Student Demographics and Fall-to-Fall Retention

Objective and Scope

Examine the correlation between various student demographics and fall-to-fall retention to help identify characteristics of students that, on average, have higher or lower likelihood of being retained.

Analysis included fall semester first-time post-secondary full-time bachelors degree-seeking students over the last five years and whether they returned to ISU the subsequent fall or not. The focus of the study revolved around student demographics including Age, Sex, Race/Ethnicity, First Generation and Pell Eligibility (proxy for income).

As many factors may contribute to retention that may also be correlated with these demographics it is essential to control for the externalities that would otherwise misrepresent the ISU equity (fairness) story. As such, a multivariate logistic regression was performed to better isolate if, after controlling for a closer to complete picture of the student, differences in demographics still exists. Control variables included various characteristics about the student prior to their arrival at ISU (e.g. high school activity), financial variables (e.g. aid received), and initial ISU activity (e.g. chosen course taking behavior). See the “Variables Considered” section for more information.

Key Findings

High School GPA was a better predictor of fall-to-fall retention than any student demographic considered in this study. Overall differences in retention between these different demographics appear to be more of a result of differing starting points, on average. For example, overall, males have lower retention rates than females. However, males start at ISU with, on average, a lower high school GPA. After controlling for high school GPA and other factors, the effect of sex was statistically insignificant. Statistically significant differences between certain demographics did exist, but with relatively small effect sizes, varied confidence intervals and sensitivity to changes in statistical modeling. A highlight of these findings can be found below:

Sex: Statistically insignificant.

Race/ethnicity: Students who are Hispanic were slightly more likely to be retained while students who were white were slightly less likely to be retained. In both cases, statistically significant but small effect sizes and sensitive to model changes.

Age: Older students were slightly more likely to be retained after controlling for other factors. Significant but effect size was relatively small. In addition, low sample size on older entering students is a limitation to this finding.

First generation: Students who were first generation college students were slightly less likely to be retained.

Pell eligibility: Students who were pell eligible were slightly less likely to be retained.

Variables Considered

The interactive tables below displays the various variables considered, how each was defined and how retention varies within the variable.

Demographics

Sex

Definition: Self-reported sex from the student application

Race/Ethnicity

Definition: Self-reported race/ethnicity from the student application

Age

Definition: Age at time of entry at ISU

First Gen

Definition: Self-reported response from the FAFSA in their entry year. If no FAFSA submitted it would be unknown, which is a limitation.

Pell Eligibility

Definition: Whether the student received pell grant their first year or not.

First Generation

Pell Eligibility

Financial Indicators

For each variable considered, you can review that feature, how it related to retention and also the demographics of interest for this study.

Grant Aid Received

Definition: The amount of grant or scholarship aid received by the student in their first semester at ISU.

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Loans Received

Definition: The amount of loans taken by the student in their first semester at ISU.

Retention

Sex

Number of Credits

Definitions: The number of credits taken by the student. The study focused just on full-time students, but within that, students can take a varied amount of credits

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Courses

Definition: The courses enrolled by these students their first semester at ISU. To avoid overfitting, only the 20 or so of the most popular courses were included in the analysis

Results

Modeling

The following is the result of a logistic regression with a dependent variable of retained or not against the student demographics of interest and the various other possible contributing factors to retention. The first model does not include the ACT or SAT variable, as this was the most often unavailable data point. The second model includes the ACT or SAT variable but excludes the students for which it was unavailable. For more detail on some of the due diligence and diagnostics completed for this classification analysis, see the appendix.


	Dependent variable:

	Retention
	Without ACT/SAT	With ACT/SAT
	(1)	(2)

Female	0.029 (0.073)	0.057 (0.077)
	p = 0.687	p = 0.463
Race/Ethnicity White	-0.043 (0.106)	-0.211^* (0.118)
	p = 0.685	p = 0.075
Race/Ethnicity Hispanic	0.387^*** (0.127)	0.264^* (0.139)
	p = 0.003	p = 0.058
Age	0.083^*** (0.016)	0.106^*** (0.027)
	p = 0.00000	p = 0.0002
First Generation	-0.150^** (0.075)	-0.127 (0.079)
	p = 0.045	p = 0.111
Pell Eligible	-0.206^*** (0.078)	-0.290^*** (0.085)
	p = 0.009	p = 0.001
High School GPA	1.012^*** (0.080)	1.117^*** (0.096)
	p = 0.000	p = 0.000
ACT or SAT Score		0.003 (0.010)
		p = 0.758
Athlete	-0.300 (0.228)	-0.360 (0.239)
	p = 0.188	p = 0.133
Lives Oncampus	0.338^*** (0.084)	0.323^*** (0.088)
	p = 0.0001	p = 0.0003
Fully Online	-0.228 (0.168)	-0.316^* (0.188)
	p = 0.174	p = 0.093
Some Online	0.043 (0.072)	0.041 (0.076)
	p = 0.549	p = 0.596
Some Remedial	-0.126 (0.125)	0.098 (0.142)
	p = 0.311	p = 0.492
Did Prior ISU Dual Credit	0.025 (0.074)	-0.011 (0.076)
	p = 0.737	p = 0.887
Idaho Address	0.393^*** (0.140)	0.508^*** (0.160)
	p = 0.005	p = 0.002
Grant Aid	0.0001^*** (0.00001)	0.0001^*** (0.00002)
	p = 0.000	p = 0.000
Loan Aid	0.00003^** (0.00002)	0.00003^* (0.00002)
	p = 0.044	p = 0.071
Writing and Rhetoric I	-0.072 (0.074)	-0.054 (0.079)
	p = 0.329	p = 0.498
Introduction to Psychology	-0.073 (0.074)	-0.056 (0.079)
	p = 0.329	p = 0.477
First Year Transition	0.259^*** (0.096)	0.271^*** (0.100)
	p = 0.007	p = 0.007
Introduction to Art	0.062 (0.081)	0.092 (0.087)
	p = 0.448	p = 0.293
Biology I	0.050 (0.094)	0.057 (0.096)
	p = 0.596	p = 0.552
Writing and Rhetoric II	0.129 (0.091)	0.107 (0.094)
	p = 0.157	p = 0.255
Experimental Course	-0.035 (0.103)	-0.030 (0.110)
	p = 0.731	p = 0.784
Introduction to Sociology	-0.110 (0.102)	-0.059 (0.110)
	p = 0.281	p = 0.591
Fundamentals of Oral Comm	-0.072 (0.091)	-0.098 (0.096)
	p = 0.433	p = 0.307
Intermediate Algebra	0.028 (0.110)	0.063 (0.115)
	p = 0.798	p = 0.582
General Chemistry I	0.424^*** (0.151)	0.377^** (0.156)
	p = 0.006	p = 0.016
Personal Finance	-0.003 (0.131)	-0.022 (0.139)
	p = 0.982	p = 0.876
Varsity Ath Bengal Danc Cheer	0.327 (0.220)	0.381^* (0.230)
	p = 0.137	p = 0.098
Introduction to Philosophy	0.062 (0.130)	0.037 (0.139)
	p = 0.636	p = 0.793
People and Cult of Old World	0.339^** (0.147)	0.354^** (0.156)
	p = 0.022	p = 0.023
Elementary Spanish I	-0.068 (0.130)	-0.087 (0.138)
	p = 0.603	p = 0.531
College Algebra	-0.082 (0.162)	-0.080 (0.167)
	p = 0.613	p = 0.634
Undecided	-0.228^** (0.106)	-0.197^* (0.112)
	p = 0.032	p = 0.079
Nursing	-0.076 (0.122)	-0.087 (0.127)
	p = 0.533	p = 0.498
Biology	-0.125 (0.150)	-0.067 (0.159)
	p = 0.405	p = 0.675
Health Science	0.329^** (0.158)	0.296^* (0.164)
	p = 0.037	p = 0.072
Psychology	0.120 (0.164)	0.126 (0.173)
	p = 0.463	p = 0.467
Dental Hygiene	0.167 (0.176)	0.215 (0.183)
	p = 0.342	p = 0.239
Computer Science	0.078 (0.179)	0.180 (0.204)
	p = 0.666	p = 0.379
General Business	-0.379^** (0.180)	-0.301 (0.196)
	p = 0.035	p = 0.126
Pharmacy	-0.148 (0.212)	-0.093 (0.220)
	p = 0.484	p = 0.673
Radiographic Science	0.219 (0.219)	0.234 (0.232)
	p = 0.318	p = 0.315
Elementary Education	-0.231 (0.211)	-0.234 (0.220)
	p = 0.274	p = 0.288
Secondary Education	0.022 (0.226)	-0.006 (0.236)
	p = 0.922	p = 0.980
Mechanical Engineering	-0.160 (0.233)	-0.098 (0.241)
	p = 0.493	p = 0.686
Communication	-0.005 (0.254)	-0.039 (0.271)
	p = 0.986	p = 0.887
Physical Education	-0.349 (0.245)	-0.279 (0.261)
	p = 0.155	p = 0.284
Nuclear Engineering	0.224 (0.302)	0.362 (0.330)
	p = 0.460	p = 0.273
Physical Therapist Assistant	-0.043 (0.254)	-0.004 (0.261)
	p = 0.866	p = 0.987
Management	-0.294 (0.258)	-0.167 (0.278)
	p = 0.255	p = 0.550
Accounting	-0.016 (0.273)	0.060 (0.291)
	p = 0.953	p = 0.836
Social Work	-0.302 (0.291)	-0.301 (0.309)
	p = 0.300	p = 0.330
Fiscal Year 2020	-0.076 (0.099)	-0.045 (0.103)
	p = 0.442	p = 0.663
Fiscal Year 2021	0.115 (0.116)	0.126 (0.122)
	p = 0.322	p = 0.300
Fiscal Year 2022	0.248^** (0.113)	0.245^** (0.120)
	p = 0.028	p = 0.042
Fiscal Year 2023	0.455^*** (0.117)	0.473^*** (0.125)
	p = 0.0001	p = 0.0002
Constant	-5.201^*** (0.462)	-6.107^*** (0.651)
	p = 0.000	p = 0.000

Observations	5,309	4,845
Log Likelihood	-3,000.180	-2,694.612
Akaike Inf. Crit.	6,116.360	5,507.225

Note:	p<0.1; p<0.05; p<0.01

After controlling for all the variables discussion, the following are the results for the demographics of interest:

Sex: Statistically insignificant.

Race/ethnicity: Students who are hispanic were slightly more likely to be retained while students who were white were slightly less likely to be retained. In both cases, statistically significant but small effect sizes and sensitive to model changes.

First generation: Students who were first generation college students were slightly less likely to be retained.

Pell eligibility: Students who were pell eligible were slightly less likely to be retained.

Based on the absolute value of the z-score and effect sizes, High School GPA was the strongest predictor of fall-to-fall retention. A few other findings include: Students who lived on-campus was also positively correlated with retention. Students with an Idaho address were more likely to be retained. The more grant or scholarship aid received, the more likely a student would be retained. Students who did not declare a major were slightly less likely to be retained.

Analysis

To better illustrate the findings from the modeling process, the resulting predicted probability of retention was visualized against the variables of interest for the demographics that were statistically significant. This was done by calculating an “average” student in fiscal year 2023 by taking the mean of each variable and then changing the variable of interest to visualize the evolving probability of retention. As a logistic regression does not assume a linear relationship, the change in probability due to a particular factor is also not linear. The purpose of this exercise was not for precision, as an “average” student doesn’t really exist. It is simply intended as a means to visualize the “average” effect of a particular variable while holding other variables constant.

In addition, as determined, high school GPA is likely the strongest predictor of fall-to-fall retention. As such, comparisons of retention between high school GPA and the student demographics are also included as another visualization and perspective of the takeaways from this study.

High School GPA

As shown above, a .5 difference in high school GPA leads to a noticable change in the likelihood of being retained. As shown below, the change in probabilty (effect size) for the demographics in this study appear to have less impact relative to high school GPA.

Sex

As sex was statistically insignificant, predicted probability was not visualized.

Cross tabulation of High School GPA with Sex, we see the difference between female and males in retention diminish. The more stark trend is students who are male start at ISU with a lower High School GPA on average (3.32 vs 3.48 for females).

Race/Ethnicity

The following displays the change in predicted probability of retention by taking the “average student” (mean value of all variables) and whether they were white, hispanic or not.

Cross tabulation of High School GPA with Race/Ethnicity, the lower probability of retention for white students and higher probability of retention for hispanic students jumps out a bit more.

Age

The following displays the change in predicted probability of retention by taking the “average student” (mean value of all variables) and their age.

Cross tabulation of High School GPA with Age, we see the slightly positive relationship between age and retention.

First Gen

The following displays the change in predicted probability of retention by taking the “average student” (mean value of all variables) and whether they were first gen or not

Cross tabulation of High School GPA with first generation status, we see the slightly lower retention rate of first gen students.

Pell Eligibility

The following displays the change in predicted probability of retention by taking the “average student” (mean value of all variables) and whether they were pell eligible or not.

Cross tabulation of High School GPA with pell eligibility status, we see the slightly lower retention rate of pell eligible students.

Appendix

Model Due Diligence

K-Fold Cross Validation

As a means of exploring the sensitivity of the results, K-fold cross validation was used to add another perspective. As discussed in the main sections of the report, some of the demographics experienced some sensitivity to being statistically significant or not. The highly correlated factors of retention (e.g. high school GPA and grant aid) were resilient to different folds of the data being isolated in the modeling. It is worth noting that with each fold being a little over 1,200 records, sample size becomes a small limitation to this method.


	Dependent variable:

	Retention
	Full Model	Fold A	Fold B	Fold C	Fold D
	(1)	(2)	(3)	(4)	(5)

Female	0.057 (0.077)	-0.194 (0.162)	0.167 (0.159)	0.004 (0.165)	0.224 (0.162)
	p = 0.463	p = 0.232	p = 0.294	p = 0.983	p = 0.167
Race/Ethnicity White	-0.211^* (0.118)	-0.342 (0.262)	0.060 (0.265)	-0.083 (0.234)	-0.622^*** (0.231)
	p = 0.075	p = 0.192	p = 0.821	p = 0.722	p = 0.008
Race/Ethnicity Hispanic	0.264^* (0.139)	-0.009 (0.295)	0.418 (0.313)	0.619^** (0.282)	-0.078 (0.274)
	p = 0.058	p = 0.977	p = 0.182	p = 0.028	p = 0.778
Age	0.106^*** (0.027)	0.112^** (0.049)	-0.012 (0.056)	0.142^** (0.065)	0.252^*** (0.067)
	p = 0.0002	p = 0.024	p = 0.833	p = 0.029	p = 0.0002
First Generation	-0.127 (0.079)	-0.217 (0.164)	-0.101 (0.169)	0.109 (0.174)	-0.209 (0.163)
	p = 0.111	p = 0.185	p = 0.549	p = 0.532	p = 0.200
Pell Eligible	-0.290^*** (0.085)	-0.238 (0.183)	-0.433^** (0.178)	-0.062 (0.180)	-0.395^** (0.172)
	p = 0.001	p = 0.192	p = 0.015	p = 0.730	p = 0.022
High School GPA	1.117^*** (0.096)	1.632^*** (0.213)	1.169^*** (0.196)	0.950^*** (0.206)	0.990^*** (0.192)
	p = 0.000	p = 0.000	p = 0.000	p = 0.00001	p = 0.00000
ACT or SAT Score	0.003 (0.010)	-0.022 (0.021)	-0.005 (0.021)	0.043^** (0.022)	0.007 (0.020)
	p = 0.758	p = 0.295	p = 0.803	p = 0.048	p = 0.714
Athlete	-0.360 (0.239)	-0.449 (0.504)	-0.125 (0.478)	-0.431 (0.527)	-0.538 (0.515)
	p = 0.133	p = 0.374	p = 0.794	p = 0.414	p = 0.296
Lives Oncampus	0.323^*** (0.088)	0.448^** (0.190)	0.397^** (0.183)	0.639^*** (0.191)	-0.029 (0.178)
	p = 0.0003	p = 0.019	p = 0.030	p = 0.001	p = 0.871
Fully Online	-0.316^* (0.188)	-0.906^** (0.381)	-0.236 (0.406)	0.296 (0.408)	-0.285 (0.395)
	p = 0.093	p = 0.018	p = 0.562	p = 0.469	p = 0.470
Some Online	0.041 (0.076)	-0.224 (0.160)	0.194 (0.158)	0.273^* (0.164)	0.026 (0.160)
	p = 0.596	p = 0.163	p = 0.219	p = 0.095	p = 0.873
Some Remedial	0.098 (0.142)	0.212 (0.310)	0.280 (0.292)	-0.397 (0.288)	0.144 (0.293)
	p = 0.492	p = 0.494	p = 0.338	p = 0.169	p = 0.623
Did Prior ISU Dual Credit	-0.011 (0.076)	-0.208 (0.161)	0.049 (0.159)	0.063 (0.160)	-0.057 (0.154)
	p = 0.887	p = 0.197	p = 0.761	p = 0.693	p = 0.713
Idaho Address	0.508^*** (0.160)	0.553 (0.345)	1.001^*** (0.334)	0.479 (0.349)	0.369 (0.304)
	p = 0.002	p = 0.110	p = 0.003	p = 0.170	p = 0.225
Grant Aid	0.0001^*** (0.00002)	0.0001^*** (0.00004)	0.0002^*** (0.00003)	0.0001^** (0.00003)	0.0001^*** (0.00003)
	p = 0.000	p = 0.002	p = 0.00000	p = 0.014	p = 0.0002
Loan Aid	0.00003^* (0.00002)	-0.00002 (0.00004)	0.0001^* (0.00004)	0.0001^* (0.00004)	0.00004 (0.00004)
	p = 0.071	p = 0.599	p = 0.068	p = 0.083	p = 0.291
Writing and Rhetoric I	-0.054 (0.079)	-0.194 (0.168)	-0.001 (0.165)	0.162 (0.169)	-0.129 (0.160)
	p = 0.498	p = 0.249	p = 0.993	p = 0.338	p = 0.423
Introduction to Psychology	-0.056 (0.079)	0.120 (0.168)	-0.196 (0.160)	0.274 (0.171)	-0.331^** (0.160)
	p = 0.477	p = 0.476	p = 0.222	p = 0.110	p = 0.039
First Year Transition	0.271^*** (0.100)	0.326 (0.209)	0.329 (0.218)	0.468^** (0.216)	0.120 (0.195)
	p = 0.007	p = 0.118	p = 0.131	p = 0.031	p = 0.539
Introduction to Art	0.092 (0.087)	0.227 (0.183)	-0.051 (0.179)	0.133 (0.189)	0.098 (0.174)
	p = 0.293	p = 0.216	p = 0.777	p = 0.483	p = 0.575
Biology I	0.057 (0.096)	0.062 (0.201)	0.099 (0.195)	0.067 (0.209)	0.060 (0.198)
	p = 0.552	p = 0.760	p = 0.614	p = 0.751	p = 0.762
Writing and Rhetoric II	0.107 (0.094)	0.027 (0.197)	-0.014 (0.196)	0.331^* (0.197)	0.095 (0.195)
	p = 0.255	p = 0.890	p = 0.945	p = 0.093	p = 0.626
Experimental Course	-0.030 (0.110)	0.110 (0.243)	0.145 (0.223)	-0.086 (0.228)	-0.192 (0.225)
	p = 0.784	p = 0.652	p = 0.514	p = 0.708	p = 0.393
Introduction to Sociology	-0.059 (0.110)	-0.234 (0.231)	-0.084 (0.230)	0.002 (0.216)	-0.049 (0.236)
	p = 0.591	p = 0.311	p = 0.717	p = 0.994	p = 0.835
Fundamentals of Oral Comm	-0.098 (0.096)	-0.168 (0.206)	-0.001 (0.197)	-0.152 (0.196)	-0.150 (0.200)
	p = 0.307	p = 0.415	p = 0.995	p = 0.438	p = 0.453
Intermediate Algebra	0.063 (0.115)	0.327 (0.239)	-0.326 (0.246)	-0.029 (0.245)	0.297 (0.231)
	p = 0.582	p = 0.171	p = 0.185	p = 0.905	p = 0.199
General Chemistry I	0.377^** (0.156)	0.406 (0.352)	0.548^* (0.330)	0.120 (0.300)	0.297 (0.312)
	p = 0.016	p = 0.250	p = 0.097	p = 0.690	p = 0.342
Personal Finance	-0.022 (0.139)	-0.082 (0.299)	-0.341 (0.263)	0.069 (0.306)	0.537^* (0.321)
	p = 0.876	p = 0.784	p = 0.195	p = 0.822	p = 0.095
Varsity Ath Bengal Danc Cheer	0.381^* (0.230)	-0.016 (0.451)	0.338 (0.510)	0.393 (0.521)	0.987^** (0.495)
	p = 0.098	p = 0.972	p = 0.508	p = 0.450	p = 0.047
Introduction to Philosophy	0.037 (0.139)	-0.347 (0.256)	0.131 (0.283)	0.071 (0.325)	0.382 (0.326)
	p = 0.793	p = 0.176	p = 0.643	p = 0.827	p = 0.242
People and Cult of Old World	0.354^** (0.156)	0.595^* (0.357)	0.212 (0.319)	0.521 (0.347)	0.221 (0.282)
	p = 0.023	p = 0.096	p = 0.507	p = 0.134	p = 0.434
Elementary Spanish I	-0.087 (0.138)	-0.220 (0.304)	0.080 (0.305)	-0.068 (0.289)	-0.069 (0.264)
	p = 0.531	p = 0.471	p = 0.792	p = 0.816	p = 0.795
College Algebra	-0.080 (0.167)	-0.493 (0.345)	0.010 (0.354)	0.749^* (0.410)	-0.487 (0.332)
	p = 0.634	p = 0.154	p = 0.979	p = 0.068	p = 0.144
Undecided	-0.197^* (0.112)	-0.461^** (0.226)	-0.192 (0.226)	-0.006 (0.238)	-0.196 (0.237)
	p = 0.079	p = 0.042	p = 0.396	p = 0.979	p = 0.410
Nursing	-0.087 (0.127)	0.472 (0.291)	-0.057 (0.256)	-0.724^*** (0.264)	-0.081 (0.256)
	p = 0.498	p = 0.106	p = 0.826	p = 0.007	p = 0.751
Biology	-0.067 (0.159)	0.018 (0.319)	-0.081 (0.335)	-0.243 (0.330)	-0.163 (0.333)
	p = 0.675	p = 0.956	p = 0.809	p = 0.462	p = 0.625
Health Science	0.296^* (0.164)	0.462 (0.336)	-0.001 (0.342)	0.504 (0.392)	0.247 (0.315)
	p = 0.072	p = 0.169	p = 0.997	p = 0.199	p = 0.433
Psychology	0.126 (0.173)	-0.257 (0.334)	0.196 (0.372)	0.412 (0.398)	0.215 (0.347)
	p = 0.467	p = 0.443	p = 0.599	p = 0.302	p = 0.536
Dental Hygiene	0.215 (0.183)	0.546 (0.397)	-0.113 (0.371)	0.652^* (0.371)	-0.266 (0.384)
	p = 0.239	p = 0.169	p = 0.762	p = 0.079	p = 0.489
Computer Science	0.180 (0.204)	0.128 (0.413)	0.464 (0.424)	0.336 (0.477)	-0.054 (0.397)
	p = 0.379	p = 0.757	p = 0.274	p = 0.482	p = 0.892
General Business	-0.301 (0.196)	-0.260 (0.438)	-0.099 (0.391)	-0.650^* (0.389)	-0.354 (0.415)
	p = 0.126	p = 0.553	p = 0.801	p = 0.095	p = 0.395
Pharmacy	-0.093 (0.220)	0.382 (0.622)	-0.040 (0.440)	0.254 (0.440)	-1.014^** (0.418)
	p = 0.673	p = 0.540	p = 0.929	p = 0.564	p = 0.016
Radiographic Science	0.234 (0.232)	-0.138 (0.496)	0.632 (0.556)	0.358 (0.463)	0.046 (0.447)
	p = 0.315	p = 0.782	p = 0.256	p = 0.440	p = 0.919
Elementary Education	-0.234 (0.220)	0.365 (0.624)	-0.704^* (0.421)	-0.397 (0.440)	-0.098 (0.433)
	p = 0.288	p = 0.559	p = 0.095	p = 0.368	p = 0.821
Secondary Education	-0.006 (0.236)	0.578 (0.516)	0.197 (0.452)	-0.558 (0.486)	-0.276 (0.540)
	p = 0.980	p = 0.263	p = 0.663	p = 0.251	p = 0.610
Mechanical Engineering	-0.098 (0.241)	-0.341 (0.465)	-0.072 (0.518)	-0.332 (0.496)	0.396 (0.528)
	p = 0.686	p = 0.464	p = 0.890	p = 0.504	p = 0.454
Communication	-0.039 (0.271)	-0.099 (0.560)	0.815 (0.677)	-0.280 (0.553)	-0.428 (0.505)
	p = 0.887	p = 0.860	p = 0.229	p = 0.613	p = 0.398
Physical Education	-0.279 (0.261)	-0.567 (0.522)	-0.317 (0.572)	0.116 (0.584)	-0.556 (0.520)
	p = 0.284	p = 0.277	p = 0.580	p = 0.844	p = 0.286
Nuclear Engineering	0.362 (0.330)	0.782 (0.848)	0.325 (0.600)	-0.187 (0.603)	0.759 (0.813)
	p = 0.273	p = 0.357	p = 0.588	p = 0.757	p = 0.351
Physical Therapist Assistant	-0.004 (0.261)	-0.195 (0.517)	0.431 (0.546)	0.162 (0.602)	-0.387 (0.527)
	p = 0.987	p = 0.707	p = 0.431	p = 0.789	p = 0.463
Management	-0.167 (0.278)	-0.539 (0.652)	-0.585 (0.510)	-0.597 (0.577)	1.113^* (0.669)
	p = 0.550	p = 0.409	p = 0.252	p = 0.301	p = 0.097
Accounting	0.060 (0.291)	-0.813 (0.532)	0.218 (0.638)	0.860 (0.696)	0.492 (0.634)
	p = 0.836	p = 0.127	p = 0.733	p = 0.217	p = 0.439
Social Work	-0.301 (0.309)	-0.056 (0.615)	-0.872 (0.702)	-0.773 (0.663)	0.088 (0.608)
	p = 0.330	p = 0.928	p = 0.214	p = 0.244	p = 0.886
Fiscal Year 2020	-0.045 (0.103)	0.060 (0.209)	-0.331 (0.219)	0.161 (0.223)	-0.003 (0.209)
	p = 0.663	p = 0.775	p = 0.131	p = 0.471	p = 0.988
Fiscal Year 2021	0.126 (0.122)	0.336 (0.257)	-0.152 (0.246)	0.205 (0.258)	0.225 (0.249)
	p = 0.300	p = 0.192	p = 0.537	p = 0.429	p = 0.368
Fiscal Year 2022	0.245^** (0.120)	0.383 (0.251)	-0.131 (0.245)	0.326 (0.257)	0.599^** (0.252)
	p = 0.042	p = 0.128	p = 0.593	p = 0.205	p = 0.018
Fiscal Year 2023	0.473^*** (0.125)	0.370 (0.256)	0.246 (0.259)	0.642^** (0.266)	0.841^*** (0.262)
	p = 0.0002	p = 0.150	p = 0.342	p = 0.016	p = 0.002
Constant	-6.107^*** (0.651)	-6.988^*** (1.277)	-4.735^*** (1.298)	-7.597^*** (1.493)	-8.003^*** (1.500)
	p = 0.000	p = 0.00000	p = 0.0003	p = 0.00000	p = 0.00000

Observations	4,845	1,208	1,204	1,212	1,221
Log Likelihood	-2,694.612	-635.765	-656.376	-631.921	-669.250
Akaike Inf. Crit.	5,507.225	1,389.530	1,430.753	1,381.841	1,456.500

Note:	p<0.1; p<0.05; p<0.01

Multicollinearity

Variance Inflation Factor (VIF) scores were used to examine if multicollinearity exists in the model. With scores well below 5, multicollinearity is not a major concern with the models.

VIF - Model Without Act or SAT Score

##                         GVIF Df GVIF^(1/(2*Df))
## FEMALE_MODEL        1.279037  1        1.130945
## WHITE_MODEL         2.286948  1        1.512266
## HISPANIC_MODEL      2.300773  1        1.516830
## AGE                 1.208819  1        1.099463
## FIRST_GEN_MODEL     1.108077  1        1.052652
## PELL_MODEL          1.507513  1        1.227808
## HS_GPA              1.650997  1        1.284911
## ATHLETE_MODEL       2.898171  1        1.702401
## LIVE_CAMPUS_MODEL   1.351480  1        1.162532
## ONLINE_ALL_MODEL    1.174106  1        1.083562
## ONLINE_SOME_MODEL   1.305520  1        1.142593
## REMEDIAL_SOME_MODEL 1.208453  1        1.099297
## PRIOR_DUAL_MODEL    1.261902  1        1.123344
## STATE_MODEL         1.647271  1        1.283461
## GRANT_AMT           2.207644  1        1.485814
## LOAN_AMT            1.176942  1        1.084870
## ENGL_1101           1.323224  1        1.150315
## PSYC_1101           1.213106  1        1.101411
## ACAD_1104           1.379707  1        1.174609
## ART_1100            1.053619  1        1.026460
## BIOL_1101           1.298588  1        1.139556
## ENGL_1102           1.256751  1        1.121049
## ROAR_1199           1.225213  1        1.106893
## SOC_1101            1.127051  1        1.061627
## COMM_1101           1.088452  1        1.043289
## MATH_1108           1.208440  1        1.099291
## CHEM_1111           1.211595  1        1.100725
## FIN_1115            1.152259  1        1.073433
## PEAC_1190           2.546984  1        1.595927
## PHIL_1101           1.034646  1        1.017176
## ANTH_2237           1.051008  1        1.025187
## SPAN_1101           1.032717  1        1.016227
## MATH_1143           1.075734  1        1.037176
## MAJOR_UNDC          1.409350  1        1.187160
## MAJOR_HPNU          1.469047  1        1.212042
## MAJOR_BLBL          1.306861  1        1.143180
## MAJOR_HSHS          1.230671  1        1.109356
## MAJOR_PGPS          1.246188  1        1.116328
## MAJOR_HPDH          1.226243  1        1.107359
## MAJOR_EGCS          1.156553  1        1.075431
## MAJOR_BUGB          1.221010  1        1.104993
## MAJOR_PHPD          1.129795  1        1.062918
## MAJOR_HPRS          1.116815  1        1.056795
## MAJOR_EDED          1.112283  1        1.054648
## MAJOR_EDSE          1.072133  1        1.035439
## MAJOR_EGME          1.120438  1        1.058508
## MAJOR_CMCO          1.062997  1        1.031018
## MAJOR_EDPE          1.085549  1        1.041897
## MAJOR_EGNE          1.080170  1        1.039312
## MAJOR_TPTA          1.100528  1        1.049060
## MAJOR_BUMG          1.088842  1        1.043476
## MAJOR_BUAC          1.081054  1        1.039737
## MAJOR_SWSW          1.088357  1        1.043244
## FISCAL_YEAR         2.057432  4        1.094374

VIF - Final Model (With ACT of SAT score)

##                         GVIF Df GVIF^(1/(2*Df))
## FEMALE_MODEL        1.288956  1        1.135322
## WHITE_MODEL         2.503830  1        1.582350
## HISPANIC_MODEL      2.528344  1        1.590077
## AGE                 1.098764  1        1.048220
## FIRST_GEN_MODEL     1.111064  1        1.054070
## PELL_MODEL          1.588374  1        1.260307
## HS_GPA              1.882393  1        1.372003
## ACT_SAT_SCORE       1.937077  1        1.391789
## ATHLETE_MODEL       2.543481  1        1.594829
## LIVE_CAMPUS_MODEL   1.349960  1        1.161878
## ONLINE_ALL_MODEL    1.152442  1        1.073519
## ONLINE_SOME_MODEL   1.312212  1        1.145518
## REMEDIAL_SOME_MODEL 1.276839  1        1.129973
## PRIOR_DUAL_MODEL    1.249210  1        1.117680
## STATE_MODEL         1.632255  1        1.277598
## GRANT_AMT           2.295743  1        1.515171
## LOAN_AMT            1.167407  1        1.080466
## ENGL_1101           1.362671  1        1.167335
## PSYC_1101           1.209537  1        1.099790
## ACAD_1104           1.386641  1        1.177557
## ART_1100            1.062439  1        1.030747
## BIOL_1101           1.294076  1        1.137575
## ENGL_1102           1.263519  1        1.124064
## ROAR_1199           1.246198  1        1.116332
## SOC_1101            1.137009  1        1.066306
## COMM_1101           1.094756  1        1.046306
## MATH_1108           1.227899  1        1.108106
## CHEM_1111           1.234842  1        1.111234
## FIN_1115            1.153598  1        1.074057
## PEAC_1190           2.254345  1        1.501448
## PHIL_1101           1.035844  1        1.017764
## ANTH_2237           1.053310  1        1.026309
## SPAN_1101           1.037134  1        1.018398
## MATH_1143           1.082025  1        1.040204
## MAJOR_UNDC          1.425661  1        1.194011
## MAJOR_HPNU          1.479580  1        1.216380
## MAJOR_BLBL          1.306547  1        1.143043
## MAJOR_HSHS          1.240785  1        1.113905
## MAJOR_PGPS          1.241597  1        1.114270
## MAJOR_HPDH          1.241581  1        1.114263
## MAJOR_EGCS          1.141664  1        1.068487
## MAJOR_BUGB          1.208719  1        1.099417
## MAJOR_PHPD          1.135077  1        1.065400
## MAJOR_HPRS          1.122116  1        1.059300
## MAJOR_EDED          1.120226  1        1.058407
## MAJOR_EDSE          1.076351  1        1.037473
## MAJOR_EGME          1.123592  1        1.059996
## MAJOR_CMCO          1.062431  1        1.030743
## MAJOR_EDPE          1.090628  1        1.044331
## MAJOR_EGNE          1.084883  1        1.041577
## MAJOR_TPTA          1.109028  1        1.053104
## MAJOR_BUMG          1.091264  1        1.044636
## MAJOR_BUAC          1.084340  1        1.041316
## MAJOR_SWSW          1.091807  1        1.044896
## FISCAL_YEAR         2.101056  4        1.097248

Student Demographics and Fall-to-Fall Retention

Thomas Sharpe, Senior Data Scientist - Idaho State University

April 2024

Objective and Scope

Key Findings

Variables Considered

Demographics

Sex

Race/Ethnicity

Age

First Gen

Pell Eligibility

High School Activity

High School GPA

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

ACT or SAT

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Prior Dual Credit

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

In-State or Out-of-State

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Financial Indicators

Grant Aid Received

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Loans Received

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

ISU Initial Activity

Athlete

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Living Arrangement

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Online Enrollment

Retention

Sex

Race/Ethnicity

Age

First Generation

Pell Eligibility

Participation in Remedial Education

Retention