Characterizing intercampus migration in a private university of Baja California, Mexico

Theoretical references of university dropout

One of the most relevant theoretical models of school dropout is Tinto (1975), which indicates that dropout is related to race, gender, ability, social status, previous academic experiences, and residency. In addition, Tinto emphasizes variables that represent motivation, such as the expectations of the chosen career and resilience to achieve the academic degree. The previous factors indicate the students’ commitment to their objectives, which, according to Tinto, can be decisive in their decision to drop out. Tinto’s model serves as the basis and is complemented by the theories of Pascarella & Terenzini (1980); Ethington (1990); Bean (1985); Spady (1970), and Astin (1999) on the existence of exogenous factors with the ability to influence dropouts. For example, financial factors and the perception of benefits (student investment against what he receives).

Bean and Metzner (1985) emphasize the academic, social, psychological, and environmental factors at the time of entering the university as variables that define the student’s academic performance in his career. Cabrera, Nora, and Castaneda (1993) integrate some variables from the Tinto (1975) and Bean and Metzner (1985) models in a longitudinal study during the first year of study at an academic institution in Australia. Their model emphasizes the need for students to receive financial support and the cost-benefit ratio since these variables directly influence the decision to dropout from school.

Concerning private institutions, the student’s perception (what they pay for) plays a crucial role in school dropout. So, desertion is affected by the financial support system, prestige, educational quality, and university faculty (Cabrera et al., 1993; Pascarella and Terenzini, 1980; Ethington, 1990).

Some case studies of dropout and migration

The literature on student dropout seeks to reduce it and increase terminal efficiency. Analyzing different variables, such as self-efficacy (Charris et al., 2017), is sought to find a correlation between personal attributes and the students’ permanence. For example, Navarro et al. (2017) studied a sample of 322 students from the 2015-1 period, male and female, active and dropouts at a university in Barranquilla, Colombia. Using the General Self-Efficacy Scale (EAG), Navarro et al. did not find a significant correlation between efficacy and permanence or a substantial correlation between effectiveness and attrition. However, they find that dropouts increase among students with a job compared to those without jobs. Thus, students who are not full-time have a higher risk of dropping out.

The grade point average (GPA), the years of advancement in the career, and the university selection test score represents students’ academic performance in a university. Ramírez and Grandón (2018) analyze student dropout considering a sample of 5,288 Chilean students belonging to four consecutive student cohorts from 44 university programs. Using decision trees with optimized parameters, they analyze the impact on dropout by considering factors classified in demographics (age and gender), university history (admission exam score, grade point average in the last period), economic (family income level and type of high school), and academic performance (progress, and general grade point average).

Students who move from their places of residence to continue their university studies are also possible causes of desertion. Hernández et al. (2016) predict the risk of desertion for 134 students of the academic program “Engineering in Information Technology and Communications” at the Higher Technological Institute of Misantla, Mexico. By applying logistic regression, clusters generation, decision trees, and neural networks, Hernández et al. conclude that the student’s place of origin significantly impacts school dropout. Simillarly, Eckert and Suénaga (2015) characterize students’ attrition for the “Computer Engineering” degree at the Gastón Dachary University in Argentina. By applying the Classifier Algorithm C4.5, Decision Trees, Naïve Bayes Augmented to Tree (TAN), and OneR Rules, the authors find that the place of origin and the number of failed subjects in the first year of studies are factors with a significant impact on desertion.

Regarding the migration or transfer of students between different institutions, which from the student’s perspective is not about dropping out or abandonment but about persistence and change, Veloso and Rodríguez-Gómez (2020) carried out a study in a Chilean university to identify the main factors influencing students’ migration. They find that students move to other institutions due to faculty, personal expectations, and academic failure perceptions, which accumulate until generating a break in the student who chooses to migrate.

At an international level, particularly in the United States, students’ migration to other campuses has to do with transportation and mobility to reach the campus (Chamely-Wiik et al., 2021). In other words, those who do not live in the campus’ dormitories deal with transport costs, which increase the risk of desertion. Students’ migration is quite natural since Americans face it many times: from community colleges to universities, from a four-year bachelor’s program to two-year bachelor’s program, or from public to private universities (Ishitani & Flood, 2018). So, this branch of the literature concerns generating adaptation strategies (Chamely-Wiik et al., 2021) to support and integrate students from other campuses or regions (York & Fernandez, 2018). For instance, accrediting institutions evaluate the previous programs for students from other countries or regions (Anwar & Richards, 2018).

Data mining and supervised learning

The use of data mining facilitates decision-making since it enables new approaches to problem-solving by discovering hidden patterns and relationships in datasets. Hence, data mining allows an inductive approach to decision support systems (Decision Support Systems, DSS). The data mining algorithms are divided into supervised and unsupervised.

The supervised methodologies require a group of previously classified data and knowing the value of the attributes in advance. On the other hand, the supervised learning algorithms use pre-established input variables known as independent variables, which can have a quantitative, qualitative, or categorical value, to predict the importance of the outputs or dependent variables, whose nature can be quantitative or categorical. The fundamental purpose is to identify a pattern to predict the expected response (Hastie et al., 2013).

The supervised techniques are those where the data does not have any label or classification; that is to say, no categorical or numerical objective value is known a priori (Gironés et al., 2017). The most widely used learning algorithms are linear predictors since they are easy to interpret. However, these models seek to respond with a single value (linear regression) or a binary classification (logistic regression), among others, by ignoring complex relationships (Shalev-Shwartz & Ben-David, 2013).

Ethical approval

The ethical research committee of CETYS University granted retrospective approval for this study and publication of the results, in the resolution D-CEI100 on March 25^th, 2022. Based on Mexican regulations pertaining research for health purposes, the ERC stated that data of the research are anonymous, and there is no need for individual informed consent for this study.

Setting

Our case study refers to a non-profit private University System located in Baja California, Mexico, which a group of Counselors sponsors. The system has three campuses located in the cities of Mexicali, Tijuana, and Ensenada. The institution’s academic offer concentrates on three levels: high school, professional, and postgraduate (CETYS University, 2010).

The Ensenada campus is the international campus of the University System. It offers two high school programs, 12 bachelor’s degrees (six from the business and management school and six from the engineering school), five master’s programs, and a doctorate program. It is the smallest campus in the university system, with 1107 students enrolled from August to December 2019. In contrast, the Mexicali and Tijuana campuses have 3724 and 3421 students, respectively (Cierre de Campaña 2019, CETYS Universidad Campus Ensenada, 2019).

The current dropout rate in Ensenada’s undergraduate programs is 30%, which is not desirable since the institutional goal is 20% (CETYS University, 2018). Although the Ensenada campus has special financial support (CETYS Universidad, 2016), its dropout rate is higher than other campuses, except for 2017 and 2018, where the Tijuana campus reports the highest dropout rate, and 2009 where the Mexicali deals with the highest desertion rate, see Figure 1.

Figure 1. Dropout System Cohorts 4^th year 2008-2018 (CETYS University, 2018).

The three campuses have the same academic programs, educational model, philosophy, mission, educational principles, and values; the financial support programs also apply to all the campuses. However, the Ensenada Campus has an exclusive scholarship, called PAFENI, that the rectory grants to support high scholars who want to start their undergraduate studies. It is important to note that scholarships can be transferred from one campus to another except for the PAFENI scholarship since such a scholarship pretends to boost enrolling at the Ensenada campus.

The distribution of undergraduate enrollment in the system, as can be seen in Figure 2, is mainly concentrated between the Mexicali campus and the Tijuana campus.

Figure 2. Distribution of undergraduate enrollment in the CETYS University System (CETYS University, 2019).

The data

Our database considers dropout students from all undergraduate programs in the Ensenada Campus between January 2008 and June 2018. The database comprises 356 records, of which 26% relate to campus migration. The data extraction was carried out as follows: first, we identify the current and historical data sources, formal and informal, that contain relevant information to fulfill the purpose of this study.

Consequently, the information generated around the student was gathered, from their first contact with the Ensenada Campus to the moment when they leave the campus without completing their studies. So, the data were obtained from the university’s main digital sources such as promotion, scholar WEB System, finance, student information portal, and the Education Center for Student Development. The data was collected to build a database whose logical model represents the different dimensions that characterize the dropout students. Table 1 shows the database classification. Note that we consider four groups: personal details, entrance to the university, academic program attributes, and institutional experience. We process these data through the R programming tool version 4.1.2, and we use the BigML cloud application to determine the best logistic regression model (Alban & Mauricio, 2019).

The independent variables shown in Table 1 were classified according to what the theorists of attrition observed from pioneering authors such as Tinto (1975), Bean (1985), Spady (1970), Ethington (1990), to some of the most recent authors such as Donoso and Schiefelbein (2007), Manyanga et al., (2017), Aljohani (2016), Morrison and Silverman (2012). In particular, when talking about dropout or retention, the previous authors mention two relevant moments: when the student enters the university and their experience during their stay. As we can see in Table 1, the variables that characterize these moments are categorized in various contexts.

The variable “MotivoBaja” is the dependent variable of this study, while the student’s attributes represent the model’s independent variables. It is worth noticing that the dependent variable points out the reason for attrition, which is a categorical variable. To analyze intercampus migration, we transform this variable into a dichotomous logistic operator that takes values 0 and 1, where 1 represents migration to another campus and 0 any other reason for leaving.

At entering the university, the personal context is composed of the student’s attributes such as age, gender, socioeconomic level, place of origin (foreign or local), and previous relationship with the university. The academic context considers variables related to intellectual attributes. The third context, identified as Institutional, refers to the educational program and the percentage of scholarship granted.

Regarding the second moment, it points out the experience within the institution. Here, we consider variables that explain the academic and financial evolution during the students’ time at the university.

Table 2 shows descriptive statistics of the database we are considering. The dropout students mainly belong to a medium socioeconomic level since the second income quartile is the most common, and many students come from the university’s high school (Figure 3c). Interestingly, the GPA of migrant students is high; note that the Kurtosis of this variable is positive and equal to three, which means that the distribution is skewed to the right of the mean.

Figure 3. a. Socioeconomic level (IBM SPSS Statistics). b. Final average (IBM SPSS Statistics). c. Entrance school (IBM SPSS Statistics). d. Academic program (IBM SPSS Statistics).

In addition, we use the IBM SPSS Statistics application, version 25, to perform a descriptive analysis and characterize students’ migration. The variables that show a high concentration of values are the socioeconomic level (Figure 3a), the final average when dropping out (Figure 3b), the entrance school (Figure 3c), and the academic programs per school (Figure 3d).

We build a mathematical model based on the logistic regression methodology to predict a student’s probability of migrating to another campus. The dependent variable is denoted as Y, while the explanatory variables, or independent, are X1, X2,., Xn. The dependent variable Y refers to students’ migration: Y = 1 means that the students drop out from the Ensenada campus to another campus, and Y = 0 represents students’ desertion caused by other reasons.

The impact factor of each variable is β1, β2, …, βn; and we also consider β0, which is the value of the intersection of Y when we expect the predictor to be zero. Then, each β1, β2, …, βn indicates the slope or adjustment of each independent variable to predict Y. If this value is positive or negative, for each unit that is reduced or increased, the closest explanatory variable is predicting the value of Y. So, the impact factors capture the relationship between the explanatory variables and the probability of migrating to other campuses within the same educational system. Mathematically, we have that

Using R programming (R Core Team, 2013), we split the database into a training set (75%) and a testing set (25%), which we use to build and validate different models, one for each classification in Table 1. By considering the most significant variables of each model, we construct a fifth model with them. We find that the most relevant explanatory variables of the phenomenon are: age, the result of the admission exam by areas (mathematical, verbal, and writing), the GPA of the student’s last period, the number of failed subjects, how many years the student was in the university and its average scholarship. So, the prediction model that we consider is

Predictive model

We construct the best predictive model by adding explanatory variables related to the different dimensions that characterize students’ desertion. Table 3 shows the results of such models that we get using R programming language; it is worth recalling that not all variables are significant, so we delete them from the final model. The Akaike information criterion (AIC) indicates that the model that best fits the training data is model 1. The Bayesian Information Criterion (BIC) shows that the confounding variables that impact the decision to migrate to another campus by students are age, the result of the area of mathematics, the grade point average that the student had at the time of migrating, and the scholarship percentage at the time of leaving the campus. Then, the best predictive model is the following:

Figure 4a, b, and c visualize the relationship between the decision to migrate among the model variables in. We observe that migration reduces as age increases, but the impact is the opposite concerning dropping out from the system, the older the lower the probability of migrating to another campus but increase the probability of dropping out of the system. However, the probability of migrating to another campus increase as the score on the admission test in mathematical reasoning, the higher the GPA and the scholarship percentage increase.

Figure 4. Migration probability given a. Dropout rate, b. Mathematical reasoning results, c. GPA at the migration decision and d. Having a scholarship.

Figure 6 illustrates the model assessment concerning its performance, with a 75.28% accuracy (accuracy) and 55.6% precision. The first indicates how close the predicted value is to the actual value, while the second indicator measures how many predicted values are true from all predicted correctly. In addition, the area under the Receiver Operator Characteristic curve (ROC) (Figure 6) shows the diagnostic capacity of the model with a 67% probability that the prediction is correct. The confusion matrix (Figure 5) validates the previous results since the model classifies five true positives, 62 true negatives, four false positives, and 18 false negatives, representing a good precision.

Figure 5. Confusion matrix.

Figure 6. Receiver Operator Characteristic curve (ROC).

We get 77 and 56%, respectively, regarding the model’s specificity and sensitivity. Both metrics indicate the ability of the model to discriminate positive cases from negative ones. In particular, sensitivity measures the positive possibilities, while specificity measures the correct classification of negative instances. The F1 factor of the model is 0.99, indicating a positive relationship between the precision and the ability of the model to predict correctly; this factor is widely used as it suggests the relationship between accuracy and sensitivity, where the model is perfect when F1 = 1. This factor is obtained through the formula:

Underlying data

Zenodo: Desercion a otros campus. https://doi.org/10.5281/zenodo.6377479 (Beltran, 2022)

This project contains the following underlying data:

Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).