Analysis of the Influence of Learning State before UniversityAdmission to College Dropout Using Hierarchical Bayesian Model
SHIRATORI Naruhiko (1), TAIRI Shintaro (2), OISHI Tetsuya (3), MORI Masao (4),
MUROTA Masao (5)Kaetsu University, Japan (1)Yokohama College of Commerce, Japan (2)Tokyo Institute of Technology, Japan (3)Tokyo Institute of Technology, Japan (4)Tokyo Institute of Technology, Japan (5)Abstract
In this research, we express the probability of college students dropping out using a hierarchical
Bayesian model and derive to what extent the variables before admission influence college dropout. InJapan, about 5% of students entered university, but they drop out without graduation. Many studies
have shown that the proportion of dropout students varies from university to university and correlateswith university scale and deviation value. Many researches have been made to forecast dropouts inadvance, but studies have not been made to express how the dropout probability dynamicallychanges depending on the situation before admission. It is assumed that the change in the dropout
probability varies according to the variables before enrollment (number of absences at high school,
type of high school etc.). Variables used in the model consist of pre-admission variables and postadmission variables, and the post-admission variables are the number of units per semester and GPA.
We created a hierarchical Bayesian model using pre-admission variables and post-admission
variables to derive the drop-out probability for that term. It was found that the probability of droppingout depends on the variables before entering the school, especially the type of high school and thenumber of absences. The probability of withdrawal is increased because the type of high school iscommunication system and the number of days absent at high school is large. Furthermore, we foundthat the change in the probability of dropout for each term differs for each variable before enrollment.
Keywords: Hierarchical Bayesian Model, Logistic Regression, Dropout;

1. Introduction
The dropout rate in universities in Japan has been rising since the 1990s and is becoming a serious
problem [1]. Tellingly, the student dropout rate has become a major point of interest in the annual
survey conducted by the Yomiuri Shimbun and is increasingly used in university evaluations [2].
Overall, 8% of Japanese students drop out of college, with a lower rate at the national and publicuniversities and a higher rate at private universities. Since the rate of graduation in Japan is higher
than other OECD countries, there is not much to discuss dropouts in Japan. Especially at Kaetsu
University where the author belongs, it shows a high dropout rate of 34.7% in the survey of 2014.
In this research, we express the probability of college students dropping out using a hierarchical
Bayesian model and derive to what extent the variables before admission influence college dropout.Topredict dropping out, you can do a regression using the results of the semester and the unit number.
However, the score and the number of credits will change depending on the state before enrollment. In
this research, we group state before enrollment and create a dropout prediction model with the groupdifference taken into account using hierarchical Bayesian model. After that, by examining the results ofthe dropout prediction model with the group difference taken into consideration and the results of thenonadditional model, we examine how much the group difference before entering the classroom isheard.

2. Related Works
Research on predicting student dropouts and establishing the underlying causes is widely conducted.
It has been shown that there are a number of variables affecting the decision to dropout, including
gender, teacher-student ratios, deviation values, university size, economic factors and variables
related to dropping so far.
Tajiri analyses the relationship between educational history and dropping out at a business universityand derives a set of micro variables for leaving students [3]. He found a low probability of female
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students dropping out within four years, but found that the probability is reversed beyond the four-yearperiod. He also identified factors such as academic ability tests, grades, and number of credits being
taken as significant micro variables related to dropout.
According to Kondo [4], a dropout prediction can be made at the beginning of the third year by using
prior data (sex, undergraduate, entrance examination class, attendance rate, etc.). He compares
various methods for making dropout predictions, including a logistic regression model, a support
vector machine, and the random forest algorithm. In the U.S., where retention rate (school enrolmentrate) is often used rather than dropout rate, Bingham et al. [5] used a logistic regression model toshow that enrolment rate differs according to the parents’ educational background and ethnicity.

3. Methods
3.1 Data
The data in this study is from students who entered K University in Tokyo, Japan, from 2012 to 2014.
The university is a college that teaches the social sciences. Transfer students and graduate students
are excluded from this data. There are 657 students with no missing data, of which the number ofdropouts is 194 people.
It is known that dropping out has a correlation with the results at the first and second semester in theuniversity. For example, in the study of Kondo [4], at the end of the 5th week of the 1st springsemester, it is estimated that about 40% of students who drop out by the beginning of the third year
can be predicted.
In the graph 1 below, it is a box plot chart showing the GPA of the 1st spring semester of a dropout
student and a regular student. The median value of GPA of students who dropped out is 2.36, and themedian value of GPA of regular students is 1.43. As can be seen from this figure, there is a clear
difference between the dropout student and the other students after entering the university.

Fig. 1: GPA of 1st semester between dropout student or not
Next, it checks whether the number of absence days at high school which is a pre-admission variable
has a relation with GPA which is a variable after admission. Figure 2 below is a box plot showing therelationship between absence days at high school and GPA of 1st semester. The X axis is adiscretized number of absent days at high school. On the X axis 1 represents absent days from highschool days 0 to 9, 2 from 10 to 19 days, 3 from 20 to 29 days, and 4 represents over 30 days. The Y
axis is GPA of 1st semester. The median value of each is 2.25, 2.11, 1.82, 1.58. From this we can seethat the variables after enrollment are influenced from the pre-admission variables.

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Fig. 2: GPA of 1st semester and high school absent days

3.2 Variables
Among the data, the variables to be used this time are the following five.
- 1. Fulltime Highschool or not: a student in fulltime high school or not (0,1)- 2. Number of Absence in high school (1,2,3,4)- 3. 1-1 GPA: GPA in the 1st semester (numerical, lower=0, upper=4)- 4. 1-1 credits (numerical, lower=0, upper=24)- 5. dropout (A student who dropout of the college or not): (0,1)
In this study, we use 1. high school type and 2. high school absent days as pre-admission variables.
High school type represents whether it is full-time high school or not, high school absent days are
discretized into 4 and used. 1 in high school absence days represents absent days from 0 to 9, 2 isfrom 10 to 19, 3 is from 20 to 29, and 4 is over 30 days. As the variable after enrollment, use 3.1st
semester's GPA and 4.1st semester unit number. However, since the variables 3 and 4 afterenrollment are highly correlated (corr = 0.81), only the GPA of 3 is used as a variable after admission.
The relationship between the GPA of the variable 3 after admission and the unit number of the postadmission variable 4 is represented by the following scatter diagram, Fig.3.

Fig. 3: scatter diagram of GPA & Credits

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3.3 Model
Using pre - admission variables and post - admission variables, we can verify how much we canpredict dropping out. For verification, the following three models are defined. In addition, logistic
regression models are used for each model.
Model 1: using only post-admission variablesn = 1, 2, ..., N. N represents the number of students and n represents the index of the student. Yrepresents dropout/not. a - 1 is a GPA variable, and b is an intercept
Model 2: using post-admission variables for each group of pre-admission variablesn = 1, 2, ..., N. A 1 and b for logit function change for each absence group. N represents the number ofstudents and n represents the index of the student. Y represents dropout/not.
Model 3: using groups of pre-admission variables and post-admission variables, Bayesian hierarchicalModel

In model 3, a [k] of each group is divided into terms expressing a common overall average in all
Absence groups and terms expressing each group difference. a_all and b_all are average values ofthe entire group, a_group, b_group are variables representing each group difference. Each groupdifference is assumed to follow the average 0 and standard deviation σ. k is 4 representing thenumber of absent groups in high school.
These three models were modeled by Stan and Bayesian estimation was performed using PyStan andMCMC (Markov Chain Monte Carlo methods). For model 1 and model 2, Iteration was used 2000times, warmup was 500 times, chain number was 4. For model 3, Iteration was used 7000 times,
warmup was 1000 times, chain number was 44. Results
The estimation result of the parameter of model 1 is as follows. The average value of a1 is -1.32, theaverage value of b is 1.63, and both of Rhat are 1.1 or less, and even if you look at the graph, it
converges.

The estimation result of the parameters of Model 2 is as follows. The slope and intercept for eachgroup converged because Rhat is less than 1.1.

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The estimation result of the parameters of Model 3 is as follows. The slope and intercept for eachgroup converged because Rhat is less than 1.1.

5. Discussion
By comparing models 1, 2 and 3, it became possible to express common items and differences foreach pre - admission variable group. The average of common coefficients was -1.27, the intercept was
1.84, and we could derive the parameter difference for each pre-entrance variable group. For
example, look at the case of a student whose GPA is 1, the probability of dropout in model 1 is 0.576,
and in case of model 2 it varies from 0.519 to 0.74 according to the number of absences before
enrollment. Furthermore, in the case of Model 3, it can be represented as high precision of the systemin the form of common variables and group differences.

Acknowledgment
This work was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research C 15K04380.

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Seizonjikan Bunseki, The Japan Society for Educational Sociology 65th Annual Report 120-121,2013.
Kondo Nobuhiko, Hatanaka Toshiharu: “Modelling of Students' Learning States Using Big Data ofStudents through the Baccalaureate Degree Program” Japanese Society for Information andSystems in Education 33(2), 94-103, 2016
Bingham, M. A., & Solverson, N. W.: “Using Enrollment Data to Predict Retention Rate.” Journalof Student Affairs Research and Practice, 53(1), 51–64. 2016

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