institutional experience of students through their academic and social integration, particularly within a department or program. Thus parttime students may have limited interactions with faculty or peers as their time on campus is limited due to other commitments. The interim outcomes of academic and social integration in turn influence the movement of students from the transition stage [begin taking doctoral classes and adjusting to the differing expectations within graduate school] to the next phase, the development stage. Within the institutional context, students are having varying experiences with faculty, graduate/research assistantships, courses, and peers. In the development stage, doctoral students complete their coursework thus acquiring the skills needed to be a doctoral candidate and develop a specific research agenda. At this time, specific relationships develop with faculty. This stage usually ends with presentation of a dissertation proposal. The final stage is the research stage where students complete their research and defend their dissertation (Ampaw 2010). In the final stage, financial support and external commitments continue to be salient. Students may drop out at any stage for a variety of reasons. Tinto suggests that little empirical work has been conducted on his model nor have the variables been clearly operationalized to ascertain their impact. To understand the factors that may affect persistence and retention at the various stages, this study empirically tests some of Tinto s concepts in his longitudinal model of doctoral persistence as well as incorporates human capital variables. Doctoral students make a decision to re-enroll each semester and according to Tinto (1993), external factors will affect that decision. Enrollment behavior has been modeled to

4 Res High Educ (2012) 53: respond to changes in expected costs (e.g., financial aid) (Kane 1999; Paulsen 1998; McPherson and Schapiro 1991; St. John 1990). However, the literature largely ignores the effects of changes in expected benefits. For doctoral students changes in the expected benefits or costs of education will play a role in persistence decision making (Ehrenberg 1991). Including human capital theory in the conceptual framework of this study helps to encapsulate cost-benefit ideas and better explain the decision process of doctoral students. Economists and higher education researchers have used human capital theory to explain how and why individuals decide to invest in higher education (Becker 1962, 1964; Paulsen 2001). The theory postulates that individuals choose to pursue higher education when the benefits they expect from the investment exceed the expected costs. The expected benefits can be intrinsic (such as a sense of accomplishment) and/or extrinsic (such as expected future earnings). Doctoral students have already made the decision to attend; thus, their decision to exit the process, according to human capital theory, occurs when there is a change in either their benefits or costs. Changes could include lower forgone earnings as would be the case during a recession (Paulsen 2001) and measured through changes in labor market conditions. This study focuses on the extrinsic benefits and costs that affect a student s decision making process as intrinsic benefits and costs are individual in nature, difficult to adequately measure, and possibly lacking in policy implications. Further, the data set in this study did not include measures that could be used to model intrinsic costs. Human capital theory is helpful in understanding the financial aspects of the decisionmaking process, though it does not completely explain the complex processes involved in doctoral student retention, as it does not include the critical stages of a doctoral student s degree seeking process. Figure 1 presents the conceptual model guiding this study. The three stages of successful persistence transition, development, and research form the outcomes of the model. Students may leave their degree program at any stage. The factors affecting completion of each stage were derived from concepts related to Tinto s (1993) persistence model, human capital theory, and available data. Although Tinto s model suggests that factors affecting retention may differ at each stage, empirical research has yet Time-invariant Predictors Age Race Citizenship Gender Academic Ability Prior Graduate Degree College Time-varying Predictors Assistantships Semester FT/PT Status Semester GPA Grants Loans Faculty Turnover Students per Faculty Labor Market Conditions Completed Transition Stage Dropout Completed Development Stage Dropout Completed Degree Dropout Censored Observations Fig. 1 Conceptual framework

5 644 Res High Educ (2012) 53: to demonstrate this to be the case nor does empirical research suggest which factors should be included at each stage. This study is exploratory in that it examines the effects of various factors on all three stages. The contents of the first box are the time-invariant measures, which are constructed from Tinto s (1993) factors of student attributes, prior educational experiences, and background characteristics. The time-invariant values remain constant throughout the doctoral program; yet, may have differential effects on persistence at each stage. The time-varying variables reflect the institutional experiences and labor market factors, which change throughout the student s education. The institutional experiences affect how integrated students may be in their respective departments. Students with research assistantships and those enrolled full-time will likely be more academically and socially integrated within their departments given their abilities to connect with peers and faculty. Faculty turnover and the number of student advisees per faculty member influence student faculty relationships and in turn their integration. Assistantships, grants, and loans affect the financial resources of students and thus their expected costs of the program. Labor market conditions affect the expected benefits of graduating from the program as well as the expected costs in terms of opportunity costs of attending school full-time and not working. Literature Review Previous research has focused on the effects of students demographic characteristics on persistence. Nerad and Cerny (1991) found no significant differences in time-to-degree between men and women or minority and non-minority students. In addition, research by Ott et al. (1984) showed that the gender of the student does not predict graduate persistence, except as an interaction term with the department/field of study. Yet, Stiles (2003) showed that women were 16% less likely to complete their programs than men and international students were more likely to complete their programs than their U.S. counterparts. Minority U.S. students were 28% less likely to complete their programs than U.S. students. Lott et al. (2009) s longitudinal study of doctoral student attrition in STEM fields explained that dropout rates for women in these fields were not different from men prior to the seventh year, but women were twice as likely to drop out after the seventh year. Previous research has not demonstrated that the level of academic preparation measured by undergraduate grade point average (GPA) is a consistently significant predictor of degree completion and persistence (Girves and Wemmerus 1988; Pyke and Sheridan 1993). Lovitts (2001) showed that completers and non-completers had comparable undergraduate GPAs. Further, Girves and Wemmerus (1988) demonstrated that grades obtained in graduate school could not significantly predict doctoral student persistence. In relation to enrollment status, research by Ott et al. (1984) found that students who enrolled part-time were less likely to persist in a doctoral program. In terms of the expected costs of doctoral education, the literature has demonstrated that having some form of financial support increases the probability of completing the doctoral degree (Pyke and Sheridan 1993). The type of financial support does matter, however. Research (Gillingham et al. 1991; Ehrenberg and Mavros 1995) showed that having a teaching assistantship increased the time to degree and decreased the probability of degree completion and holding a research assistantship decreased time to degree and increased completion compared to other fully funded students. Andrieu and St. John (1993) found that graduate students in public institutions were 0.23 percentage points less likely to

6 Res High Educ (2012) 53: graduate with every $100 increase in tuition. Subsidies on tuition did not limit this effect, as the amount of graduate assistantship stipends was negatively related to the within-year persistence of students at public universities. Financial support is thus an important variable in predicting doctoral student retention. Limited research has been conducted on the effects of expected benefits of education on doctoral persistence and completion (Andrieu and St. John 1993; Ehrenberg and Mavros 1995). Previous work has shown that expected earnings can predict a positive effect on the probability of completing a doctoral degree. The effects of other labor market factors have not been included in any other research studies. Thus, by investigating the effects of both expected costs and benefits on the three stages of doctoral education, this research adds an important element to the discussion of doctoral persistence. Methodology Data Source and Sample The research sought to understand doctoral student persistence at various stages of a graduate program, making it appropriate to use a longitudinal explanatory research design (Johnson 2001). The site of the study is a land-grant institution located in the southeast part of the U.S. The institution has an annual enrollment of approximately 30,000 students, 7,000 of whom are graduate students. It has a Carnegie classification of very high research activity with STEMdominant programs. Doctoral degrees are offered in 61 different fields within 10 colleges. The study used transcript and admissions information from a sample of 2,068 doctoral students who enrolled at the institution between the academic years of 1994/1995 and 1998/1999. This allowed the observation of 10-year degree completion rates for the most recent cohorts and enough variation in economic conditions to estimate their impact on persistence. A 10-year completion rate was chosen since it is the maximum time allowed at the institution for matriculation to completion of a degree program. Students were considered to have stopped out of the institution if they failed to enroll in a particular semester(s) but re-enrolled within the study period. The analyses excluded these stop out periods because students cannot attain an event (e.g. degree) during this time. If students failed to enroll for a semester and did not re-enroll at any other time during the study period, the study considered them to have dropped out. There were 32 students still enrolled at the institution at the end of the study period. These students were included in the analysis as right censored since neither their degree completion nor drop out was observed during the study period. This approach is appropriate for survival analysis techniques, as these students still provide valuable information to the analyses (Allison 2010). Unemployment and weekly earnings data for the different fields of study in the sample obtained from the Current Population Study of the Bureau of Labor Statistics (BLS) provided measures of labor market conditions. The National Faculty Salary Survey by Discipline and Rank in Four Year Colleges and Universities administered by the College and University Professional Association for Human Resources (CUPA-HR) generated the expected earnings information. Variables Each stage of the model characterizes an event in the study, and completion of a stage is the dependent variable for the study. The first stage, the transition stage, begins at

7 646 Res High Educ (2012) 53: matriculation and ends after the student completes eighteen credits. The development stage ends when the student attains candidacy. Degree completion marks the end of the research stage. At this institution 18 credits marked the end of the transition stage because doctoral students choose an advisor and file a plan of work after completion of 18 credits. The plan of work signifies the first-step in the research process and is often tied to some type of preliminary exam. Typically, students at this institution take 9 credits per semester; thus, 18 credits coincide with Tinto s transition phase lasting approximately 1 year. The independent variables used in the analyses fall into three categories: student information, department information, and labor market information. Not all constructs from Tinto s model were able to be used in the model; all those for which data was available were included. The analyses excluded Tinto s factors of student advisor relationship and occupational goals. Student information consisted of time-invariant measures of gender, race, age, citizenship, academic ability, and college; and time-varying measures of enrollment status (FT/PT), GPA, and financial information. Race was categorized as White, Asian, and minority students (categorized as one variable due to a lack of representation in the sample). Academic ability is a construct developed from the student s undergraduate GPA and graduate test scores. This variable was categorized as exceptional, above average, average, and below average based on the average GPA for the various majors and the Educational Testing Services (ETS) published GRE percentage distribution of scores for various fields of study (ETS 2003). A student s enrollment status was operationalized as a time-varying measure based on the number of credit hours a student registered for in a semester. Prior to entering the research stage, students were classified as part-time if they registered for less than nine credits. Most students moved in and out of part-time status each semester especially during the development stage. During the research stage, a student could register for two types of credit hours dissertation research credits or special credits aimed at maintaining student status. Students were considered full-time if they registered for the dissertation research and part-time if they registered for the special credits. The financial information included in the analyses were assistantships, grants, and loans. In any given semester a student may use any combination of these to finance their study. Research assistantships and teaching assistantships were dummy-coded and included in the analyses for each semester for which a student held the position and the excluded category was no assistantship held in the particular semester. External and internal grants (excluding assistantship stipends) were also included as a measure of fellowship information. Two measures of student educational loans, the loan amount in the current semester as well as the cumulative loans taken up to that semester since the start of the doctoral program, were used in the analyses. Both measure were used since the current loan may represent a temporary reduction in the cost of attendance within the current semester but the cumulative loan represents the accruing cost of the program. The opportunity cost of attendance was represented by labor market information consisting of the unemployment rates and weekly wages of college-educated workers within the student s field of study. Despite the fact that not all doctoral students go into academia as assistant professors, the salaries of new assistant professors within the field of study was used as a proxy for expected earnings as it provided the best, readily available and most reliable form of data capturing earnings for graduates of doctoral programs. A 1 year lagged value was used for all the labor market values to utilize the information available to a student at each semester.

8 Res High Educ (2012) 53: Analytical Method The primary goal of the analyses was to compare the effects of the factors on persistence at the different stages of doctoral education. Event History Analyses (EHA) is used as the analytical method (Cox 1972). Originally developed in medical literature to study the timing of human deaths, EHA uses longitudinal data to estimate the factors that predict the likelihood of an event occurring with time-varying variables (Blossfeld and Rohwer 2002). The technique is increasingly being used in educational research as it provides better measures than logistic regression when handling longitudinal data, time-varying variables, and censoring, all of which are present in this study. Cross-sectional techniques such as logistic regression assume variable effects remain constant across the event of interest and variables that change over a particular period have to be modeled as a different variable giving up degrees of freedom in the estimation. EHA overcomes this limitation by incorporating variables that change value across time. EHA has been used in the higher education literature to model undergraduate student departure (Chen 2007; DesJardins et al. 1999, 2002; Gross 2008; Ishitani and DesJardins 2002). DesJardins (2003) provides further explanation on EHA especially as applied to higher education issues. Discrete-Time Hazard Model To answer the research questions, a particular type of EHA model was used, the discrete time hazard model. This model was used because the observation of the students occurs on a semester basis, which is a discrete time measure. There were also a large number of ties in the data large numbers of students attaining an event every semester which provided another reason for the use of this model. The hazard model estimated was specified as: Log hðþ¼ t X30 t¼1 / t T t þ ½b 1 X 1 þ b 2 X 2 þþb n X n Š þ ½c 1 Y 1t þ c 2 Y 2t þþc m Y mt Š þ u 1 log Z 1t þ u 2 log Z 2t þþu p log Z pt The left side of the equation features the log transformation of the hazard rate. The right side features four groups of terms. The first group (T) consists of the intercepts, which are a coefficients multiplied by the risk periods. These are the baseline of the hazard function and measure the effect of time on completing an event when all the factors equal zero. The second group (X) represents the time-invariant variables discussed in the conceptual model. The third group (Y) is composed of the non-monetary time-varying variables, and the fourth group (Z), the time-varying monetary variables for which the natural log transformation is employed to correct for the skewness. The study used a Cox proportional hazards for estimation since it is a general model that did not require a restrictive assumption of the error distribution (Allison 2010; Cox 1972). The analysis is done in Stata with marginal likelihood determined by employing the exactm option. The assumption with the use of this model is that the hazard of student A is a fixed proportion of student B, which is tested post-estimation with the use of Schoenfeld residuals (Schoenfeld 1982).

9 648 Res High Educ (2012) 53: EHA Terms In this section, we provide a brief description of the EHA terms used in the rest of the paper. Risk period is defined as the period during which a student may experience an event, in this study defined as a semester. Risk set is the part of the analytical sample that has not experienced an event yet or dropped out. Students in the risk set for a risk period are able to experience the event. The hazard ratio is similar to the odds ratio in logistic regression and reports the effect independent variables have on the probability that an event occurs in the risk period given that it has not occurred previously. Limitations The main limitation of this study comes from the use of secondary data. The estimation is thus limited to the variables available. The study used data from a single institution, which limits the doctoral fields included to programs available at the institution. Student advisor relationships is one such variable that was not available in the data despite its known affect on doctoral degree completion (Lovitts 2001; Nyquist 2002; Stolzenberg 2006). The analysis technique presents limitations as well. EHA models are particularly sensitive to unobserved heterogeneity (an example being an ability within each student not measured by any other variables within the model that increases their likelihood of persistence). Allison (2010) notes that unobserved heterogeneity tends to produce estimated hazard functions that decline with time (p. 230.) This limitation exists with models analyzed by logistic regression as well (Mood 2010). The effect of this limitation is that the coefficients may be biased towards zero. However, it has no effect on the standard errors and test statistics (Gail et al. 1984). Another limitation of EHA models is that they assume that censoring occurs randomly (i.e., non-informative censoring). For this analysis, we have 32 students in the sample that neither dropped out nor graduated prior to the end of the study period. The analysis assumes that this occurred randomly. The time limit requirements imply that these students needed extensions to remain enrolled at the institution, which may or may not violate the non-informative censoring assumption. Results Table 1 presents a breakdown of the students at each stage. Students were reset to time 0 upon entering each subsequent stage and the risk set only included students that completed the previous stage. Of the 2,068 doctoral students that enrolled during the study period, 88% (1,823 students) persisted after 18 credits. The 1,823 students then became the risk set for second stage, of which 70% (1,270) students completed the second stage; and 1,039 students completed their degree. Thus of the 2,068 students in the initial sample, 61% attained candidacy and 50% completed the doctoral degree. Over 50% of the dropouts occurred at the development stage. Once students attained candidacy, 81% completed the degree. On average, students enrolled for their 19 th credit hour after 2 semesters/1 year, attained candidacy at the end of 6 semesters/3 years, and graduated at the end of nine semesters. Table 2 presents the descriptive statistics for the time-invariant variables for each stage of the estimation and represents only students who entered that stage. The initial analytical sample consisted of 61% male and 39% female. Whites made up 61% of the sample, Asians 27%, and Minorities 12%. International students made up 33% of the doctoral

10 Res High Educ (2012) 53: Table 1 Number of students that attained each event Event Person-semester Risk set Number attained % Semesters to event Mean Median Max Transition stage 6,622 2,068 1, Development stage 10,440 1,823 1, Research stage 5,106 1,270 1, Table 2 Descriptive statistics of non time-varying categorical variables Stage: Transition Development Research Variable Number % Number % Number % Gender Male 1, , Female Race White 1, , Asian Black Hispanic Native American Citizenship U.S. citizen/resident 1, International student Academic ability Exceptional Above average Average Below average Degree No masters degree 1, Previous masters degree College Engineering Education Physical and mathematical sciences Agriculture and life sciences Veterinary medicine Humanities and social sciences Natural resources Management Textiles Design

11 650 Res High Educ (2012) 53: students enrolled. Forty-five percent of the sample had masters degrees before enrolling in their doctoral programs, and 55% of the sample enrolled with a bachelor s degree. The frequency distribution of the variables only slightly differed within the smaller risk sets in the development and research stages. The descriptive statistics do not demonstrate a clear pattern of changes in the demographic profile of the students. Table 3 presents descriptive statics of the continuous variables. The average age at which doctoral students began their program was 31 years. About 58% of the students, though, were between the ages of 20 29, and the oldest student was 67 years old. The mean grant received by students was $6,182 and the mean loan students took out was $9,462 To understand the probability of attaining any event within a particular period, this section presents graphs of the estimates of the hazard rate across time for the three events. Graphs comparing this hazard rate for different groups of students are also presented. An Epanechnikov kernel function with the optimal bandwidth is used to smooth the graphs (Allison 2010). The shaded area represents the 95% confidence interval. Figure 2 presents a graph of the hazard rate of completing the transition stage. The graph shows that the likelihood of persisting after 18 credits was an increasing function of time. The hazard rates of persistence were high ranging, from 35% in the third semester, to approximately 55% in the ninth semester. This implies that even after the eighth semester, the likelihood of completing this stage remains high at over 50%. Figure 3 displays the hazard rate graph of attaining candidacy. The likelihood of attaining candidacy across time is an increasing function of time up until the eleventh semester and then becomes a decreasing function of time. This suggests that if students do Table 3 Descriptive statistics of continuous independent variables Variables Mean Standard deviation Age Grants $ $ Loans $ $ Faculty turnover rate Doctoral students per faculty Semester GPA Hazard estimates Semester 95% CI Smoothed hazard function Fig. 2 Smoothed hazard estimates of completing the transition stage

12 Res High Educ (2012) 53: Hazard estimates Semester 95% CI Smoothed hazard function Fig. 3 Smoothed hazard estimates of attaining candidacy for all students Hazard estimates Semester 95% CI Smoothed hazard function Fig. 4 Smoothed hazard estimates of degree completion for all students not attain candidacy by their eleventh semester, the likelihood of attaining candidacy decreases with every semester they remain enrolled. Figure 4 presents the hazard function of degree completion as increasing with time for a period, stable across the peak, and then becomes a decreasing function of time. This implies that a student who has not completed their degree 8 years after matriculation will face a decreasing likelihood of ever completing. Figure 5 displays the hazard function of degree completion by students citizenship. To test the hypothesis that the two graphs are equal, a Cox test of equality is conducted. The Chi-squared test estimate was , rejecting the null hypothesis that the two graphs are equal. The chart shows that international students have higher hazard rates of degree completion than U.S. citizens and resident students. The chart also illustrates that although both U.S. and international students experience an increasing hazard function of time during the earlier semesters, international students have a much steeper gradient (that is, the function increases at an increasing rate). Thus, this suggests that international graduate students are more likely to complete the degree at every stage.

13 652 Res High Educ (2012) 53: Hazard Rate Semester U.S. Citizen/Resident International Student Fig. 5 Smoothed hazard estimates of degree completion by citizenship Hazard Rate Semester White Minority Asian Fig. 6 Smoothed hazard estimates of degree completion by race Figure 6 presents the hazard function of degree completion by race for all students. A Cox test of equality rejects the null hypothesis that the three curves are equal with a Chisquared of Asian students have the highest likelihood of completing the degree. Minority students, which included students from all other races except White and Asian as the numbers were insufficient to be treated as a unique variable, have the lowest likelihood of degree completion. Table 4 presents the results for the proportional hazard regressions of the three stages of doctoral education: transition stage, development stage, and research stage. The results demonstrate that gender has no effect on the likelihood of completing any stage. Age has a negative effect on completing the transition and development stages but not on the research stage. International students had a 66% increased odds of completing the transition stage, 56% increased odds for the development stage, and 68% for the research stage. Minority students are not significantly different form White students in completing the transition and research stage but have a 25% decreased odds of completing the development stage.

14 Res High Educ (2012) 53: Table 4 Results of proportional hazards for the stages of doctoral education Stage: Transition stage Development stage Research stage Variable Hazard ratio Standard error Hazard ratio Standard error Hazard ratio Standard error Student characteristics Female Age 0.982*** *** International student 1.658*** *** *** Asian Minority student *** Academic ability-good Academic ability-average Academic ability-below average 0.756** Previous master degree 0.848** ** Enrollment information Semester GPA 3.426*** *** Part-time 0.680*** *** *** Labor market information Unemployment rate 1.113*** *** New assistant professor salary (log) *** Earnings (log) ** Financial aid information Research assistantship 2.139*** *** ** Teaching assistantship 1.753*** ** Cumulative loan (log) 1.102*** *** Grant (log) *** *** Loan (log) 0.930** ** Department information Doctoral students per faculty 0.973*** member Faculty turnover College (engineering) Education 0.594** *** *** Physical and mathematical sciences *** *** Agriculture and life sciences *** Veterinary medicine Humanities and social sciences/ management Natural resources/textiles/design 0.591** *** Significance *** p \ 0.01; ** p \ 0.05 Higher unemployment rates in a student s field increases his or her hazard rate of completing the transition stage and the development stage. Increases in assistant professor salary increases the odds of completing the research stage, and increases in forgone

15 654 Res High Educ (2012) 53: earnings increase the odds of completing the development stage. Students with research assistantships have a higher odds of completing all three stages; whereas, students with teaching assistantships have a higher odds of completing the transition and development stages but not the research stage. Grants increase students odds of completing the development stage but reduce it for the research stage. Total loans accumulated during the doctoral program increase the odds of completing the transition stage but reduce the odds of completing the development stage, whereas the loans taken in a particular semester reduce the odds of completing the transition and research stages. Discussion Despite the gender gap in degree completion shown in the literature (Bowen and Rudenstine 1992; Stiles 2003) for studies using descriptive statistics and bivariate measures, studies that have used multivariate analyses provide similar results to this study in that there are no gender differences in degree completion once assistantships and the field of study are controlled (Ehrenberg and Mavros 1995; Nerad and Cerny 1991). This implies that females are as likely to be retained at the institution as males, but the observed gender differences in degree completion may emanate from the assistantships received and the field of study chosen. International students are more likely to persist and complete doctoral programs. Most research confirms this finding. (Bowen and Rudenstine 1992; Ehrenberg and Mavros 1995; Stiles 2003). There has been some speculation in the literature as to why international students appear to be graduating at higher rates than U.S. students. These reasons include policies such as visa requirements, international students better preparation, and/or the social isolation faced by the students (Aslanbeigui and Montecinos 1998; Stiles 2003). International students are also required to maintain continuous full-time enrollment at their institution thus reducing stop outs. The observed differences in White and Minority students in degree completion are occurring mainly at the development stage of a doctoral program, at which time students are expected to develop a research agenda. Research studies on minority students in doctoral programs suggest that these students experience isolation, marginalization, and less effective interactions with program faculty (Ellis 2001; Gay 2004; Jaeger et al. 2009). Morelon-Quainoo et al. (2009) s study demonstated that doctoral students of color believe that developing a collegial relationship with their faculty contributes to success in their work. Academic and social integration could prove more challenging for students from diverse backgrounds. Anderson (1990) found that for STEM minority students, the curriculum becomes a source of alienation due to the lack of diverse viewpoints and perceived irrelevance to their society. Thus, these students may have further problems finding an advisor who is willing and interested in working with them as members of the faculty are often not as diverse as the students with whom they teach. The development stage, which requires students to develop a particular interest in their respective field and choose a dissertation topic, may prove troublesome for minority students. Research suggests that students of color seek coherence in their research topic and cultural identity (Haley et al. 2010). Students attributes and external commitments, according to Tinto (1993), affect the way they participate and engage in the institutional experience thus impacting their academic and social integration. Students of diverse backgrounds with strong cultural

16 Res High Educ (2012) 53: identities (Haley et al. 2010) may struggle to develop relationships with peers and faculty who do not share similar attributes or experiences. The positive effect of part-time status on completing the development and research stage is counter intuitive. The results imply that for doctoral education, when the goals of completing the stage go beyond completing coursework, part-time students may be better positioned to attain the event. Tinto (1993) suggests that part-time study is more than limited time commitments of part-time students. It extends to the degree to which a student is able to become involved in the intellectual and social life of the student and faculty communities. His conceptualization is plausible but does not help explain this finding. A human capital perspective can help clarify the increased likelihood of completing the degree for part-time students. Part-time students are more likely to be working full-time and thus have reduced opportunity costs of education. Thus, increases in the other costs of the education or reductions in the benefits from education do not affect them as much as full time students for whom a loss in financial aid may be detrimental to the continuation of their study. Students who are below the average in terms of academic ability have difficulty completing the transition stage but beyond that the variable has no significant effect on completing any of the other stages. This supports previous research results that suggest academic preparation has no effect on degree completion (Girves and Wemmerus 1988; Pyke and Sheridan 1993). Students in departments with a high student to faculty ratio have a lower likelihood of completing the transition stage but not the other stages. This suggests that high student to faculty ratio is not an impediment to academic and social integration especially necessary in the development and research stage. Faculty turnover in a department has no significant effects on completion of any stage in the doctoral program. Previous research has established that students who receive financial assistance in the form of assistantships are more likely to complete their degrees than students who rely on their own resources (Ehrenberg and Mavros 1995). Previous research (Pyke and Sheridan 1993; Gillingham et al. 1991) measured aid at one point in time when we know students aid fluctuates throughout their doctoral experience. Bowen and Rudenstine s (1992) bivariate analyses suggested that completion rates tend to be higher for students with teaching assistantships than for students with fellowships, at least in the humanities and social sciences. This study shows that students with research assistantships are more likely to complete each stage of doctoral education than students with any other type of financial support. Students with teaching assistantships are more likely to complete the transition and development stage but are no different from students with no assistantships with respect to the likelihood of completing the research stage. This implies that the benefits of research assistantships go beyond the financial resources they provide in increasing the likelihood of persistence. A research assistantship, particularly in the sciences, provides students with direct contact to peers and faculty. According to Tinto (1993), a student s academic and social integration is much more narrowly defined by the immediate communities of the department and the limited number of people who inhabit the department (p. 234). Research assistantships offer opportunities for students to connect with that limited number of people within a department and develop substantial relationships with a particular faculty member. Given that students academic and social networks are often within the local department, academic and social experiences are intertwined (Tinto) and critical to students persistence. Teaching assistantships in the research stage may be distractions that take students away from their research and may not foster the academic integration needed to complete this crucial stage of doctoral work. These results are further enhanced by

17 656 Res High Educ (2012) 53: students on grant support. They are more likely to complete the development stage but less likely to complete the research stage. This study also reveals that labor market conditions do affect persistence and doctoral degree completion. Higher unemployment rates increase the likelihood of attaining all the events within doctoral education. Faced with the higher likelihood of unemployment, students will remain in doctoral programs. Assistant professors salaries have no effect early in a program, but significantly increase completion of the research stage and the degree. This is in line with human capital theory, in that higher expected benefits will motivate students and increase their likelihood of degree completion. Graduate students in the early phases of their programs may not have solidified their career plan, thus not dramatically affected by salary levels. Yet, as students move through the development and research phases they are more likely to be motivated by the salary levels of positions that are in the not-so-distant future for them. Conclusions and Implications This research study shows that demographic factors such as age and citizenship status have similar effects on doctoral student persistence across all three stages. The impact of other factors such as race and part-time enrollment depend on the doctoral student s stage of education. Financial aid and labor market conditions have differential impacts on persistence, and among all financial aid types, students with research assistantships have the highest likelihood of completing the degree. On average only 40% of doctoral students received a teaching or a research assistantship in this sample. The percentage of enrolled doctoral students receiving assistantships was at its peak during the third year with 60% receiving assistantships; this percentage reduced gradually thereafter. This implies that fewer assistantships were awarded to students after the third year and thus students were less likely to receive assistantships later on in a program. Research assistantships had a large and significant effect on degree completion during the research stage; thus, departments, colleges, and universities could utilize research assistantships to improve graduate degree completion. Teaching assistantships; however, had no effect on completion rates during the research stage. This suggests that as tools to aid in retention, teaching assistantships should be awarded to students who are in the transition and/or development stages. Although a gender gap exists in doctoral degree completion (Bowen and Rudenstine 1992), this study shows that gender is not a significant predictor of doctoral persistence. Lower degree completion rates for females may be stemming from gender differences in the other variables in the model. This implies that females may have less access to research assistantships, may be more likely to attend part-time during the transition stage, or may be enrolling in colleges with lower degree completion rates. Practices aimed at closing the gender gap should focus on increasing the access of females to research assistantships. One such practice could entail increasing the awareness of research assistantships to prospective female applicants as well as increasing the number of assistantships actually awarded to women. Another practice change could entail designing support for females that would enable them to enroll full-time during the transition stage. According to the results, minority students are more likely to drop out during the development stage of their doctoral education. Considering how minority students integrate within their local communities (departments) is important. Previous research suggests that minority students may experience difficulties connecting (Ellis 2001; Gay 2004;

18 Res High Educ (2012) 53: Haley et al. 2010; Jaeger et al. 2009) to faculty and identifying suitable research topics. This research identified the most influential stage, development stage, for students of color in their pursuit of a doctoral degree. In order to increase the degree completion rates of minority students, programs should find ways to better meet the needs of these students and to help them achieve the goals of the development stage. Part-time enrollment reduces persistence during the transition stage but increases both candidacy attainment during the development stage and degree completion during the research stage. Graduate schools and individual programs should consider residency requirements during the transition stage, which could reduce the early attrition rates and increase degree completion rates. Although residency requirements also carry with them significant financial considerations and such policy discussions are beyond the scope of this study, educators would be well served to consider the purposes of residency requirements. Such individuals should consider whether the purposes of such requirements (e.g., limit time to degree or improve social and academic integration) are being met by the requirements. Could changing requirements for students who wish to enroll part-time over the development and research stages lead to positive outcomes? Considering how part-time students are impacted in terms of financial aid during the research stage is also worth pursuing. Residency requirements are infrequently considered in discussions of persistence and retention; yet, may contribute to improved degree completion rates during the research stage. Although this research is conducted on students at a single institution, the study contributes to the theory of doctoral education by confirming the applicability of Tinto s longitudinal model of doctoral persistence and shows that discussions of doctoral student persistence and degree completion should take place within a longitudinal context. The varying effects of factors on the three stages of doctoral education imply that a model of doctoral persistence should include the multiple degree requirements that create different stages of the process. The study also incorporated human capital theory into the conceptual framework to explain the labor market s effect on doctoral student persistence. Human capital theory plays a role in the persistence of doctoral students and needs to be modeled in these studies as some variables, such as enrollment status, could not be fully explained using Tinto s model. The results from this study have highlighted some important issues that need further exploration. The reduced likelihood that minority students have of completing the development stage needs further investigation. Future studies should address the academic and social integration of minority students into their department and field of study. Further research should also explore the influence of race on electing a dissertation advisor and topic, two key elements of the development stage. Another important aspect that requires further explanation is the effect of department policies on the retention of students. As noted by Tinto (1993), the local community (department) becomes the primary educational community for a student s graduate career. There are varying department policies that govern doctoral education and the efficacies of these policies as it relates to retention have not been investigated. A study using a hierarchical linear model could ascertain how various departments policies may affect doctoral student retention. This research article emphasizes the need to examine doctoral education as not just a temporal process but one made up of various stages. This implies that educators working with doctoral students should consider retention issues with this in mind and provide distinct support mechanisms at each stage.

19 658 Res High Educ (2012) 53: References Allison, P. D. (2010). Survival analysis using the SAS system: A practical guide. Cary, NC: SAS Publishing. Ampaw, F. (2010,). The effect of labor market conditions and financial aid packages on doctoral students retention. Unpublished dissertation, North Carolina State University. Ampaw, F., & Jaeger, A. J. (2010, May). The effect of labor market conditions and financial aid packages on degree completion of doctoral students. Paper presented at the annual meeting of Association for Institutional Research, Chicago. Anderson, B. (1990). Minorities and mathematics: The new frontier and challenge of the nineties. Journal of Negro Education, 59(3), Retrieved from Andrieu, S. C., & St. John, E. P. (1993). The influence of prices on graduate student persistence. Research in Higher Education, 34(4), doi: /bf Aslanbeigui, N., & Montecinos, V. (1998). Foreign students in US doctoral programs. Journal of Economic Perspectives, 12, Retrieved from Association of American Medical Colleges (AAMC). (2007). Medical school graduation and attrition rates. Analysis in Brief, 7(2), 1 2. Retrieved from Becker, G. S. (1962). Investment in human capital: A theoretical analysis. The Journal of Political Economy, 70(5), doi: / Becker, G. S. (1964). Human capital: A theoretical and empirical analysis, with special reference to education. New York: National Bureau of Economic Research. Berg, H. M., & Ferber, M. A. (1983). Men and women graduate students: Who succeeds and why? Journal of Higher Education, 54(6), Retrieved from Blossfeld, H. P., & Rohwer, G. (2002). Techniques of event history modeling: New approaches to causal analysis. Hillsdale, NJ: Erlbaum. Bowen, W. G., & Rudenstine, N. L. (1992). In pursuit of the PhD. Princeton, NJ: Princeton University Press. Chen, R. (2007) Socioeconomic and racial/ethnic gaps in student dropout risks: A longitudinal model to examine the differential effects of financial aid. Unpublished doctoral dissertation, University of Michigan, Ann Arbor, MI. Council of Graduate Schools (CGS). (2008). Ph.D. completion and attrition: Analysis of baseline demographic data from the Ph.D. completion project. Washington, DC: Author. Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34(2), Retrieved from DesJardins, S. L. (2003). Event history methods: Conceptual issues and application to student departure from college. In J. C. Smart (Ed.), Higher education: Handbook of theory and research (Vol. XVIII, pp ). Boston: Kluwer. DesJardins, S. L., Ahlburg, D. A., & McCall, B. P. (1999). An event history model of student departure. Economics of Education Review, 18(3), doi: /s (98) DesJardins, S. L., Ahlburg, D. A., & McCall, B. P. (2002). Simulating the longitudinal effects of changes in financial aid on student departure from college. Journal of Human Resources, 37(3), doi: / Dodson, T. F., & Webb, A. L. (2004). Why do residents leave general surgery? The hidden problem in today s program. Current Surgery, 62(1), doi: /j.cursur Educational Testing Service (ETS). (2003). Graduate record examination : Guide to the use of scores. Princeton, NJ: Educational Testing Service. Ehrenberg, R. G. (1991). Academic labor supply. In C. T. Clotfelter, R. G. Ehrenberg, M. Getz, & J. J. Siegfried (Eds.), Economic challenges in higher education (pp ). Chicago: University of Chicago Press. Ehrenberg, R. G., & Mavros, P. (1995). Do doctoral students financial support patterns affect their times-todegree and completion probabilities. The Journal of Human Resources, 30(3), doi: / Ellis, E. M. (2001). The impact of race and gender on graduate school socialization, satisfaction with doctoral study, and commitment to degree completion. The Western Journal of Black Studies, 25(1), Gail, M. H., Wieand, S., & Piantadosi, S. (1984). Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates. Biometrika, 71, Retrieved from Gay, G. (2004). Navigating marginality en route to the professoriate: Graduate students of color learning and living in academia. International Journal of Qualitative Studies in Education, 17(2), doi: /

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