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Jurnal Matematika MANTIK 

Vol. 5, No. 1, May 2019, pp. 28-34 

 

How to cite: B. R. A. Febrilia, S. Rahayu, and B. D. Korida, “Ordinal Logistic Regression 

Analysis of Factors Affecting the Length of Student Study”, mantik, vol. 5, no. 1, pp. 28-34, May 

2019. 

Ordinal Logistic Regression Analysis of Factors Affecting the 

Length of Student Study 
 

 

Baiq Rika Ayu Febrilia1, Suning Rahayu2, Baiq Dewi Korida3  

Institut Keguruan dan Ilmu Pendidikan Mataram, rikafebrilia@ikipmataram.ac.id1 

Institut Keguruan dan Ilmu Pendidikan Mataram, suningrahayu1198@gmail.com2 

Institut Keguruan dan Ilmu Pendidikan Mataram, dewikorida12@gmail.com3 

 
doi: https://doi.org/10.15642/mantik.2019.5.1.28-34 

 

 
Abstrak: Lama waktu seorang mahasiswa untuk menyelesaikan masa studi menjadi ukuran prestasi 

mahasiswa tersebut dan kesuksesan program studinya. Oleh karena lama masa studi cukup 

berpengaruh terhadap kualitas suatu program studi dan proses pembelajaran di dalamnya, maka perlu 

dilakukan studi lebih mendalam mengenai faktor-faktor yang mempengaruhi lama studi mahasiswa. 

Penelitian ini bertujuan untuk memodelkan faktor-faktor yang mempengaruhi lama masa studi 

mahasiswa menggunakan regresi logistik ordinal. Faktor-faktor tersebut adalah IPK mahasiswa dan 

jenis kelaminnya. Data mengenai lama studi, IPK dan jenis kelamin diambil untuk mahasiswa 

Program Studi Pendidikan Matematika IKIP Mataram yang lulus pada tahun 2017 dan 2018. Hasil 

penelitian menunjukkan bahwa kedua faktor berpengaruh signifikan terhadap lama masa studi 

mahasiswa. 

 

Kata kunci: regresi logistik ordinal, masa studi 

 

 

Abstract: The length of time a student completes the study period is a measure of the student's 

achievement and the success of his study program. Because the duration of the study period is quite 

influential on the quality of a study program and the learning process in it, it is necessary to do a 

more in-depth study of the factors that influence the duration of student studies. This study aims to 

model the factors that influence the length of the study period of students using ordinal logistic 

regression. These factors are the student's GPA and gender. Data on the length of study, GPA and 

gender were taken for students of the Mathematics Education Department, IKIP Mataram, who 

graduated in 2017 and 2018. The results of the study showed that the two factors had a significant 

effect on the length of the study period. 

 

Keywords: ordinal logistic regression, length of the study 

 

 

 

 

  

Jurnal Matematika MANTIK 

Vol. 5, No. 1, May 2019, pp. 28-34 

 

ISSN: 2527-3159 (print)2527-3167 (online) 

http://u.lipi.go.id/1458103791
http://u.lipi.go.id/1457054096


B. R. A. Febrilia, S. Rahayu, B. D. Korida 

Ordinal Logistic Regression Analysis of Factors Affecting the Length of Student Study 

29 

 

1. Introduction 
 

The duration of the student's study period is determined by how long a student can 

complete all his obligations in college until he is entitled to a bachelor's degree. The 

duration of the study period determines the success of learning at the college level, 

especially at the smallest unit level, especially on the study program [1]. The length of 

time a student completes the study period is also a measure of student achievement [2]. 

Under normal conditions, students must be able to complete their studies at the college 

level for eight semesters [3]. Thus, if there is a study program with an average length of 

the study period of more than eight semesters or four years, then the student achievement 

in the study program is not so good [4]. The duration of the study period is also one of the 

very important factors in determining the accreditation of study programs [5]. Therefore, 

managers of study programs need to pay special attention to the factors that affect the 

length of time student’s study. 

There are many factors that can affect the length of time student’s study. Two factors 

include the Grade Point Average (GPA) and student gender. GPA is one of the 

determinants of one's study period [6] because the value of student achievement, in this 

case, the IP / GPA value, determines how many Semester Credit Systems (SKS) can be 

taken by the student. The higher the GP / GPA of a student, the student is allowed to take 

more credits. Thus, students with high GP / GPA will be able to shorten their study period 

or graduate for less than four years. In terms of student gender, female students are 

known to pay more attention to their study process than male students. Female students 

are more disciplined with time and they have sufficiently high motivation to be able to 

complete the study period on time. One of the results of the study also shows that female 

students' academic performance is better than male students [7]. Likewise, for learning 

motivation, female students have higher learning motivation than male students [8]. 

Therefore, gender is also a long-standing determinant of student studies. To determine 

whether GPA and gender are factors that significantly influence the length of a person's 

studies, further and more detailed statistical analysis is needed. 

A review of the factors that influence the length of the study period can be analyzed 

using regression analysis. Regression analysis is a tool in statistics to show a causal 

relationship between two or more variables, where one variable acts as a response 

variable and another variable as a predictor variable so that one variable can be predicted 

through another variable [2]. Regression analysis can be either linear regression or 

nonlinear regression. Because the data used is categorical or ordinal data, then the 

regression analysis that can be used is ordinal logistic regression [9]. Previous research 

shows that ordinal logistic regression analysis can provide information that the factors 

that influence the predicate of student graduation are faculty, gender, admission path, 

father's job, mother's work, and income [2]. Using the same analysis, [3] indicates that the 

student graduation time is influenced by the department taken and its gender and provides 

a good model in explaining the relationship between the three variables. In contrast to 

previous research, this study will analyze the extent of the influence of GPA and student 

gender on the duration of student studies 

This study aims to describe the old characteristics of the student's study period, and 

the model is based on the factors that influence it. The results of this study are expected to 

contribute knowledge to managers of study programs regarding the study period of 

students as well as a reflection in improving the management system that is at the level of 

study programs. 

 

2. Ordinal Logistic Regression 
 

In the regression model, if the response variable is binary or dichotomous, then the 

analysis will use a logistic regression model, which in its parameter estimation must use a 



Jurnal Matematika MANTIK 

Vol. 5, No. 1, May 2019, pp. 28-34 

30 

 

connecting function [10]. Ordinal logistic regression has the characteristics of response 

variables and predictors that have an ordinal scale. Suppose that the 𝑌 response variable 
has 𝑘 categories with 𝑥𝑖 = (𝑥𝑖1, 𝑥𝑖2 , . . . , 𝑥𝑖𝑝 ) is a vector of predictor variables, 𝑝, at the 

value of the first observation with 𝑖 = 1,2, . . . , 𝑛. Opportunities of the 𝑘-response variable 
with predictor 𝑋 are expressed as 𝑃[𝑌 ≤ 𝑘|𝑥] [11]. Cumulative opportunities are as 
follows [12]. 

𝑃[𝑌 ≤ 𝑘|𝑥] = 𝜋(𝑥) =
exp(𝛽0𝑘 + ∑ 𝛽𝑟 𝑥𝑖𝑟

𝑝
𝑟=1 )

1 + exp(𝛽0𝑘 + ∑ 𝛽𝑟 𝑥𝑖𝑟
𝑝
𝑟=1

)
 

 

The cumulative logit model is defined using the following formula. 

 

𝑙𝑜𝑔𝑖𝑡 (𝑃[𝑌 ≤ 𝑘|𝑥]) = log (
𝑃[𝑌 ≤ 𝑘|𝑥]

𝑃[𝑌 > 𝑘|𝑥]
) 

= log (
𝑃[𝑌 ≤ 𝑘|𝑥]

1 − 𝑃[𝑌 ≤ 𝑘|𝑥]
) 

= 𝛽0𝑘 + ∑ 𝛽𝑟 𝑥𝑖𝑟

𝑝

𝑟=1

 

 

which are 𝑘 =  1,2, . . . , 𝐾 − 1 and 𝛽 are vector regression coefficients. 
   

3. Research Methods 
 

This study uses secondary data obtained from the academic section of the 

Mathematics Education Study Program, IKIP Mataram. This type of research is a 

quantitative type with a case study of factors that influence the duration of study of 

undergraduate students in the Mathematics Education Study Program year passed 2017 

and 2018 through an ordinal logistic regression approach. The variables used in this study 

were divided into two types, namely the duration of the study period as the response 

variable (𝑌) and GPA and gender as predictor variables (𝑋1 and 𝑋2). This response 
variable consists of three categories, namely:  

 
 1 = 𝑌 < 4 years 

 2 = 4 ≥ 𝑌 ≤ 4 years 6 months 

 3 = 𝑌 > 4 years 6 months. 
 

The 4 years 6 months is adjusted to the second period of graduation at the IKIP Mataram. 

This period is still assumed to be a normal category.  

Each predictor variable that will be used in this study consists of several categories, 

such as the following. 

𝑥1,𝑖 = Student GPA, 

which is 𝑖: 1 = 𝐺𝑃𝐴 > 3,50  

 2 = 3,00 < 𝐺𝑃𝐴 ≤ 3,50    

 3 = 𝐺𝑃𝐴 ≤ 3,00    

𝑥2,𝑖  = gender 

which is 𝑖:  1 = male 

 2 = female. 



B. R. A. Febrilia, S. Rahayu, B. D. Korida 

Ordinal Logistic Regression Analysis of Factors Affecting the Factors Affecting the Length of Student Study 

31 

 

This study consists of several steps. The first step is to make cross-tabulations to 

analyze student characteristics. The next step is followed by estimating the ordinal 

logistic regression parameter. Then test the significance of the parameters simultaneously 

and partially. After that, the test of model suitability was followed by concluding the 

results of the study. 

 

4. Results and Discussion 
 

Before estimating parameters, the collected data were analyzed for characteristics 

based on the length of the study period on the GPA and length of study period by gender. 

 
Table 1. Characteristics based on the length of the study period and student GPA 

Student GPA range 

Length of study 

Total 
𝒀 < 𝟒 year 

𝟒 ≥ 𝒀 ≤ 𝟒 years 
6 months 

𝒀 > 𝟒 years 6 
months 

𝐺𝑃𝐴 > 3,50 2 (28.6%) 3 (42.8%) 2 (28.6%) 7 (100%) 

3,00 < 𝐺𝑃𝐴 ≤ 3,50 1 (0.95%) 42 (40%) 62 (59.05%) 105 (100%) 

𝐺𝑃𝐴 ≤ 3,00 0 (0%) 0 (0%) 22 (100%) 22 (100%) 

 
Based on Table 1, information was obtained that the characteristics of students of 

Mathematics Education Study Program in the years of 2017 and 2018 had the most study 

period of more than 4 years 6 months and were dominated by graduates with GPA in the 

range of 3.00 to 3.50. This shows that the study period of Mathematics Education Study 

Program students in graduating 2017-2018 is quite long. This is possible due to a number 

of things such as, students having difficulty in receiving the given lecture material or the 

final project being worked on, students have external problems, such as family problems 

or lack of tuition fees which require them to work while studying. 
 

Table 2. Characteristics based on the length of the study period and student gender 

Gender 
Length of study 

Total 
𝒀 < 𝟒 year 𝒀 < 𝟒 year 𝒀 < 𝟒 year 

Male 0 (0%) 8 (15,4%) 44 (84,6%) 52 (100%) 

Female 3 (3,66%) 37 (45,12%) 42 (51,22%) 82 (100%) 

 
Table 2 explains that the characteristics of the students of Mathematics Education 

Study Program in the year of 2017 and 2018 in terms of length of the study period and 

gender are more than those who studied for more than 4.6 years and were dominated by 

male students at that time. Female students dominated more during the study period under 

4 years or in the range of 4 to 4 years 6 months. This phenomenon is possible because 

usually female students pay more attention to the study process than male students.  

Then the parameter estimation of the ordinal logistic regression model is performed 

using the help of SPSS software. The estimation results can be seen in more detail in 

Table 3 below. 
 

Table 3. Parameter estimation of ordinal logistic regression model 

Variable Category 
Coefficient 

(𝜷) 
Standard Error 

Coefficient 
Exp (𝜷) P-value 

Length of study 
Constant 1 -22,158 0,633  0,000 

Constant 2 -18,540 0,245  0,000 



Jurnal Matematika MANTIK 

Vol. 5, No. 1, May 2019, pp. 28-34 

32 

 

Variable Category 
Coefficient 

(𝜷) 
Standard Error 

Coefficient 
Exp (𝜷) P-value 

Range of students 

GPA 

𝐺𝑃𝐴 > 3,50 -20,349 0,907 1,454 0,000 

3,00 < 𝐺𝑃𝐴
≤ 3,50 

-18,632 0,000 8,095 . 

𝐺𝑃𝐴 ≤ 3,00 0 . 1 . 

Gender 
Male 1,455 0,467 4,284 0,002 

Female 0 . 1 . 

 

Table 3 shows there are two constant values obtained in the model because there are 

three response variables that have coefficient values. This will produce two logit models. 

Table 3 also shows the odds ratio (𝐸𝑥𝑝 (𝛽)) of students who graduate with a GPA from 
3.00 to 3.50 is at 8,095. This shows that students with a GPA of 3.00 to 3.50 have an 

opportunity of 8.095 times greater than other GPA categories. Based on gender, students 

with male gender have an odds ratio of 4.284 or in other words, male students have a 

chance of 4.284 times greater than women. Next will be the suitability test of the model 

and the significance of the model both simultaneously and partially. 

Model suitability test is needed to find out whether the model obtained is appropriate 

or not. The results of this test are presented in Table 4. This test uses the null hypothesis 

(H0) and the alternative hypothesis (H1) as follows. 

H0 : Model is fit 

H1 : Model is not fit 

Table 4. Test goodness of fit model using Deviance 

 Chi-Square df P-value Decision 

Deviance 3,676 5 0,597 Accepted H0 

 
Table 4 shows that the P-value = 0.597 >  0.05, then the decision is H0 accepted or it can 

be concluded that the ordinal logistic regression model obtained is appropriate. 
 

Table 5. Model test using Likelihood Ratio 

Model 𝑮𝟐 Chi-Square df P-value Decision 

Intercept only 57,000     

Final 18,414 38,586 3 0,000 Rejected H0 

 
To test the meaning of β coefficients together, simultaneous testing was carried out 

on the ordinal logistic regression model. This test is carried out using the 𝐺 2 Test or also 
known as the Likelihood Ratio Test. Based on Table 4, it is known that the value of 𝐺 2 >
𝜒(0.05;3) = 7.815, which means that H0 is rejected or in other words, the β coefficient is 

significant for the ordinal logistic regression model. This result is also in accordance with 

the P-value = 0.000 < 0.05. 

Partial testing using the Wald test is intended to determine whether the variables in 

the ordinal logistic regression model are significant or not. This test uses the following 

statistical hypothesis. 

H0 : 𝛽𝑘 = 0 
H1 : 𝛽𝑘 ≠ 0, 𝑘 = 1, 2 

Partial test results can be seen in Table 3 of the sixth column through the P-value value. 

Through Table 3, it is known that all variables have variable values less than 0.05. These 



B. R. A. Febrilia, S. Rahayu, B. D. Korida 

Ordinal Logistic Regression Analysis of Factors Affecting the Factors Affecting the Length of Student Study 

33 

 

results indicate that these variables are significant. 

Based on the results of data analysis, the logit model of the length of the study 

period in terms of student GPA and student gender as many as 2 (two) models, as 

follows. 

 

𝐿𝑜𝑔𝑖𝑡 (𝑦1) = 𝑙𝑜𝑔 (
𝑦1

1 − 𝑦1
) = −22,158 + (−20,349𝑋1,1) + (1,455𝑋2,1) 

𝐿𝑜𝑔𝑖𝑡 (𝑦2) = 𝑙𝑜𝑔 (
𝑦2

1 − 𝑦2
) = −18,540 + (−20,349𝑋1,1) + (1,455𝑋2,1) 

 
5. Conclusion 
 

Based on the results of the research and discussion, it was found that the 

characteristics of the students of the Mathematics Education Study Program were 

dominated by graduates with a GPA from 3.00 to 3.50, but the length of the study period 

of students was more than 4 years 6 months. The length of the study period for more than 

4 years and 6 months is dominated by male students. The test results simultaneously and 

partially indicate that the factors that affect the length of the study period are GPA and 

gender. 

 

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