1. Eastern Michigan University
Using HGLM to Examine the Influence of College- and Student-Level Factors on Graduation
Meng Chen & Bin Ning
Eastern Michigan University
MIAIR · November 4, 2016

2. Outline Introduction and Context Analysis and Results
Model Diagnostics
Conclusion

3. Institutional Context
EMU: ~18,000 UG and 4,000 GR
Sizes of entering FTIAC cohort fluctuated around 2,700
Carnegie
Before 2016—Master’s large
Starting 2016—Doctoral R3
Low 6-year graduation rate of 36-40%
Five distinctive colleges

4. Average High School GPA
Academic Colleges
Fall 2016
FTIAC Enrollment
Average ACT
Average High School GPA
Total UG Enrollment
Arts & Sciences (AS)
1,008
22.3
3.28
6,374
Business (BU)
290
21.8
3.20
2,425
Education (ED)
184
22.7
3.34
1,398
Health & Human Services (HH)
469
21.3
3.32
3,828
Technology (TC)
251
21.6
3.19
1,824
College Undecided
585
22.0
3.26

5. Purpose of the study
The characteristics of each colleges vary significantly
In this study, we want to identify the factors at college and individual student levels that can affect graduation

6. Research Questions
What factors at college and student levels affect graduation rate?
Does affiliation of academic college affect graduation rates?

7. Variables College-level variables Individual student variables
College affiliation
Percentage of freshman level classes taught by full-time faculty
Percentage of part-time faculty
Percentage of instructional budget in total budget
Individual student variables
Age, gender, residency, high school GPA, ACT composite score, on-campus living,
first-generation, low income, honor college indicator and class size

8. Dataset First-time, full-time, baccalaureate degree seeking students
Admitted in Fall 2006, 2007, 2008, 2009, 2010 at Eastern Michigan University
There were 10,685 students who were first-year, full-time, and seeking a baccalaureate degree
Admitted between 2006 and 2010
Among them 4,130 students obtained a bachelor’s degree from EMU within six years after starting

9. Data processing
College undecided students were distributed into each college based on their last college on record
Records with missing values were removed

10. Method Multi-level models More suitable for complex data structure
Can avoid reporting underestimated standard errors
More efficient than other techniques
Satisfy all criteria of a general linear model
Can perform many types of analyses
There levels of linear model: General, Generalized, and HGLM. HGLM assumes that all conditions are the same as general linear model.

11. Hierarchical generalized linear modeling (HGLM)
HGLM originally developed to deal with hierarchical data
Especially when the dependent variable is dichotomous
In hierarchical model, distribution of an observation is determined by
A common structure among all clusters
The specific structure of the cluster where a specific observation belongs
HGLM allows extra error components in the linear predictors of generalized linear models
Distribution of these components include normal, Poisson-gamma, binomial-beta and gamma-inverse gamma
Poisson-gamma, binomial-beta and gamma-inverse gamma are distributions for different types of data.

12. Hglm in R
R provides a package that is designed for fitting Hierarchical Generalized Linear Models
It can be used for linear mixed models and generalized linear mixed models with random effects for a variety of links and a variety of distributions for both the outcomes and the random effects

13. Analysis Fixed effect Random effect
graduated~year+age+gender+ethni+residency+hs-gpa+act+honor+major
+expenditure+ faculty + campus living + low income+ first generation(Binomial distribution (link=logit))
Random effect
College (Beta distribution (link=logit))
Hierarchical model picks the higher level measures as random. In research, BIC number can help decide random vs fixed

14. Summary of the fixed effects estimates
Pr(>|t|)
Gender(Male)
-0.063
1.26e-05 ***
Age
-0.022
0.044 *
HS_GPA
0.261
< 2e-16 ***
ACT
0.008
0.001 **
Honor_indicator
0.056
3.51e-06 ***
Low_income
-0.035
0.031 *
First_generation
-0.072
4.86e-07 ***
Fixed estimate based on individual variables.
Log p/(1-p) Log odds remission

15. Summary of the random effects estimates
Std. Error
CollegeAS
0.0978
CollegeBU
0.1033
0.1031
CollegeED
0.0485
0.1024
CollegeHH
0.0199
0.1102
CollegeTC
0.1135
Random effect estimate.

16. Model diagnostics
After fitting a regression mode, it is important to determine whether all the necessary model assumptions are valid
Assumptions are the response y to the explanatory variable were linear in the parameters
Model diagnostics helps identify the effect of outliers. It is common to use model diagnostics when using linear model analysis.

17. Two model diagnostic methods
Assessing leverage—Hat values
Deviance Score

18. 1. Assessing Leverage: Hat-Values
Leverage is a measure of how far away the independent variable values of an observation are from those of the other observations
Most common measure of leverage is the hat-value
H: hat value; ffffffff fitted value

19. Hat-values for each observation & each level in the random effect
High leverage, but not necessarily high influence
Hat value within 2 times of the average does not affect the model accuracy. More than 2 times in theory should be removed and rerun the analysis. We did not rerun.

20. 2. Model Fit: Deviance
Deviance is a quality-of-fix statistic for a model used for statistical hypothesis testing
Deviance uses the sum of squares of residuals in ordinary least squares to cases where model fitting is achieved by maximum likelihood
The deviance for a model M0, based on a dataset y is defined
: fitted values of the parameters in the model M0; : fitted parameters for the saturated model
The lower value of deviance is, the better the model fits Θ:

21. Deviance diagnostics for each observation & each level in the random effect

22. Model Deviances
Figure 1 shows a strong correlation between deviance and gamma, HGLM model treats error components as gamma distribution, and figure 1 shows evidence it assumption is met.
Figures 3 and 4 shows a very low deviance values for random effect.

23. Conclusion College has an effect on student graduation
Student level significant predictors
Age, gender, high school GPA, ACT composite score, low income, first- generation and honor college
College has an effect on student graduation
HGLM model provided good fit to this case

24. Other Considerations
For analysis that involves more than two levels, use HGLMMM package.