Implementation of a statistical monitoring system to track university dropout rates

Gadiel Felipe Castillo Martínez, Master's student in Estatistics. Credit: researcher's courtesy.

Professional educational dropout, in public and private universities, is a halt in the academic training of many students, who, for personal reasons, see their professional futures truncated when they are unable to complete their studies. Based on this premise, a research project used the strategy of integrating a statistical monitoring system with human mortality modeling techniques. Its results are aimed at creating tools that help educational institutions to know how dropout rates among their students have evolved and, through early warnings, to intervene and make the necessary changes to prevent the phenomenon from increasing. 

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Use of the Lee Carter's model and multivariate control charts in the field of college dropout 

Given the usefulness of methodologies used to measure phenomena related to human mortality, Gadiel Felipe Castillo Martínez, a student of the Master's in Statistics at the Universidad del Valle, utilized Lee Carter's model in order to provide a temporal analysis of the phenomenon of university dropout, using a methodology that would allow associating the different variants and visualizing their evolution over time. Based on this, a statistical monitoring system was adapted to identify the academic periods which presented alerts due to their variation in the trend, as well as the ages that explained these variations.  

His research, directed by Jaime Mosquera Restrepo, professor and researcher at School of Statistics of the Faculty of Engineering and member of the INFERIR research group in Applied Statistics, was based on the adaptation of information analysis models traditionally used in the field of health, in order to put them at the service of the study of university dropout.  

This adaptation was based on life tables, a theoretical-numeric model that uses biometric functions to determine the probability of death of a person at a specific age or during specific periods. For this research, such tables were conceived as dropout tables, which implied an adaptation of the biometric functions to be considered: the population to be analyzed were university students; the years reached by the population were the semesters completed by the students, both dropouts and non-dropouts; and mortality and death, measures of analysis for the life tables, were replaced by the dropouts as such, presented in each semester for each of the cohorts analyzed within the model.  

Once the life tables were adapted to the required context, the researcher Gadiel Castillo adapted the statistical monitoring system, which represented the most innovative bet in methodological terms, since it had not been proposed as a measure of analysis in this field: the Lee Carter (LC) model and its integration with dropout monitoring systems. Initially, the model, defined in 1992 and widely used in the demographic sciences, makes it possible to make estimates over time about the phenomenon of mortality in individuals, presenting a projection of the dropout trend over time, which in turn makes it possible to forecast its behavior in the future.  

"In the case of university dropouts, Lee Carter's model seeks to evaluate the evolution of this phenomenon over time and examine the trends it presents. It specifically analyzes how dropout has varied in each academic semester over the years, on which control charts are integrated to identify the academic periods where there have been significant changes in this trend," explains the researcher, adding that his objective behind the design of this methodology is to evaluate in which academic semesters there has been greater variation, both upward and downward, and its tendency to increase or decrease as the career progresses.  

The integration of the statistical monitoring system is based on the residuals generated by the Lee Carter model. These residuals contribute to identify which are the most significant variations of the measurement, as well as the academic semesters involved in each of these variations.   

A statistical monitoring system was implemented to monitor dropout. According to the researcher, this is one of the added and differential values of this methodology.  

For the research, real data from the Statistics program of the Universidad del Valle were used, in cohorts from 2000 to 2019, taking into account each of the academic semesters of each cohort and its evolution in terms of incoming and outgoing students. It was necessary to adapt the information, previously obtained after a request to the academic registration area of the University, to be used by the Lee Carter model. Then, the mentioned adaptation of the life tables, the adjustment of the Lee Carter model and the extraction of the residuals of the model and the statistical monitoring system were made. 

Results after adoption of the Lee Carter model 

Currently, the research has led to conclusions that show the wisdom of developing this methodology for monitoring university dropouts. "The first significant conclusion is that this methodology makes it possible to analyze the evolution of the phenomenon over time and by cohorts, and that the adaptation of the statistical monitoring model facilitates segmentation to identify the groups responsible for variations in the dropout trend," comments researcher Gadiel Castillo, adding that the study confirmed the effectiveness of the monitoring system developed by carrying out simulated scenarios based on specific scenarios. The results obtained by the system were consistent and congruent with the established expectations. 

In terms of the information analyzed, the research also allowed drawing conclusions about the phenomenon of desertion in the Statistics program at Universidad del Valle during the years analyzed: "The model reveals that the probability of desertion is higher in the first academic semesters, decreasing as the student progresses. This is due to the fact that in the first semesters there are greater risks for students, since they have less connection with the academic environment. Another conclusion, more specific, is that desertion is much lower in women than in men". The researcher clarifies that, although this may be due to the fact that the number of men enrolled in the Statistics program is usually higher, the dropout rate measured relatively among those who enrolled and dropped out is still significantly lower in the case of women.   

The usefulness of the methodology developed from this research in terms of replicability lies in the fact that it can be extended to any academic university program, both at the professional, technical and technological levels, inside and outside the Universidad del Valle. The possibility of generating early warnings, derived from the statistical monitoring model, opens the spectrum, in turn, so that even financial analyses can be carried out.  

For researcher Gadiel Castillo, these reasons allow him to be optimistic about the impact this methodology will have on the academic sector. "This is an innovative tool. Since an early warning can be generated, actions for risk prevention or mitigation can also be implemented for specific groups, unlike what happens with other methodologies, which do not allow us to disaggregate what is happening at such a detailed level. And it also helps to show what are the consequences of external conjunctural events such as a pandemic, social outbursts or macroeconomic phenomena such as cycles of economic expansion," he concludes. 

If interested in being in touch with the Master's student or any further information about the investigation, please write the Faculty of Engineering Communications Office: comunicaingenieria@correounivalle.edu.co.