I ran the following logistic regression in R where the dependent variable (Success) is 1 if the student graduates and 0 if the student does not graduate:
Call:
glm(formula = Success ~ Core.GPA + Lab.Yr.Taken + Frn.Lang.Yr.Taken +
SAT.Converted + Incoming.Test, family = binomial, data = df)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.7123 -1.2211 0.6501 0.8495 1.3955
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.094e+00 6.007e-01 -6.816 9.39e-12 ***
Core.GPA 1.024e+00 9.916e-02 10.329 < 2e-16 ***
Lab.Yr.Taken 1.220e-01 2.904e-02 4.200 2.66e-05 ***
Frn.Lang.Yr.Taken 6.335e-02 3.115e-02 2.034 0.042 *
SAT.Converted 9.867e-05 3.759e-04 0.262 0.793
Incoming.Test 4.018e-02 3.332e-03 12.056 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 7022.5 on 5947 degrees of freedom
Residual deviance: 6573.9 on 5942 degrees of freedom
(1108 observations deleted due to missingness)
AIC: 6585.9
Number of Fisher Scoring iterations: 4
Here are the Odds Ratio for that model:
(Intercept) Core.GPA Lab.Yr.Taken Frn.Lang.Yr.Taken
0.01666638 2.78504399 1.12973489 1.06540330
SAT.Converted Incoming.Test
1.00009867 1.04099486
My interpretation here (using Incoming.Test as an example) is: "Odds of success increase by 4.1% for each additional one unit increase in Incoming Test Credit" (1.04099486-1) x 100
However, I'd like to know if being a first generation student impacts these odds ratio and if so how? (i.e., does the likelihood that a student graduates based on any of my independent variables differ for a first gen and non first gen student?) To determine this, I ran the model again and set First Generation as an interaction variable with all variables in model.
Call:
glm(formula = Success ~ (Core.GPA + Lab.Yr.Taken + Frn.Lang.Yr.Taken +
SAT.Converted + Incoming.Test) * firstGen, family = binomial,
data = df)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.6380 -1.1061 0.6362 0.8186 1.8288
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.5094889 0.6705484 -5.234 1.66e-07 ***
Core.GPA 1.0698918 0.1087680 9.836 < 2e-16 ***
Lab.Yr.Taken 0.0971983 0.0316549 3.071 0.00214 **
Frn.Lang.Yr.Taken 0.0377991 0.0338970 1.115 0.26480
SAT.Converted -0.0001896 0.0004232 -0.448 0.65418
Incoming.Test 0.0358615 0.0035690 10.048 < 2e-16 ***
firstGenYes -1.7697353 1.6092509 -1.100 0.27145
Core.GPA:firstGenYes 0.3528697 0.2899914 1.217 0.22367
Lab.Yr.Taken:firstGenYes 0.0928141 0.0811118 1.144 0.25251
Frn.Lang.Yr.Taken:firstGenYes 0.1247308 0.0900435 1.385 0.16598
SAT.Converted:firstGenYes -0.0009749 0.0010075 -0.968 0.33319
Incoming.Test:firstGenYes 0.0296594 0.0106095 2.796 0.00518 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 7022.5 on 5947 degrees of freedom
Residual deviance: 6483.5 on 5936 degrees of freedom
(1108 observations deleted due to missingness)
AIC: 6507.5
Number of Fisher Scoring iterations: 4
and odds ratio:
(Intercept) Core.GPA
0.0299122 2.9150640
Lab.Yr.Taken Frn.Lang.Yr.Taken
1.1020789 1.0385226
SAT.Converted Incoming.Test
0.9998104 1.0365123
firstGenYes Core.GPA:firstGenYes
0.1703781 1.4231457
Lab.Yr.Taken:firstGenYes Frn.Lang.Yr.Taken:firstGenYes
1.0972578 1.1328434
SAT.Converted:firstGenYes Incoming.Test:firstGenYes
0.9990255 1.0301036
What I'm hoping to learn from these models is:
1. For Non-First Gen students, the odds of success increase/decrease by _% for each additional one unit increase in Incoming test Credit.
My assumption on this so far is: The odds ratio for Incoming.Test (1.0365123) represents the odds ratio for NON-first Generation students (aka, for non-first gen students odds of success increase by 3% for each additional increase in incoming test credits).
2. Same question as above, but for First Gen students.
??? Is a calculation needed to determine this?
3. What is the difference in odds between first gen and non first gen students
My assumption so far: The odds ratio for IncomingTestxFirstGen (1.03010136) represents the difference in odds between first gen and non first gen???
4. Is First Generation status significant or non significant when considering odds of success based on Incoming test credits?
My assumption: Yes, the difference is significant because IncomingTestxFirstGen is significant.
5. What does the "firstGenYes" odds ratio in the second model indicate/represent?
???
I would appreciate any feedback regarding my initial interpretation attempts! I have reviewed questions similar to this that have already been asked, but have not came across any explanation that fully encapsulates what I’m after. Thank you.