Department of Applied Mathematics and Statistics
Capstone Project
Analysis of New Jersey Institutions'
Undergraduate Students Retention Rates
from 2013 to 2021
May/2023
Advisor:
Haiyan Su, PhD
Associate Professor of Statistics/Biostatistics
Author
Monica DD Matos
Master’s in Statistics
Monica Matos - Spring 2023 -page: 1
Abstract
This project analyzed the differences and similarities in undergraduate students’ retention rates among
New Jersey “Public,” “Public-Mission,” “Proprietary,” and “Religious” Institutions from 2013 to 2021, as
well as compared retention rates amongst each of the New Jersey Public Institutions for the same
period.
Student retention rate measures the percentage of graduations from the number of enrollments. It is an
emergency subject as the government and educational organizations engage in research and discussions
to improve students’ persistence and completion and reduce school debits.
The data was collected from the Office of the Secretary of Higher Education of the State of New Jersey
(the web address was defined in part 5 of this paper, “Data Collection and References”).
The information refers to graduation rates for full-time, first-time degree-seeking students in bachelor’s
degree programs for New Jersey institutions. It contains the number of students that graduated after 4,
5, and 6 years from the first year registered. The project will use three data files, one with the cohort
year of 2013 and the number of students graduating in 2017, 2018, and 2019. (Part 6, Appendix, has the
row data sample images). The second file has the cohort years of 2014, with the number of students
who graduated in 2018, 2019, and 2020. The third file has the cohort years of 2015, with the number of
students who graduated in 2019, 2020, and 2021.
Each one of the files with cohort years of 2013, 2014, and 2015 had individual computation and analysis.
The project compared the three files and presented insights about a trend line.
The method of analysis was the Generalized Linear Models (GLM) that fits well with binary data, Logistic
Regression Model. The study defined the GLM components (Random Component, Linear Predictor, and
Link Function), used the odd ratios to compare the Public Institutions that presented similarities with
Montclair State University.
The analysis used Bar Graphs and Whisky Box plots to give insights about the data, and then used the
GLM model to support the decision to define others model’s fits. The new fir model was called Peers
Institutions.
The hypotheses considered were:
1. H0: Public Institutions, Public-Mission, Proprietary, and Religious Institutions all have the same
retention rates. Against
Ha: At least one of them is different.
2. H0: All the New Jersey Public Institutions have the same retention rates. Against
Ha: At least one of them is different.
3. H0: All the New Jersey Peers Institutions have the same retention rates. Against
Ha: At least one of them is different.
Montclair State University will be the base explanatory variable to facilitate future investigations
for Public and Peers Institutions, and additional calculations will include new models for better
fit.
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Table of Contents
1. Introduction ……………………………………………………………………………………………….. 04
2. Methods
…………………………………………………………………………………….. 05
2.1 Data Collection
.……………………………………………………………… 05
2.2 Data Preparation
………………………………………………………………. 05
2.3 Methodology of Analyzing
3. Results
……………………………………………………. 06
………………………………………………………………………………………….……... 07
3.1 Descriptive analysis………………………………………………………………………….……….. 07
3.1.1 Numbers and Percentages…………………………………………………….………… 07
3.1.2 Bar Plots……………………………………………………………………………………...…. 08
3.1.3 Box Plots…………………………………………………………………………………………. 10
3.1.4 Peers Institution Definition……………………………………………………………… 13
3.1.5 Peers Institution Timeline Graphics……………………………………………….. 13
3.1.6 Statistical Analysis………………………………………………………………………….. 15
3.1.6.1
The GML Logit Link Model for Peers’ Institutions ………………. 15
3.1.6.2
Colored Heat Table for Peers’ Institutions Odds Rates……….. 18
3.2 Analysis results…………………………………………………………………………………………. 19
4. Summary
……………………………………………………………………………………... 20
5. Data Collection’s File and Reference ……………………………………………………………….. 21
5.1 Data Collection’s File……………………………….………………………………………………... 21
5.2 References………………………………………………………………………………………………… 21
6. Appendix…………………………………………………………………………………………………………. 22
6.1 Raw Data …………………………………………………………………………………………………… 22
6.2 Code ………………………………………………………………………………………………………….. 23
Monica Matos - Spring 2023 -page: 3
1. Introduction
This study identified the similarities and differences among retentions in New Jersey Institutions among
the Secretary of Education’s partition as Public, Public-Mission, Proprietary, and Religious Institutions,
and then compared only the Public Institutions with each other, using Montclair State University as the
base explanatory variable.
Retention rate measured the percentage of graduations from the number of enrollments. It is an
emergency subject as the government and educational organizations engage in research and discussions
to improve persistence and completion and reduce school debits. The literature about retention papers
suggests interventions to increase the graduation rate, as described in the following paragraphs.
In their 2019 article “Educational Opportunity Fund Program and Community College Student Retention,
" Watson and Chen declare that the New Jersey educational opportunity fund program increases the
retention of first-semester community college students. [1]
Martin, T. and Davies, R., in their 2022 paper named “Student Retention and Persistence in University
Certificate-First Programs.” reflects on students earning professional certificates in the attempt to
prepare for and complete postsecondary education, suggesting that earning a certificate increased
students’ confidence and motivation to persist in school. [2]
Croft, P. and Lozada, N., in their 2020 publication, “Proactive Retention Through Integrated Modeling of
Engagement (prime),” describe a model development for Kean University that propose a new strategy
to increase retention that includes anticipations of workflow and student support services. [3]
In 2020, the paper “University student retention: Best time and data to identify undergraduate students
at risk of dropout,” written by the Spanish team Ortiz-Lozano, Rua-Vieites, Bilbao-Calabuig, and
Casadesús-Fa, defended that first-year interventions are crucial to prevent non-completion and that
factors as sociodemographic and academic records help identify students with more potential to
withdraw. [4]
Barry, and Mathies from Canada, in their 2011 paper titled “An Examination of Master’s Student
Retention & Completion,” examined master’s degree at a public university in the southeastern United
States retentions and they concluded that full-time and younger students are more likely to graduate,
and assistantship may impact in some cases. [5]
In the 2021 South African Journal of Higher Education, the paper named “Big Data-Driven Early Alert
Systems as Means Of Enhancing University Student Retention And Success,” Cele claims that an
extensive data framework about socio-economic and academic increase support students' success. [6]
Monica Matos - Spring 2023 -page: 4
2. Methods
2.1 Data Collection
The data was collected from the Office of the Secretary of Higher Education of the State of New Jersey,
and the web link was defined in part 5 of this paper, “Data Collection and References”. The data referred
to graduation rates for full-time, first-time degree-seeking students in bachelor’s degree programs for
New Jersey institutions. It included the number of students that graduated after 4, 5, and 6 years.
The project used three data files, as table 2.1 below explains. One with the cohort year of 2013 and the
number of students graduating in 2017, 2018, and 2019. (As we presented the raw image of those files in
Part 6, Appendix). The second file had the cohort years of 2014, with the number of students who
graduated in 2018, 2019, and 2020. The third file had the cohort years of 2015, with the number of
students who graduated in 2019, 2020, and 2021.
Data for graduation rates for full-time, first-time degree-seeking students
in bachelor’s degree programs for New Jersey institutions.
File 1 – Cohort 2013
First Year Student in 2013
File 2 – Cohort 2014
First Year Student in 2014
File 3 – Cohort 2015
First Year Student in 2015
Number of students
Graduated in 2017
Number of students
Graduated in 2018
Number of students
Graduated in 2019
Number of students
Graduated in 2018
Number of students
Graduated in 2019
Number of students
Graduated in 2020
Number of students
Graduated in 2019
Number of students
Graduated in 2020
Number of students
Graduated in 2021
Table 2.1 Cohort Year and Graduations Years for Files 1,2, and 3.
The data contained information for each undergraduate institutions in New Jersey, subdivided as “Public”,
“Public-Missionary”, “Proprietary”, and “Religious” Institutions. The “Public” group contains 12
institutions: College of New Jersey, Kean University, Montclair State University, New Jersey City University,
New Jersey Institute of Technology, Ramapo College, Rowan University, Rutgers-Camden, RutgersNewark, Rutgers- New Brunswick, Stockton University, and Willian Paterson University.
2.2 Data Preparation
The Data from the three files were transformed for further processing and analysis. Table 2.2 and 2.3
showed the percentage for NJ Institutions and Public Institutions, respectively. We showed in table 2.4
the grouped data for the “All Institutions” for 2013 Cohort Year (2013-2019), in table 2.5 the grouped data
for the” Public Institutions” for 2013 Cohort Year (2013-2019). The same data transformation was
performed for Cohort Years of 2014 (2014-2020), and 2015(2015-2021). The three files were transformed
to Excel file using Adobe Acrobat Reader, and then manually cleaned in Excel.
Table 2.2 Grouped Data with Percentage for Institutions Type in New Jersey Cohort 2013
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Table 2.3 Grouped Data with Percentage for Public Institutions. Cohort 2013
Note: The data for cohorts 2014 had the total numbers of students for Rutgers Newark as 6,409
and Rutgers New Brunswick as 1.010. It seems that the entries were switched, and we used the
data that appeared to correct. The same happened for cohort 2015 with 6,602 for Rutgers
Newark, and 1,192 for Rutgers New Brunswick.
2.3 Methodology of Analyzing
The data was nominal since there was no order of priority among the institutions; it had a binary response
variable, “Success” or “Failure” in graduating, and many potential explanatory variables.
The method of analysis was the Generalized Linear Models (GLM) that can describe patterns of
associations and interactions. The Logistic Regression Model fits well binary data. The three GLM
components were defined as:
a) The Random Component: is binomial, the response variable Y is the success (1) or fail (0) on
graduation.
b) The Linear Predictor: the explanatory variable was the institutions, α + βx.
c) The Link Function: logit link function, g(µ) = log[µ/(1-µ)], models the log of an odd and is
appropriated when µ is between 0 and 1.
The GML model was Logistic Regression, and it has the form:
log[µ] = α + β1x1 + β2x2 + …..+ βpxp. For the logit link:
The log odds ratio is:
β = log[π(1)] - log[π(0)] = log[π(1)/(1-π(1)] - log[π(0)/(1-π(0)] = log [[π(1)/(1-π(1)] / [π(0)/(1-π(0)]].
We compare odd ratios. Montclair State University (MSU) was the base institution in the fit models.
Hypotheses:
1. H0: Public Institutions, Public-Mission, Proprietary, Religious, and Independent Institutions all
have the same retention rates. Against
Ha: At least one of them is different.
2. H0: All the New Jersey Public Institutions have the same retention rates. Against
Ha: At least one of them is different. And we are going to use Montclair State University as the
main base, to facilitate future investigations.
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The Bar Graphs and Whisky Box plots gave a visual insight into the data, then the GLM model for further
analysis. Montclair State University (MSU) was the base institution. The model's explanatory variables
were also defined by a correlation study between public universities to reduce the number of variables.
The fit also prioritized MSU's "Peers Institution," the colleges or universities that present similarities with
MSU, like the number of students, kind of programs, location in New Jersey, and others.
Each one of the files with cohort years 2013, 2014, and 2015 had individual computation and analysis. The
three results' comparison provided extra insights as a trend line, and suggested ideas for future research.
3. Results
3.1 Descriptive analysis
3.1.1 Numbers and Percentages
The two tables below show the number of students that graduated in 4, 5 and 6 years and the
percentage from each one of the three-cohort group, 2013, 2014, and 2015. Table 3.1 refers to Type of
New Jersey Institutions, and table 3.2 to the Public Institutions group.
Table 3.1 NJ Institutions - Number of students who graduated in 4, 5, and 6 years and percentage from
the total of their cohort groups, 2013, 2014, and 2015.
Table 3.1 Public Institutions - Number of students who graduated in 4, 5, and 6 years and percentage
from the total of their cohort groups, 2013, 2014, and 2015.
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3.1.2 Bar Plots
The next step was a visual analysis to give insights into the data. The three bar plot graphics below,
Table 3.3, refer to cohorts 2013, in blue, 2014, in orange, and 2015, in green. They compare the four
New Jersey Institutions: Public, Public Missionary, Proprietary, and Religious. Each bar represents the
percentage of the total cohort for students that graduated in 4, 5, and 6 years. The three reference lines
in each bar graph mark the Public Institutions' rate for graduating in 4, 5, and 6 years. The reference line
intends to facilitate the visual contrast between the public group and each of the other three groupings.
Table 3.3 shows Percentage of students graduated in 4, 5 and 6 years from their group for NJ
Institutions.
The percentage bar graph comparing New Jersey institutions for the three cohort years and students
graduating in 4, 5, and 6 years allowed us the following considerations. Public institutions seem to have
a slightly smaller percentage of graduation in 4 years and a somewhat higher rate in 6 years than Public
Missionary Institutions. Proprietary and Religious Institutions showed a much smaller graduation
percentage than the Public.
The three tables below are bar plot graphics comparing each percentage of students who graduated in
4, 5, and 6 years with their specific cohort year for the Public Institutions. Table 3.4, in blue, refers to the
2013 cohort group. Table 3.5, in orange, refers to the 2014 cohort group. And Table 3.6, in green, refers
to the 2015 cohort group. The three red reference lines in each bar graph mark Montclair State
University's graduation rate in 4, 5, and 6 years. The reference line intends to facilitate the visual
contrast between the MSU percentages and each of the other institutes in the group.
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Table 3.4 shows the Percentage of students who graduated in 4, 5, and 6 years from their
group for Public Institutions with cohort 2013.
The red reference lines refer to Montclair State University’s rates.
Table 3.5 shows the Percentage of students who graduated in 4, 5, and 6 years from their
group for Public Institutions with cohort 2014.
The red reference lines refer to Montclair State University’s rates.
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Table 3.5 shows the Percentage of students who graduated in 4, 5, and 6 years from their
group for Public Institutions with cohort 2015.
The red reference lines refer to Montclair State University’s rates.
The visual analysis shows that Montclair had an improvement in the graduation rate in 4 years from
cohort 2013 to 2015, and a higher point in graduation in 6 years in cohort 2014. The table 3.6 below
shows MSU’s rates.
Cohort Years
2013-2019
2014-2020
2015-2021
Graduate in 4 years
44.8%
45.3%
47.5%
Graduate in 5 years
66.9%
64.7%
63.7%
Graduate in 6 years
67.0%
67.9%
67.3%
Table 3.6 Montclair State University graduation rates in 4, 5 and 6 years
for cohort 2013, 2014, and 2015.
Compared with other institutions, Kean University, New Jersey City University, and Willian Paterson had
graduate rates much smaller than Montclair. The College of New Jersey had the highest percentage,
followed by Rutgers New Brunswick, Ramapo College, and Stockton University. Public institutions with
similar rates as Montclair seem to be the New Jersey Institute of Technology, and Rowan University.
3.1.2 Box Plots
The next graphs are boxplot where we can visually analyze outliers’ institutions for the same three cohort
years and graduation rates in 4,5, and 6 years. Table 3.7 shows the box plot for the percentage graduated
in 4, 5 and 6 years for Type of New Jersey Institutions
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3.7 Box Plot for the percentage of Type of New Jersey Institutions Cohort 2013, 2014 and 2015
graduated in 4, 5, and 6 years.
The boxplot also shows the Public Institutions and Public Missionary Institutions with similar rates on the upper top,
and the Religious and Proprietary in the lower percentage. Proprietary Institutions had a change in percentage
among the three cohort years reflecting on small variability as the years increased.
Table 3.8, 3.9 and 3.10 shows the box plot for the percentage graduated in 4, 5 and 6 years for Public
Institutions, for the cohorts’ years 2013, 2014, and 2015, respectively.
3.8 Box Plot for the percentage of Public Institutions cohort 2013, graduated in 4, 5, and 6 years.
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3.9 Box Plot for the percentage of Public Institutions cohort 2014, graduated in 4, 5, and 6 years.
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3.10 Box Plot for the percentage of Public Institutions cohort 2015, graduated in 4, 5, and 6 years.
The boxplot visual analysis indicated that, for the three cohort years, Montclair State University, MSU,
was constantly around 50 percent of the data. For graduating in 4 years, the MSU was about 50 percent
for all three cohort years. For graduating in 5 years, MSU was on the 50 percent mark or higher. For
graduating in 6 years, MSU was on the line of 50 percent or slightly lower.
The boxplot for Public Institutions showed three outliers. Two were for New Jersey City University,
NJCU, the cohort year of 2014, the first for graduating in 5 years, and the second for 6 years. The third
outlier was Kean, the cohort year of 2015, and graduating in 6 years. In addition, The College of New
Jersey, TCNJ, was always on the line that divides the upper outliers.
For the institutions with percentages higher than the third quartile, 75%, we had Rutgers New Brunswick
and Stockton University in all three cohorts, and Ramapo College in 2014,
For the institutions with percentages lower than the first quartile, 25%, we had Kean University and New
Jersey City University for all three cohorts, Willian Paterson in the first and last cohort, Rutgers Newark
in 2015, and Rutgers Camden on the line of 25% for in cohort 2013.
3.1.4 Peers Institution Definition
We called MSU's "Peers Institution”, the colleges or universities that presented similarities with MSU on
graduation rate, number of students, kind of programs, location in New Jersey, and others, based on the
results of bar plots and box plots. First, we eliminated the two institutions that were outliers and
constantly in the lower than the first quartile, Kean University and New Jersey City University, NJCU. We
also removed The College of New Jersey because they were always on the line that divided the upper
outliers. We removed Rutgers New Brunswick because they not only had higher rates, but they also have
double of the number of MSU’s students. Then we pulled Stockton University and Willian Paterson
because they were frequently out of the 50 percent box, out of the area between the first and third
quartile, being the first in the higher part and the second in the lower. In addition, those two institutions
have programs with minor similarities to MSU. At least we removed Rutgers Camden because they have
less than a quarter of the MSU's students. Table 3.11 presents the list of the Peers Institutions.
Table 3.11 - List of the Peer’s Institutions.
3.1.5 Peers Institutions’ Timeline
The Table 3.12, 3.13, and 3.14 below presented a Peer’s Institutions timeline for the percentage of
graduate students in 4, 5, and 6 years for the cohort years of 2013, 2014, and 2015, respectively. It will
guide the visual analysis for the institutions that presented similarities with MSU.
Monica Matos - Spring 2023 -page: 13
Table 3.12 Timeline for the percentage of graduate students in 4, 5, and 6 years for the cohort years of 2013.
Table 3.13 Timeline for the percentage of graduate students in 4, 5, and 6 years for the cohort years of 2014.
Monica Matos - Spring 2023 -page: 14
Table 3.14 Timeline for the percentage of graduate students in 4, 5, and 6 years for the cohort years of 2015.
The timeline graphs showed MSU slightly higher than the middle position of the graphs for the three
cohorts’ years.
Rowan was on the top for cohort 2013; they slightly declined for middle positions. Ramapo presented
the opposite behavior; they started in the middle of 2013 and moved up for the last two graphs. Rutgers
Newark had a middle position for the first analysis and decreased their rates. NJIT had lower
percentages than MSU for students graduating in 4 and similar for 5 and 6, except for the cohort 2015,
when they improved their graduation rates in 6 years.
3.1.6 Statistical Analysis
3.1.6.1 The GML Logit Link Model for Peers Institutions
After the visual analyses, we did statistical evaluation to check if the visual insights were accurate.
Generalized Linear Models (GLM) fits well for binary data modeling the mean with a link function,
Logistic model, with the response variable Y as the success (1) or fail (0) on graduation as random
component; the institutions as the explanatory variable for the linear predictor; and the logit link
function to link the response and the explanatory variable. For the Public group, Montclair State
University (MSU) was the base reference institution in the logistic models.
This study used R code to fit the GLM Logistic Regression Model to the data for Binomial Random
Component with grouped data, using link function Logit. First, we called the library “dplyr” to recode
explanatory variable. Then we used the “glm: function with code:
glm(y/n ~ x, family=binomial(link=logit), weights=n, data=”data for each group
where: y was the response variable, the number of students graduating, n was the number of students
for the cohort year (number in the first year of undergraduate program), and x was the explanatory
Monica Matos - Spring 2023 -page: 15
variable, institutions’ names. The canonical link for binomial is logit, so "(link=logit)" was not necessary;
and "weights" indicates sample proportion yes/n is based on n observations. After that, we fit the model,
called for summary, and used the library “car” to fit Analyses of Variance test, Anova test. The codes are
in the appendix. The hypotheses for each group for New Jersey Institutions were:
H0: Public Institutions, Public-Mission, Proprietary, Religious, and Independent Institutions
all have the same retention rates. Against
Ha: At least one of them is different.
Table 3.15 below presents the P-Values from “Anova” test for each cohort group, and graduating in 4,5,
and 6 years for the New Jersey Institutions analyses.
New Jersey Institutions
Cohort 4 Years
5 Years
6 Years
LR Chisq
Df Pr(>Chisq)
LR Chisq
Df Pr(>Chisq)
LR Chisq Df Pr(>Chisq)
2013
1259.3
3
<0.01
443.63
3
< 0.01
1054.2
3
< 0.01
2014
1184.5
3
< 0.01
334,7
3
< 0.01
1025.7
3
< 0.01
2015
1421.8
3
< 0.01
324.6
< 0.01
976.5
3
< 0.01
Significantes codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Table 3.15 – P-Values for Anova test Public Institutions
All the P-Values were less than α =0.05, and all test for the group New Jersey Institutions had the same
result, we rejected the null hypothesis, H0, that there is no difference among the graduation for New
Jersey Types of Institutions, and we accepted the alternative hypothesis that there is at least one of the
institutions had a significant difference in rate for the other. The result was as expected by the visual
analysis that showed clear differences among the groups.
The hypotheses for each group for Public Institutions were:
H0: All the New Jersey Public Institutions have the same retention rates. Against
Ha: At least one of them is different. And we are going to use Montclair State University
as the main base, to facilitate future investigations.
Table 3.16 below presents the P-Values from “Anova” test for each cohort group, and graduating in 4,5,
and 6 years for the Public Institutions analyses.
Public Institutions
Cohort 4 Years
5 Years
6 Years
LR Chisq
Df Pr(>Chisq)
LR Chisq
Df Pr(>Chisq)
LR Chisq Df Pr(>Chisq)
2013 2023
11 <0.01
214.1
11 < 0.01
190.8
11 < 0.01
2014 1973
11 < 0.01
227.8
11 < 0.01
146.3
11 < 0.01
2015 2262.5
11 < 0.01
203.1
11 < 0.01
793.0
11 < 0.01
Significantes codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Table 3.16 – P-Values for Anova test Public Institutions
All the P-Values were less than α =0.05, and all test for the group Public Institutions had the same result,
we rejected the null hypothesis, H0, that there is no difference among the graduation for Public of
Monica Matos - Spring 2023 -page: 16
Institutions, and we accepted the alternative hypothesis that there is at least one of the institutions had
a significant difference in rate for the other.
WE reduced the number of variables, and try another model using MSU Peer’s Institutions, defined on
3.1.4 on this study. The MSU Peers Institutions were defined as: NJIT, Ramapo, Rowan, Rutgers Newark,
and Rutgers New Brunswick. The hypotheses for each group for Peer’s Institutions were:
H0: All the Peers Institutions have the same retention rates. Against
Ha: At least one of them is different. And we are going to use Montclair State University
as the main base, to facilitate future investigations.
Table 3.17 below presents the P-Values from “Anova” test for each cohort group, and graduating in 4,5,
and 6 years for the Peers Institutions analyses.
Peers Institutions
Cohort 4 Years
5 Years
6 Years
LR Chisq
Df Pr(>Chisq)
LR Chisq
Df Pr(>Chisq)
LR Chisq Df Pr(>Chisq)
2013 48.8
4
<0.01
78.9
4
< 0.01
101.0
4
< 0.01
2014 479.8
4
< 0.01
107.8
4
< 0.01
59.0
4
< 0.01
2015 544.4
4
< 0.01
59.0
4
< 0.01
171.4
4
< 0.01
Significantes codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Table 3.17 – P-Values for Anova test Public Institutions
All the P-Values were less than α =0.05, and all test for the group Public Institutions had the same result,
we rejected the null hypothesis, H0, that there is no difference among the graduation for Peers of
Institutions, and we accepted the alternative hypothesis that there is at least one of the institutions had
a significant difference in rate for the other.
As we definedd on 2.3, The log odds ratio is:
β = log[π(1)] - log[π(0)] = log[π(1)/(1-π(1)] - log[π(0)/(1-π(0)] = log [[π(1)/(1-π(1)] / [π(0)/(1-π(0)]].
•
•
•
The sign of β determines whether π(x) is increasing or decreasing as x increases.
|β|, the module of β, shows rate of climb or descent. For β = 0, the curve flattens to a horizontal
straight line, and Y is independent of X.
The odds multiply by exponential of β, eβ, for every one unit increase in x.
Considering α, the intercept with Montclair State University as the base variable, and β, the coefficient,
we have the logit [π^ (x)] = σ + βx for each cohort year and for graduating in 4, 5, and 6 years as
described in the table 3.18.
logit [π^ (x)] = σ + βx
Cohort 2013
Cohort 2014
Cohort 2015
4 Years
5 Years
6 Years
^
^
logit [π (x)] = -0.21 + βx logit [π (x)] = -1.50 + βx logit [π (x)] = -3.17+ βx
logit [π^ (x)] = -0.19 + βx logit [π^ (x)] = -1.43 + βx logit [π^ (x)] = -3.39 + βx
logit [π^ (x)] = -0.10 + βx logit [π^ (x)] = -1.64 + βx logit [π^ (x)] = -3.29 + βx
^
Monica Matos - Spring 2023 -page: 17
Table 3.18 - logit [π^ (x)] = σ + βx, with MSU as Intercept.
3.1.6.2 Colored Heat Table for Peers Institutions’ Odds Rates
The odds multiply by exponential of β, eβ, for every one unit increase in x.
For example: For Ramapo, 2013, graduating in 4 years, logit [π^ (x)] = -0.21 + 0.13739*x, with σ = -0.21
and β = 0.13739. A positive value of β indicated that Ramapo had a higher rate than MSU in the period.
A logit [π^ (x)] = σ + βx leads to eβ times increase in odds. Since eβ= e 0.13739= 1.15, we interpret that the
rate of graduate in 4 years for Ramapo in 2013, was e 0.13739 time the rate for MSU was 1.15 or 15%
higher than MSU.
For example: For NJIT, 2013, graduating in 4 years, logit [π^ (x)] = -0.21 -0.32194*x, with σ = -0.21 and β =
- 0.32194. A negative value of β indicated that NJIT had a lower rate than MSU in the period. Since eβ = e
0.32194
= 0.72, we interpret that the rate of graduate in 4 years for NJIT in 2013, was 0.72 or 28% lower
than MSU.
Table 3.19 shows the results for eβ. It is a Colored Heat Table, with green representing rates higher than
MSU, red representing lower rates, and yellow showing similar rates.
Table 3.19 shows the results for eβ. It is a Colored Heat Table, with green representing rates higher than
MSU, red representing lower rates, and yellow showing similar rates. This table shows the data
organized by graduates in 4, 5 and 6 Years.
Note: The rates are with MSU.
Graduated in 4 Years
2013
2014
NJIT
0.72
0.83
Ramapo
1.15
1.84
Rowan
1.21
1.10
RutgersN
0.84
2.19
2015
0.68
1.53
0.96
2.10
Graduated in 5 Years
2013
2014
NJIT
1.50
1.27
Ramapo
0.56
0.45
Rowan
1.12
0.78
RutgersN
0.84
0.68
2015
1.31
0.68
1.10
0.79
Graduated in 6 Years
2013
2014
NJIT
1.15
1.68
Ramapo
3.49
0.56
Rowan
0.77
1.38
RutgersN
1.40
1.87
2015
4.65
0.53
1.26
1.41
Table 3.19 -e β, with MSU as Intercept – By Graduated in 4, 5 and 6 Years.
Table 3.20 shows a heat table for percentages. The table matches the bar and boxplot graphs since the
values are accumulated for each year.
Graduated in 4 Years
2013
2014
Montclair
45%
45%
NJIT
37%
41%
Ramapo
48%
60%
Rowan
49%
48%
RutgersN
40%
34%
2015
47%
38%
58%
46%
35%
Graduated in 5 Years
2013
2014
Montclair
63%
65%
NJIT
62%
64%
Ramapo
59%
70%
Rowan
69%
64%
RutgersN
64%
59%
2015
64%
58%
70%
64%
59%
Graduated in 6 Years
2013
2014
Montclair
67%
68%
NJIT
67%
70%
Ramapo
72%
72%
Rowan
73%
68%
RutgersN
69%
65%
2015
67%
73%
72%
68%
65%
Table 3.20 – Heat Table for Percentage – By Graduated in 4, 5 and 6 Years.
Again, the results show MSU slightly higher position among most Peers Institutions.
Monica Matos - Spring 2023 -page: 18
3.2 Analysis results
The study about New Jersey Undergraduate Institutions comparing Public with other kinds of institutions,
showed that there was a slight visual similarity between Public Missionary and a difference between
Proprietary and Religious. The statistics investigation demonstrated that we reject the hypothesis that the
rates for the New Jersey Institutions were the same.
The study comparing Montclair State University, MSU, with other New Jersey Public Institutions showed
that MSU rates were around the middle of the percentage of others, and varied from 45.3 % for four years
to 67.9% for six years, as seen in Table 3.6, page 10. For the period analyzed, MSU had an improvement
in rates for graduating in 4, a decrease for five years, and a higher pick for the cohort of 2014 graduating
in 6 years.
The Bar Graphs for Public, pages 9 and 10, showed that the visual considerations suggested that Kean
University, New Jersey City University, and Willian Paterson had graduate rates much smaller than
Montclair. The College of New Jersey had the highest percentage, followed by Rutgers New Brunswick,
Ramapo College, and Stockton University. Public institutions with similar rates as Montclair seem to be
the New Jersey Institute of Technology and Rowan University.
The boxplot visual analysis indicated that MSU was constantly around 50 percent of the data, pages 11
and 12. The outliers were New Jersey City University, NJCU (2014, for 5 and 6 years), and Kean (2015, for
6 years.) For the institutions with percentages higher than the third quartile, 75%, we had Rutgers New
Brunswick in all and Stockton University (all three cohorts), and Ramapo College (2014). For the
institutions with percentages lower than the first quartile, 25%, we had Kean University and New Jersey
City University for all three cohorts, Willian Paterson in the first and last cohort, Rutgers Newark in 2015,
and Rutgers Camden on the line of 25% for in cohort 2013. We defined Peers Institutions based on the
visual analysis as NJIT, Ramapo, Rowan, and Rutgers Newark.
The fit and summary of GML Logit Link Models and Anova analysis evaluation strongly suggested that for
all three groups, New Jersey Public Institutions, and Peers Institutions, we should reject the null
hypotheses that the institutions had the same graduation rate, and we accepted the alternative
hypothesis that at least one of them had different proportions.
Comparing with Peers Institutions, MSU rates were slightly higher than the middle. Compared with MSU,
NJIT was always slightly lower, Ramapo was, most of the time, slightly higher, and Rowan has a similar
rate, almost overlapping Montclair for the 2015 cohort. Rutgers Newark had a middle position for the
first analysis and decreased their rates.
Monica Matos - Spring 2023 -page: 19
4. Summary
This project analyzed the differences and similarities in undergraduate students’ retention rates among
New Jersey “Public,” “Public-Mission,” “Proprietary”, and “Religious” Institutions from 2013 to 2021, as
well as compared retention rates amongst each of the New Jersey Public Institutions for the same
period fixing Montclair State University, MSU, as a base of comparison to the other public institutions.
The intention was to illuminate similarities and differences between the groups to guide new studies to
improve students’ persistence and completion and reduce school debits. The data was collected from
the Office of the Secretary of Higher Education of the State of New Jersey, as is presented in the 5.1
Data Collection Files, and referred to the number of students that graduated after 4, 5, and 6 years from
the first year registered, for three groups with the cohort year of 2013, 2014, and 2015.
First, we analyzed New Jersey types of Institutions. The Bar and box plots and the statistical evaluation
using the generalized linear model logit link for the logistic regression model showed no similarities
among the organizations. The Public Institutions group presented the highest graduation rates, followed
by Public Missionary.
After we studied the similarities and differences among the Public Institutions, with Montclair State
University as the line reference for the bar graphs, and the base line explanatory variable for GLM
analysis. The percentage for each cohort year showed that MSU was constantly in the middle of the
rates compared to other organizations. The bar graphs and box plots illustrated that The College of New
Jersey, Rutgers New Brunswick, and Stockton University were in the top percents. Kean University and
New Jersey City University were at the bottom. The study defined Peers Institutions as the groups with
results around the first and third quartile for Public Institutions and compared them with MSU. This
group was formed by the New Jersey Institute of Technology (NJIT), Ramapo College, Rowan University,
and Rutgers University-Newark.
The statistical evaluation using the generalized linear model logit link for the logistic regression model
for all three groups, Public Institutions and Peers Institutions, showed no similarities among the
organizations.
As a conclusion, the visual analysis using bar and box plot graphics and the evaluation of the odds rates
from the GLM showed that MSU rates were somehow in the middle of the other institution. Comparing
with Peers Institutions, MSU rates were slightly higher than the middle. Compared with MSU, NJIT was
always slightly lower, Ramapo was, most of the time, slightly higher, and Rowan has a similar rate,
almost overlapping Montclair for the 2015 cohort. Rutgers Newark had a middle position for the first
analysis and decreased their rates.
Retention rate is an emergency subject, and the government and educational organizations are engaged
in research and discussions to improve completion and reduce school debits. This study intended to
define similarities and differences among New Jersey Undergraduate Institutions and support future
interventions to increase the graduation rate. Montclair State University consistently presented middlehigh graduate rates, and the comparison with similar institutions may facilitate insights for interventions
that improve students’ performance.
Monica Matos - Spring 2023 -page: 20
5. Data Collection File and References
5.1 Data Collection File
[1] N/A, (2013-2021) Office of the Secretary of Higher Education, Official Site Of The State Of New
Jersey, Dashboard Archive, Year Report 2021,2020, and 2019, Statistical Table Graduation Rates- 4Year Institutions - Graduation Rates, [Online], Available:
https://www.state.nj.us/highereducation/dashboard-archive.shtml
5.2 References
[1] Watson, A. and Chen, R., (2019, November), “Educational Opportunity Fund Program and Community
College Student Retention.”, Journal of College Student Retention: Research, Theory & Practice; Nov2019, Vol.
21 Issue 3, p384-406, 23p, 15210251, DOI: 10.1177/1521025118780329, Database: Supplemental Index,
[Online}, Available: https://journals.sagepub.com/doi/pdf/10.1177/1521025118780329, and Montclair State
University Harry A. Sprague Library’s Data Base.
[2] Martin, T.; Davies, R., (2022, August 2), “Student Retention and Persistence in University Certificate-First
Programs.”, Educ. Sci. 2022, 12, 525. [Online], Available: https:// doi.org/10.3390/educsci12080525 and [PDF]
Montclair State University Harry A. Sprague Library’s Data Base, and Montclair State University Harry A.
Sprague Library’s Data Base.
[3] Croft, P. & Lozada, N., (2020, September 1), “Proactive Retention Through Integrated Modeling of
Engagement (prime)”, [pdf] source: Kean University, New Jersey, Available: Montclair State University Harry a.
Sprague Library’s Data Base.
[4] Ortiz-Lozano, J., Rua-Vieites, A. Bilbao-Calabuig, P., Casadesús-Fa, M., (2020, February), “University student
retention: Best time and data to identify undergraduate students at risk of dropout”, INNOVATIONS IN
EDUCATION AND TEACHING INTERNATIONAL 2020, VOL. 57, NO. 1, 74–85. [Online] Available:
https://doi.org/10.1080/14703297.2018.150209, and Montclair State University Harry a. Sprague Library’s Data
Base.
[5] Barry, M., Mathies, C.,(2011, May 21-25), “An Examination of Master’s Student Retention & Completion”,
Association for Institutional Research (NJ1), Paper presented at the Annual Forum of the Association for
Institutional Research (51st, Toronto, Ontario, Canada, (ED531727), Database: ERIC, [Online], Available:
Montclair State University Harry a. Sprague Library’s Data Base.
[6] N. Cele, (2021), “BIG DATA-DRIVEN EARLY ALERT SYSTEMS AS MEANS OF ENHANCING UNIVERSITY STUDENT
RETENTION AND SUCCESS” , South African Journal of Higher Education , 2021, Vol. 35 Issue 2, p56-72, 17p.
Publisher: Sabinet Online Limited., Database: Supplemental Index, University of Zululand,
Richards Bay,
South Africa, [Online], Available: https://orcid.org/0000-0003-3689-7385 and
Montclair State University
Harry A. Sprague Library’s Data Base.
Monica Matos - Spring 2023 -page: 21
6. Appendix
6.1 Raw Data
The following image presents a sample of the row data referring to the years 2013-2019.
The following image presents a sample of the row data referring to the years 2014-2020.
Monica Matos - Spring 2023 -page: 22
The following image presents a sample of the row data referring to the years 2014-2020.
6.2 Code
NJ 2013 Cohort, 4 years. I did the same calculation for 5 and 6 years and for Cohort 2014, and 2015,
4,5, and 6 years.
Monica Matos - Spring 2023 -page: 23
Public Institution Cohort 2013, 4. I did the same calculation for 5 and 6 years and for Cohort 2014, and
2015, 5, and 6 years.
Peer’s Institution Cohort 2013, 4. I did the same calculation for 5 and 6 years and for Cohort 2014, and
2015, 4,5, and 6 years.
Monica Matos - Spring 2023 -page: 24