INTRODUCTION

A more demographically and socioeconomically diverse public has started to enter Brazilian higher education in recent decades. The sociological literature has been attentive to the expansion process (^{PRATES; COLLARES, 2014}), the policies implemented to expand access (^{HERINGER, 2014}; ^{SENKEVICS; MELLO, 2019}), and the patterns of inequality of opportunities in the sector (^{RIBEIRO, 2011}; ^{MONT'ALVAO, 2011}). However, entering higher education is only the first step; the biggest challenge lies in students' persistence and course completion.

Some studies already point to the existence of high dropout rates in Brazilian higher education, and indicate that more recent generations have been facing more difficulties to graduate (^{RISTOFF, 2013}; ^{SILVA FILHO et al., 2007}; ^{LOBO, 2012}). Thus, in addition to, analyzing student dropout and persistence is important both from a public policy standpoint and for scientific knowledge of educational systems.

This article presents a case study of a university and shows how the educational processes taking place in the university environment follow dynamics that deserve greater attention and emphasis. We intend to contribute academically by presenting ways to think about, measure, and evaluate student dropout in the context of Brazilian higher education. Institutionally this is desirable both at the level of the public higher education system and for the specific institution studied, because we systematize processes that ultimately reflect on the management of the institution and the more efficient use of resources.

In the international literature three sets of factors are pointed out as relevant to understanding dropout and completion in higher education. The first concerns educational dimensions such as students' performance before entering higher education, and variables related to the institution choice process (^{HILL, 2008}; ^{BELASCO, 2013}; ^{HOXBY; AVERY, 2013}; ^{MEROLLA, 2017}). The second set, highlights factors associated with individuals' characteristics - gender, color/race, class, income, parents' education - that would be associated with individuals' path and outcomes before and after entering higher education (^{BUCHMANN et al., 2008}; ^{BOWEN; CHINGOS; MCPHERSON, 2009}; ^{GOLDRICK-RAB, 2006}). Finally, the third set of factors, highlights the importance of students' experiences while attending higher education, especially formal academic integration - usually measured by students' performance during their studies - and social engagement (^TINTO,1975, ²⁰¹²; ^{BRAXTON et al., 2004}; ^{CHARLES et al., 2009}).

These factors can be analytically distinguished, but from an empirical point of view, they are treated as complementary. Based on this literature, this paper examines whether factors - educational and course choice, students' social and demographic background, and formal academic integration - are associated with dropout in the first three years at the Federal University of Rio de Janeiro (UFRJ). We employed the concept of course dropout, which is the student's definitive departure from the course of origin (^{LOBO, 2012}).

We treat the student dropout process as a temporal problem, that is, the factors that lead to dropout accumulate over time or only appear at a certain point in the trajectory (^{TINTO, 1975}, ²⁰¹²). In the language of research designs this means that methodologically studies ideally should be longitudinal rather than cross-sectional. The difficulty of implementing longitudinal research designs is that they demand detailed tracking of student cohorts entering higher education systems and institutions. If conducting population surveys is no longer a trivial task at one point in time, doing it for the same set of people repeatedly adds new layers of complexity. Traditional surveys have a central concern of maintaining the representativeness of the sample relative to the population (^{HENRY, 1990}). This unfolds into concerns in the construction of the sample (coverage rates, response rates, selection of observation units) and of the questionnaire (quality of application, reliability and validity of the questions asked) (^{BARNETT, 1991}; ^{GROVES, 2009}). In longitudinal surveys, the need to obtain responses from the same individuals over time causes the problems of sample representativeness to be raised again at each new round of research, which continues to have he challenge of not having biases with the additional challenge of not losing respondents (^{SINGER; WILLET, 2003}).

In this research we overcome this type of problem by using administrative records which can be defined as data that derive from the operation of information systems typically originating from public agencies (^{ELIAS, 2014}). Typically, these data are collected for the purpose of recording transactions in the provision of services (^{WOOLLARD, 2014}). The administrative records of the UFRJ enrollment system are the source of information for our research. Since the information is generated from the university sector that monitors the academic situation of students, the problem of temporal monitoring of respondents, typical of longitudinal research is circumvented, since the students' own daily administrative acts (enrolling, graduation, enrollment suspension) are our source of information. Additionally, the representativeness of our data is guaranteed because we use census information rather than a sample, that is, we treat the universe of students enrolled at the university who entered in the first semester of 2014.

In addition to the information from the administrative records of the UFRJ enrollment system, we also used variables from the socioeconomic questionnaire that is produced and applied by the institution during student pre-enrollment. This instrument presents high response rates, especially regarding variables of social and demographic origin of the students, and a diversity of questions such as socioeconomic, cultural, school, and choice aspects and expectations about the course that are not found in public and national databases.

This data structure allows us to explore the temporal dimensions of the dropout process. Crucially, we identify when students are most at risk of dropping out of courses. To answer time-related questions, longitudinal models of survival analysis are considered more appropriate (^{SINGER; WILLET, 2003}), and applied more frequently to study dropout in international research. In general, these studies seek not only to know "when" higher education dropout or completion occurs, but also, seek to identify which are the factors associated with these outcomes and when they act (^{AMERI et al., 2016}; ^{LASSIBILLE; GÓMEZ, 2008}; ^{GURY, 2011}).

In Brazil, studies working with longitudinal modeling including time in their equations to study dropout in higher education are still scarce. Therefore, this research contributes to studies on higher education in Brazil by adopting a sparsely mobilized design and a data analysis suitable to incorporate the structure of the data (see methods section). We thus produce evidence about a cohort of students that entered UFRJ in the first semester of 2014 , and the patterns of association of a set of individual factors of student origin, educational and course choice aspects, and formal academic integration for the study of course dropout.

This paper is divided into seven sections including this introduction. The second section contextualizes Brazilian higher education and also the Federal University of Rio de Janeiro (UFRJ). The third, brings a brief review of international and national literature. The fourth section of the article describes the data, and the fifth section describes the method used in the research. The sixth section brings the results and discussions, and in the seventh and last section the final considerations.

BRAZILIAN HIGHER EDUCATION AND THE FEDERAL UNIVERSITY OF RIO DE JANEIRO

In recent decades, Brazilian higher education has undergone an expansion under several aspects, such as: growth in the number of institutions, increase in vacancies and enrollment, among others (^{SANTOS et al., 2020}). During the years from 2003 to 2015, the expansion of this level of education was related to the democratization of the Brazilian campus. In this period, a set of policies and programs were implemented, aiming at the inclusion of sectors historically excluded from higher education (^{RISTOFF, 2014}).

Initiatives such as: the ProUni and the Fies, both aimed at expanding access to private higher education; the Enem/Sisu; the Reuni; the adoption of affirmative action policies; the implementation of Law No. 12.711/12 in federal institutions of higher education (Ifes) are typically cited as relevant in this context (^{SENKEVICS, 2021}; ^{ALMEIDA, 2015}). Among these measures, we will focus on the Enem/Sisu, because this initiative has modified the access to the Ifes and changed the dynamics of the course choice process, an important factor to think about the dropout of courses and understand the trajectories of students after enrolling, as already pointed out by some studies (^{MEROLLA, 2017}; ^{ELLER; DIPRETE, 2018}; ^{NOGUEIRA et al., 2017}).

The Enem was created in 1998, during the government of Fernando Henrique Cardoso, to evaluate the performance of students graduating or leaving high school. In addition, its results began to serve as a form of access to higher education. In 2009, the Ministry of Education (MEC) proposed to the Ifes that they use Enem as a test for selecting candidates instead of their own selection processes (formely known as vestibulares). For this, the MEC, through the National Institute of Educational Studies and Research Anísio Teixeira (INEP), conducted a methodological restructuring of the exam so that it could fulfill its new purpose (^{LUZ; VELOSO, 2014}).

Along with these reformulations in Enem, it was established, in 2010, the Unified Selection System - Sisu. Instituted and regulated by Normative Ordinance No. 2 of January 26, 2010, the Sisu is a computerized system managed by the MEC for the selection of candidates for vacancies in undergraduate courses offered by participating public institutions of higher education.

This system is structured in successive stages, which are constituted in the following phases: I- offer of vacancies in Sisu by the participating institutions, available for the enrollment of candidates; II- enrollment in Sisu of candidates who have participated in Enem from the previous year's edition; III- selection and classification of candidates based on their performance on Enem, observing the weights and minimum scores eventually established by the institution; IV- release of vacancies occupied in Sisu (^{BRASIL, 2010}).

Sisu can be described as a matching mechanism, i.e., a type of auction that allow for adjustments between the vacancies offered by the institutions and the individuals who compete for them (^{ABREU; CARVALHO, 2014}). During the registration period, the student, in a five-day interval, can, at any time, access the Sisu platform and choose, in order of preference, up to two course options among those offered by the institutions participating in the process. From the second day on, the system uses each student's options, "computing the matching" that would be offered to them in the next stage. After a few hours, the student, when accessing the system platform, receives information about the "computed matching" (^{ABREU; CARVALHO, 2014}).

These simulations allow students to know if they would be selected in the first call to enroll in their first or second course option, or if they would not be selected. In this process, they can observe, for each of the course options, their Enem score, the score of the last classified, and also their position in the ranking (^{ABREU; CARVALHO, 2014}). These adjustments happen four times: if the registration period began on a Monday, the student will receive signals of the choices of other competitors daily from Tuesday until Friday, the last day of registration (^{ABREU; CARVALHO, 2014}).

As soon as the student announces the vacancy he or she will apply for, on the last day, the system computes a matching based on the last list of courses announced by the student and, based on this adjustment, makes vacancy offers. If the candidate has a score to be classified in his two course options, he will be selected only for the first, because each candidate competes only for his first course option, passing to compete for the second only if he does not get a place in the first (^{BRASIL, 2010}). In addition, when classified and receiving a vacancy offer, the student can choose to accept or reject it.

It is important to point to the change in the dynamics of course choice in the selection process caused by Sisu, to the extent that, in the traditional entrance exam (vestibular), the individual applied for a course and then took the test in which he was only approved if he achieved sufficient performance to pass (^{NOGUEIRA, et al. 2017}). In Sisu, the individual first takes Enem to obtain a score and then applies to two courses, as a first and second option (^{NOGUEIRA, et al. 2017}).

We understand that it is fundamental to consider the form of access to higher education to think about the of students' dropout from undergraduate courses. As the international literature points out (^{MEROLLA, 2017}; ^{ELLER; DIPRETE, 2018}), pre-entry factors in higher education are key to understanding students' trajectories once they are enrolled. What was their previous performance? How is the institution chosen, by convenience, low cost, expectation of high financial returns (^{AINA, 2011}; ^{HOXBY; AVERY, 2013})? In the following sections we will operationalize some of these dimensions and scrutinize them empirically to understand their importance in the UFRJ dropout process.

As federal universities have autonomy to choose the format of their selective processes, it is important to take into consideration highlight the context of changes in access to the Federal University of Rio de Janeiro. Until 2008, UFRJ still selected its students through the traditional entrance exam (vestibular). This exam consisted of two-day discursive tests. The novelties in the entrance exam for undergraduate courses began to appear in the selection process that took place in 2009 for admission of the 2010 class. That year, the selection began to be carried out in two stages: in the first stage, exclusively eliminatory, UFRJ adopted Enem; in the second stage, UFRJ continued to adopt its own entrance exam (vestibular).

In 2011, UFRJ established policies to reserve spaces for students from public schools, based on a selection process that combined the results of Enem with the institution's entrance exam (vestibular). In 2012, UFRJ determined the end of the vestibular and the exclusive access to undergraduate courses through Enem/Sisu. In addition, that year, the institution increased to 30% the percentage of vacancies reserved for students from public schools and the inclusion of family income as a second criterion for disputing these vacancies. However, with the approval of the Quotas Law No. 12.711, on August 29, 2012, all federal higher education institutions should immediately implement in 2013 the Law, which provided a quota of at least 25% of vacancies for students that completed their secondary education in public high schools. Within this quota, other criteria such as income and racial self-identification were implemented. The law also imposed, a deadline of four years for full compliance with this law, i.e. 50% of vacancies per course and shift, reserved for students who completed high school in public schools (^{BRASIL, 2012}).

As of 2014, the UFRJ began to reserve 50% of vacancies in each course for affirmative action modalities and the other 50% for broad competition. Thus, we highlight that the cohort of students analyzed in this article entered only through Enem/Sisu and approximately half of the students of this cohort entered through some category of quota, due to the sanction of Law No. 12.711/12.

LITERATURE REVIEW

DATA

The database used in this study was built from the microdata of the cohort of first semester 2014 entrants at UFRJ, provided by the Student Registration Division (DRE-PR1) through a formal request and a term of ethical commitment. Most of the information is collected through a socioeconomic questionnaire produced and applied by the institution at the time of pre-enrollment, therefore, these data can be classified as secondary, since we did not create them. The aforementioned questionnaire is composed of 46 questions that address, among other information, socioeconomic, cultural, school, family composition and choice aspects and expectations about the course and the institution. The students are followed by their enrollment number, de-identified throughout their trajectory within the course. It is not possible to identify specific students due to privacy protocols that were implemented in the data. The student's relationship with the university in each semester can be classified as: enrolled, enrollment suspended, enrollment cancelation, degree conclusion, re-enrollment, exchange student, and student in academic mobility. The population of this study is composed of those entering in the first semester of 2014. A total of 4982 students are in the database. We chose to analyze only courses in the in-person modality and on the Rio de Janeiro city campus. In addition, it was necessary to exclude courses that had a maximum duration of 2 years to avoid bias in the analysis. After removing these observations (496 cases), we arrived at a total of 4486 students followed over three years.

The dependent variable used in this analysis is a binary variable that informs if the student persisted or dropped out of UFRJ. We operationalized the concept of as the student who leaves the course of origin for any reason (^{LOBO, 2012}). This variable was constructed by combining the variable of time that the individual remained in the course and the enrollment status in each semester. We considered only those students who had their enrollment in the course cancelled, except for cancellation due to degree conclusion. We chose to cut off the time until the 6th semester, that is, the first three years of the students' trajectories, to include all the courses, regardless of their duration. This cut-off is justified for empirical reasons, to meet the assumptions of statistical modeling, but it is also justified by the literature, given that international and national studies (^{SACCARO et al., 2019}; ^{SILVA, 2013}; ^{AMERI et al., 2016}; ^{LASSIBILLE; GÓMEZ, 2008}; ^{GURY, 2011}) evidence that the risk of dropout in the first years of the student is higher. This means that our data are "censored to the right," meaning that we do not know if a student dropped out of UFRJ after three years. All interpretations must take these assumptions into account.

Independent variables. Several studies highlight that factors associated with individuals' characteristics - gender, color/race, parents' education - are associated with individuals' trajectories and outcomes after entering higher education (^{BUCHMANN et al., 2008}; ^{BOWEN; CHINGOS; MCPHERSON, 2009}; ^{GOLDRICK-RAB, 2006}; ^{ELLER; DIPRETE, 2018}; ^{AINA, 2013}; etc.). Therefore, as students' sociodemographic background variables we used color/race (white=0; black and brown=1), gender (female=0; male=1), and family socioeconomic position (PSE), measured by the highest parental education of the students' father or mother (less than higher education=0; higher education=1). Taking into account the current selective process adopted by UFRJ (Enem/Sisu), and that the process of choices in accessing higher education can influence future outcomes (^{LARSEN et al, 2013}; ^{ZWICK, 2009}; ^{PERNA, 2006}; ^{MEROLLA, 2017}), we used as variables representing educational and course choice factors the information "if it was the first course choice" (yes=0; no=1) and "if the cutoff score determined the course choice" (no=0; yes=1), as well as, the Enem score divided into five performance levels separated from the quintiles. Research shows that more academically integrated students, with good performances, are less likely to drop out (^{TINTO, 2012}; ^{BRAXTON et al., 2004}; ^{BENNETT, 2009}; ^{SUHRE et al. 2007}; ^{ARAQUE et al. 2009}; ^{BELLOC et al. 2010}). Therefore, as a proxy for the student's formal academic integration into the course, we use the cumulative Coefficient of Achievement (CRa) per semester divided into five levels separated from the quintiles. The CRa is the overall performance of a student, measured by the weighted average of the final grades obtained in each subject, using as weight the number of credits (class hours) that the subject confers. Having a good CR implies getting scholarships, internships, opportunities at the institution, which can influence the students' experiences after entering the university. A course variable, covering a combination of 45 UFRJ courses, was added to the model as a control for heterogeneity.

Other independent variables from the socioeconomic questionnaire were tested in the descriptive statistical and multivariate analyses, such as age, type of high school attended, whether they had children, whether they were working at the time of entry, and whether they had to move to another city to study. These variables were not statistically significant in any of our analyses and including them in the model would decrease our population because of missing data.

In Table 1, we present descriptive statistics of the cohort analyzed. As for the general profile of the students, for the individual characteristics’ color/race, gender and family PSE, this cohort is distributed in approximately 50% for each category of these variables. As for the course choice factors, that is, the students who said it was not their first choice of course and that the cutoff score "yes" affected their choice of course, it was approximately 25%.

As for the dropout and persistence rates of students, for the variables family PSE and gender, the statistical test showed that there is a small difference of 4 percentage points between the categories of each variable (male x female, P value = 0.003; higher education x<than higher education, P value = 0.002). For the color/race variable, no difference was observed between the white x black and brown categories (P value = 0.564). For the course choice variables, the statistical test indicated a difference of 18 percentage points between the categories "no x yes"(P value = 0.000). Also, for the variables of Enem score and CRa, we noticed differences between the percentages of the categories (P value = 0.000). Here we have an initial indication that there is greater variation in dropout among the variables we call "educational and course choice" than among the social origin and demographic variables. In the results section we will assess whether this conclusion holds up from a multivariate exercise.

METHOD

To incorporate time into the study and take advantage of the longitudinal design of the data we used a discrete-time survival analysis method. This modeling strategy is used to estimate the time until a given event occurs (^{SINGER; WILLETT, 2003}). These models are suitable for investigating whether the event occurs, when it occurs, and the factors associated with the occurrence or non-occurrence of the event and its temporal heterogeneity.

^{Singer and Willett (2003}) point out three methodological features that need to be defined to conduct a survival analysis: the target event whose occurrence is being studied, the beginning of time, which is an initial starting point when no one in the study has experienced the target event, and the metric for time, which is a meaningful scale at which the occurrence of the event is recorded. In this research, the target event is course dropout, the event occurrence is the transition from course enrollment status to "cancelled," the starting point of time is entry into the university - 2014.1 cohort, and the metric for time of the event occurrence is recorded by semester. Thus, in the language of these models, time is treated as a discrete metric.

Survival methods differ from traditional statistical techniques in that they provide a way to simultaneously analyze the times of event occurrence and non-occurrence of the event. This is done through the hazard function and the survival function. The occurrence of the event in each discrete period is known as the hazard. Denoted by h (tᵢⱼ), the discrete-time hazard is the probability that individual i will experience the event in period j, given that he did not experience it in any previous period. Conditionality ensures that the hazard represents the probability of the event occurring among individuals eligible to experience the event in that period. As individuals experience the event, they drop out of the hazard set and are not eligible to experience it in later periods. Due to this conditionality, the hazard probability for individual i in period j assesses his unique hazard of event occurrence in that period (^{SINGER; WILLETT, 2003}). The hazard function assists in identifying especially risky time periods, that is, when the event is most likely to occur. In addition, it shows whether the hazard increases, decreases, or remains constant over time.

Allied to the hazard function, the survival function provides another way to describe the distribution of event occurrence over time. Unlike the hazard function, which assesses the single hazard associated with each period, the survival function accumulates these occurrence risks, period by period, to assess the probability that a randomly selected individual will "survive," that is, not experience the event. The survival function is defined as the probability that individual i survives period j. For this to happen, the individual must not experience the target event in the jth period or any previous period (^{SINGER; WILLETT, 2003}). It is important to point out that at the beginning of the process observation, when no one has yet experienced the event, everyone is surviving and, by definition, its value is 1. Over time, as events occur, the survival function decreases.

To find out the hazard between the occurrence of the event at each time period and the predictors, we use logistic regressions to regress the event indicator (dependent variable) on the time indicators (time dummies) and the selected predictors (independent variables) on the data set in person-period format, also known as the long data format. This means that the observations are nested in the individuals and repeated in the rows by the amount of time the individual remains under observation.

Importantly, the discrete-time hazard base model invokes a common but restrictive assumption: that each predictor has an identical effect across all periods studied. This restriction, known as the proportionality assumption, stipulates that the effect of a predictor does not depend on the respondent's duration in the initial state. However, it is possible that the effect of a particular predictor is not stable over time, so a non-proportional model may be more appropriate. This was the case in this research.

The interactions of time with predictors are justified by bivariate analyses and through fit statistics (^{SINGER; WILLETT, 2003}). Breaking the proportionality assumption, can be done by including statistical interactions by adding a cross-product term to a model that already includes the main component effects so that the factors associated with the event can vary over time. Our bivariate exploratory analyses showed that of the predictors analyzed those that did not follow proportional measures over time were: first course choice, grade affected course choice, Enem and CRa, so for these we added interaction with time. The equationbelow represents our model choice:

The main time effect is represented by D₁ to D յ and the interaction between X₁ and time is represented by the terms X₁ D₁ to Xյ to Dյ.

RESULTS

As mentioned in the method section, the hazard and survival functions allow us to check both sides of the phenomenon, the occurrence of the event that shows the riskiest moments of dropping out of the course, and the non-occurrence of the event that shows the proportion of students who survived. The key tool for summarizing the population distribution of event occurrence is the life table, a table that tracks the event histories of individuals from the beginning of time counting, when no one has yet experienced the target event, to the end of data collection. Table 2 presents a life table for the cohort of students who entered UFRJ in 2014.1.

The results in Table 2 show that the semesters with the highest hazard of dropping out in the period of time analyzed are the first and second, configuring the student's first year at the university, and the fifth semester. As for survival, we notice that at the end of the first year 84% of the students in the analyzed cohort remained in their original courses, and at the end of the 6th semester 68% continued in their courses.

Both international and national studies (^{SACCARO et al., 2019}; ^{SILVA, 2013}; ^{AMERI et al., 2016}; ^{LASSIBILLE; GÓMEZ, 2008}, ^{GURY, 2011}) evidence highest hazard rates of dropout in the first year of the course, so we realize that UFRJ follows in the direction of the evidence already found by other researchers. This result points to a kind of "tasting" period of the course and university environment by the students, since approximately 15% of students drop out in the first year, it is relevant to investigate how the conditions of choice of course and the format of entry into the university structure the dropout.

As this is a cohort that entered the university via the Enem/Sisu selection process, this seems to us an important result, since the Sisu induces an adaptive choice of the student based on his or her grade, and not an early choice as it occurred with previous selection processes such as the vestibular. The high dropout rate at the beginning of the course signals that the students' choices can be made with two references: to enter or not the university, and only afterwards in which course to enter, as we will show in the next analyses.

The peak hazard rate of dropout in the fifth semester seemed counterintuitive to us. Through descriptive exploration, we have conjectured the hypothesis that the high hazard of dropping out in the fifth semester may be related to a process that arises administratively (in the data) by the rules of the institution (cancellation of enrollment and other processes), for example the accumulation of locked semesters that results in the cancellation of enrollment.

Are students' social and demographic background factors associated with course dropout at UFRJ?

Through the variables of color/race, gender and family PSE, we can check whether there are indications of inequalities of results according to the social and demographic origin of the students. Chart 1 shows the predicted hazard rates of dropping out of the course according to color/race, controlling for the other independent variables. We observe that white students had a slightly higher hazard rates of dropping out of the course than black and brown students. However, the small difference between the groups' predicted hazard rates is not statistically significant at any point in time, as verified in the post-estimation tests (test: t1= -0.006; t2 =-0.008; t3= -0.005; t4= -0.003; t5= -0.008; t6= -0.005; P value>0.05). This result indicates that whites drop out as much as blacks and browns and goes in the same direction as other Brazilian studies that found no direct relationship of color/race in the dropout of students from courses (^{COSTA et al., 2018}; ^{COSTA; PICANÇO, 2020}).

As for gender, controlling for the other variables, women presented a slightly higher hazard rate risk of dropping out of the course than men, as shown in graph 2. However, the small difference between the groups' predicted values is not statistically significant at any point in time, as verified in the post-estimation tests (test: t1= -0.006; t2 = -0.008; t3= -0.005; t4= -0.003; t5= -0.008; t6= -0.005; P value>0.05). Thus, for this UFRJ cohort the findings indicate that women drop out as much as men.

Source: UFRJ / DRE/PR1. Elaborated by the author.

Chart 1: Predicted hazard rates of dropping out of a course according to color/race. 

Source: UFRJ / DRE/PR1. Elaborated by the author.

Graph 2: Predicted hazard rate of course dropout according to gender. 

The socioeconomic position of the family measured by the maximum education of the parents is presented in graph 3. Controlling for the other variables, students with parents with less than higher education (<ES) had a hazard rate of dropping out very close to students with parents with higher education (>=ES). The difference between the groups' predicted values is not statistically significant at any point in time, as verified in the post-estimation tests (test: t1= -0.005; t2 = -0.007; t3= -0.004; t4= -0.003; t5= -0.007; t6= -0.005; P value>0.05). That is, for this cohort at UFRJ, there is no direct association of family socio-economic position and course dropout.

Source: UFRJ / DRE/PR1. Elaborated by the author.

Chart 3: Predicted hazard rate of dropping out of the course according to the family's socioeconomic status. 

These results indicate little difference between the categories of the students' socio-demographic variables. They should be interpreted considering both the extensive controls we used, as well as the socioeconomic selectivity at the entrance of a university that adopts a competitive selection process. Since UFRJ is a selective university, one hypothesis is that social selection took place at the entrance of the institution, that is, at the transition from high school to higher education, or even in the previous educational stages.

This type of result is known in the sociology of educational stratification which indicates that social backgrounds influence each of the educational transitions differently (^{MARE, 1980}, ¹⁹⁸¹). In this sense, ^{Shavit and Blossfeld (1993}) point out that educational systems open up from the bottom up, so that cohorts successively and slowly advance within the educational hierarchy. However, the highest educational levels remain fairly exclusive, with the result that real bottlenecks are created in the transition to the top level (^{SHAVIT; BLOSSFELD, 1993}). This process is meaningful both from a statistical and sociological perspectives since it creates more homogeneous populations according to various sociodemographic and educational dimensions. We also caution that we insert students' courses in the models as dummy variables. This is equivalent to treating courses as fixed effects in our modeling strategy. Fixed effects are typically included to control for unobserved heterogeneity across different levels of the fixed effects variable and they essentially capture the average effect of these unobserved factors on the dependent variable. Once we take this heterogeneity in consideration in conjunction with other controls, we find that the socio-demographic factors have little differences. How course specific characteristics shape dropout rates and how they act in the suppression or amplification of individual characteristics is a topic that deserves attention in another paper.

Are educational and course choice factors associated with dropping out at UFRJ? Does this result vary along the student's trajectory in undergraduate studies?

Before entering university there is an educational and choice process that can influence future outcomes (^{PERNA, 2006}, ^{HOXBY; AVERY, 2013}; ^{MEROLLA, 2017}). Thus, we analyzed the association of course dropout with the variables "cutoff score affected course choice," "first course choice," and Enem performance quintile, controlling for the other factors.

Chart 4 shows that students who said the cutoff score affected their choice of course had a higher risk predicted hazard rate of dropping out compared to those who said the cutoff score did not affect their choice. We observed that the difference between the groups was greater at the end of the student's first year in the course, that is, in the second semester (t2). As verified in the post-estimation test, the difference between groups was statistically significant in all semesters except the 6th (test: t1= 0.049; t2 = 0.079; t3= 0.024; t4 = 0.034; t5= 0.062; P value<0.01; t6= 0.012; P value>0.05).

Source: UFRJ / DRE/PR1. Elaborated by the author.

Graph 4: Predicted hazard rate of course dropout according to whether score affected course choice over time. 

As for the variable first course option, we noticed in Graph 5 that the predicted hazard ratios of dropping out were higher for those who said the course was not their first choice, compared to those who said the course was their first choice, controlling for the other factors. According to the post-estimation test, the difference between the groups was statistically significant in all semesters except the 3rd and 6th (test: t1= 0.066; t2 = 0.092; t4 = 0.030; t5= 0.050; P value<0.01; t3= 0.013; t6= 0.014; P value>0.05). We observed that the association was higher in the first and second semester.

Source: UFRJ / DRE/PR1. Elaborated by the author.

Graph 5: Predicted hazard rate of course dropout according to first course choice over time. 

Thus, these course choice variables give us indications about the selection process used by UFRJ in the analyzed period, that is, the Enem/Sisu. Some studies have already indicated that Sisu modifies the dynamics of course choice (^{NOGUEIRA et al., 2017}). In Sisu, the student first take the Enem exams and only after knowing the score applies for a first and second course option. In this sense, ^{Nogueira et al. (2017}) state that through simulations made in the initial stage of Sisu the student tests their chances of being approved in certain courses and institutions. Therefore, the system, even if indirectly, stimulates the adjustment of original preferences to what is possible even if it is not the desired course or institution (^{NOGUEIRA et al., 2017}). Thus, the high risk of dropping out in the first year of the course, of those that the course option was not the first and that the cutoff score affected the choice, signals that possibly getting into university was more important for this cohort of students than where to enter.

As for Enem performance, graph 6 shows that the students who had the highest risk of dropping out, in the first year of the course, were those with Enem performance in the 2nd, 3rd and 4th quintiles, compared to those with low performance, i.e., in the 1st quintile, and high performance, in the 5th quintile. In the first year only the differences between the predicted hazard rates from the 2nd to the 1st quintile and from the 5th to the 4th quintile were statistically significant (P value <0.05).

Interestingly, in the students' first year in the courses, those who had lower Enem performances, i.e., in the 1st quintile, had a low dropout risk, close to that of those with high performance, in the 5th quintile. One hypothesis for this result, according to the literature, is that students with lower scores have little opportunity for mobility/choosing another discipline of study, leading them to place a higher value on their place at university (^{MAY; BOUSTED, 2004}).

We noticed that the predicted hazard rate of the performance categories changed across semesters and that after the first year, those with performance in the 5th quintile had lower hazard of dropping out of courses.

Source: UFRJ / DRE/PR1. Elaborated by the author.

Chart 6: Predicted hazard rate of dropping out according to the quintile of performance in ENEM over time. 

Therefore, we observed that the association of educational and course choice factors with dropping out are greater than the relation of students' social and demographic origins. The results of the multivariate analysis indicated that, controlling for the other variables, educational and course choice factors would be associated with course dropout in the analyzed cohort, especially in the student's first year. Again, we refer to the Sisu and its induction of the course choice logic. We emphasize that the change in the selection process was not accompanied by curricular changes in the courses, which continue with the same structure prior to the implementation of the new selection process (Enem/Sisu). It is important to point out that students make their choices in an iterative and adaptive way. When they enter university, most of the time they find courses structured in careers and subjects in a rigid way, which can contribute to dropout in the beginning of the course.

Is formal academic integration associated with course dropping out at UFRJ? Does this result vary along the student's undergraduate trajectory?

To analyze dropout in a higher education institution, we know that it is important to distinguish students' experiences within the academic and social systems of institutions (^{TINTO, 2012}). The academic system is composed of characteristics directly linked to the educational experiences of students, such as their performance in the courses, attendance, and other experiences etc. The social system, on the other hand, has informal characteristics, such as personal relationships and involvement among members of the institution, especially the contacts between students in meeting places within the university. Thus, the academic integration of students is directly linked with the formal characteristics of the system and the social integration with the informal characteristics (^{TINTO, 2012}).

The socially integrated student is not necessarily academically integrated and vice versa. For example, a student can be integrated into the social system of the university, have good relationships with colleagues and employees of the institution, participate in specific groups organized by their peers, and yet drop out because they are not academically integrated, i.e., they cannot maintain attendance, good grades, etc. (^{TINTO, 2012}). However, it is important to point out that the impact of academic integration and social integration is not necessarily symmetrical, it depends very much on each higher education institution (^{BRAXTON et al., 2004}). Maintaining an adequate level of performance in the academic system, in most higher education institutions, is the minimum formal condition for student permanence.

Thus, in this study we prioritized the measurement of formal academic integration since it was not possible to obtain information about the social integration of students. Thus, this was measured by the student's accumulated coefficient of income per semester (CRa).

Chart 7 shows that students with low CRa (1st quintile) were at higher hazard of dropping out in the entire period analyzed, compared to students in the other performance quintiles. Verification by the post-estimation test indicates that the difference between the predicted hazard from the 1st quintile to the other quintiles is statistically significant (P value <0.05).

Source: UFRJ / DRE/PR1. Elaborated by the author.

Chart 7: Predicted hazard rate of course dropout according to CRa quintile over time. 

This result shows that in the cohort and during the time analyzed, the students who had accumulated coefficient of income per semester (CRa) in the upper quintiles were those who presented lower predicted hazard rates of dropping out of the course. Having a good CRa implies getting scholarships, internships, opportunities at the institution, which may influence students' experiences after entering the university.

Several studies take students' academic achievement as a proxy for formal academic integration and point out that the higher the student's grades, during university studies, the lower the risk of dropping out (^{BENNETT, 2009}; ^{SUHRE et al., 2007}; ^{ARAQUE et al., 2009}; ^{BELLOC et al., 2010}).

Also, research highlights that students' first academic achievements significantly influence the likelihood of dropping out, in other words, students are more likely to continue at university if they get good grades early on (^{BELLOC et al., 2010}; ^{BENNETT, 2009}; ^{MONTMARQUETTE et al., 2001}; ^{PASCARELLA; TERENZINI, 2005}).

However, one must be cautious about whether CRa is in fact associated with difficulties in following the course or not, or whether it is mediated by other factors that were not observed: learning, motivation, social integration, etc. In addition, there is the limitation that the peak hazard rate in the fifth semester may be capturing a process that arises administratively (in the data) by the rules of the institution. In practice the student may have dropped out before the institution registering the departure.

FINAL CONSIDERATIONS

This paper showed that in students' first three years, the hazard rates of dropping out of the course is highest at the beginning of the courses and then in the fifth semester. Multivariate analysis revealed some counterintuitive results. White students drop out as much as black and brown students when we incorporate a multivariate analysis that incorporates individual level variables as well as the course that students are enrolled. The difference between women's predicted hazard rates of dropping out was not statistically significant compared to men. Students with parents with less than a college education had a hazard rate of dropping out of the course close to students with parents with a college education. Therefore, in aggregate for this cohort of UFRJ students, students' social and demographic background was not shown to be associated with course dropout. These results need to be interpreted taking into consideration that entering an academically selective higher education institution selects students that are more motivated and academically prepared

Nonetheless, we were able to identify educational factors and the choice of course were associated with dropping out, especially in the first year. The predicted hazard rates of those who reported that the cutoff score affected their choice of course was higher than the hazard of those who said the cutoff score did not affect their choice. Also, the hazard rates of students who said the course was not their first choice was higher than those who said the course was their first choice. As for the Enem performance quintile, the students who presented the lowest hazard of dropping out in the first year of the course were those with performance in the 1st quintile and in the 5th quintile. This result changed throughout the semesters analyzed and showed that students with high performance (5th quintile) were more resilient than the others. Another variable that was shown to be associated with course dropout was the Cumulative Coefficient of Achievement (CRa) which was used as a proxy for formal academic integration. Students with low CRa had a higher hazard of dropping out than those with CRa in the top quintiles.

We emphasize that the results verified in this article stem from a case study of a cohort of UFRJ students and cannot be extrapolated to other cohorts and institutions. Thus, we caution that all results should be interpreted as typical of the institution. In the language of case studies (^{GERRING, 2007}), we cannot state whether the studied context is typical, diverse, extreme, deviant, influential. We argue that this issue - known as a problem about the external validity of the study - is counterbalanced by the high quality of the data, that is, internal validity, the availability of a research design that allows for the incorporation of time (longitudinal data, rarely available in the Brazilian research context) and availability of the measurement of variables that point to important mechanisms in structuring the interruption and continuity of studies in a large research university.

Also, we point out that the modeling technique opted for an aggregate analysis of all students across courses. Thus, for future studies, it is necessary to ascertain how these factors affect dropout in a disaggregated and course specific way, since there are different undergraduate courses, and the heterogeneity that permeates the institution was not known.

Even with these limitations, our analysis allows us to make some considerations regarding the cohort analyzed. We found an early dropout period, in the first year of the course, which may be working, on the part of the student, as a period to experience how the course and the university works and decide to stay or drop out of the course. As educational and course choice factors showed greater influences in the student's first year, our hypothesis is that the process of course choice, through the current format of access to the university, is possibly structuring an early dropout in the courses. Even if indirectly, Enem/Sisu induces an adaptive choice of the student based on his/her score, and not an early choice as it occurred in the vestibular. These results indicate that efficiency gains in the system as a whole, which may have occurred with the adoption of Sisu - cost reduction for students, centralization of the selection - are counterbalanced by efficiency loss at the institution level.

Based on the results, some indications can be made. First, most energy should be put into establishing precautions/measures to reduce dropout in the early stages of courses, because that is where the issues of student dropout and transfer are most pertinent.

Another issue to be considered, to try to improve the formal academic integration of the student, is to carry out curricular adaptation in the first semesters of the courses. Some international research shows that several higher education institutions try to avoid problems - such as too many demands at the beginning of the course, too many exams, too much material for study - by offering better conditions for students, reforming curricula, offering transition courses to compensate for educational gaps, and making mentors and tutors available for the first year (LARSON et al., 2013; ^{HEUBLEIN, 2014}).

Anyway, these are just a few suggestions among many that can be studied according to the case of each higher education institution to decrease course dropout and increase student graduation. Along with the creation and implementation of measures to reduce dropout, it is essential to consider the monitoring and evaluation of the impact of these initiatives.

Preprint

DOI: https://preprints.scielo.org/index.php/scielo/preprint/view/3339