College Enrollment Odds Among Black Students: A Logit Model

Source: www.redbubble.com

1. Introduction

This project examine the factors that may account for the differences in college enrollment odds among black people. Native born Blacks. Literature on the topic shows that in the Black community (everyone considered as having African origins), college enrollment rates for students with immigrant parents are higher than those for students with parents born in the U.S. Understanding this question may help measure the scale of societal discrimination versus other factors that account for the education success gap.

Among a number of others, this analysis seeks to mainly answer the question: is there a difference in college enrollment odds between children from US-born Black households and those from immigrants households? Lower college enrollment rates for students with native-born Black parents than Black students with immigrant parents would imply that discrimination alone does not explain the success gap.

2. Data

The data used in this project comes from the Current Population Survey (CPS) - a monthly survey of U.S. households conducted by the Bureau of Labor Statistics for the Census Bureau. The CPS data used here is from the March 2013 survey and was accessed through the IPUMS project of the Minnesota Population Center at the University of Minnesota.

Before uploading the I load the packages containing the various functions we will be using for the analysis. They include tidyverse, visdat, summarytools, plotly, among others.

Let’s upload the data.

Here are the top and bottom rows of the data.

Head

Tail

Now, let us look at the summary and structure of the data.

Data Frame Summary

IPUMS

Dimensions: 202634 x 32
Duplicates: 878

Variable

Stats / Values

Freqs (% of Valid)

Graph

Valid

Missing

STATEFIP [numeric]

Mean (sd) : 27.6 (16.1)

min ≤ med ≤ max:

1 ≤ 27 ≤ 56

IQR (CV) : 30 (0.6)

51 distinct values

202634 (100.0%)

0 (0.0%)

AGE [numeric]

Mean (sd) : 35.5 (22.3)

min ≤ med ≤ max:

0 ≤ 35 ≤ 85

IQR (CV) : 37 (0.6)

82 distinct values

202634 (100.0%)

0 (0.0%)

SEX [numeric]

Min : 1

Mean : 1.5

Max : 2

1	:	98304	(	48.5%	)
2	:	104330	(	51.5%	)

202634 (100.0%)

0 (0.0%)

RACE [numeric]

Mean (sd) : 167.1 (170.1)

min ≤ med ≤ max:

100 ≤ 100 ≤ 830

IQR (CV) : 0 (1)

26 distinct values

202634 (100.0%)

0 (0.0%)

MARST [numeric]

Mean (sd) : 3.8 (2.3)

min ≤ med ≤ max:

1 ≤ 5 ≤ 6

IQR (CV) : 5 (0.6)

1	:	79444	(	39.2%	)
2	:	2121	(	1.0%	)
3	:	3368	(	1.7%	)
4	:	15094	(	7.4%	)
5	:	7926	(	3.9%	)
6	:	94681	(	46.7%	)

202634 (100.0%)

0 (0.0%)

ASIAN [numeric]

Mean (sd) : 95.5 (15)

min ≤ med ≤ max:

10 ≤ 99 ≤ 99

IQR (CV) : 0 (0.2)

10	:	1931	(	1.0%	)
20	:	2340	(	1.2%	)
30	:	1906	(	0.9%	)
40	:	971	(	0.5%	)
50	:	1004	(	0.5%	)
60	:	1126	(	0.6%	)
70	:	2095	(	1.0%	)
99	:	191261	(	94.4%	)

202634 (100.0%)

0 (0.0%)

BPL [numeric]

Mean (sd) : 13428.3 (10549.5)

min ≤ med ≤ max:

9900 ≤ 9900 ≤ 96000

IQR (CV) : 0 (0.8)

162 distinct values

202634 (100.0%)

0 (0.0%)

CITIZEN [numeric]

Mean (sd) : 1.5 (1.2)

min ≤ med ≤ max:

1 ≤ 1 ≤ 5

IQR (CV) : 0 (0.8)

1	:	173572	(	85.7%	)
2	:	1211	(	0.6%	)
3	:	1644	(	0.8%	)
4	:	11644	(	5.7%	)
5	:	14563	(	7.2%	)

202634 (100.0%)

0 (0.0%)

NATIVITY [numeric]

Mean (sd) : 1.9 (1.5)

min ≤ med ≤ max:

0 ≤ 1 ≤ 5

IQR (CV) : 1 (0.8)

0	:	215	(	0.1%	)
1	:	149846	(	73.9%	)
2	:	4846	(	2.4%	)
3	:	4281	(	2.1%	)
4	:	14488	(	7.1%	)
5	:	28958	(	14.3%	)

202634 (100.0%)

0 (0.0%)

HISPAN [numeric]

Mean (sd) : 43.7 (129.6)

min ≤ med ≤ max:

0 ≤ 0 ≤ 610

IQR (CV) : 0 (3)

0	:	165314	(	81.6%	)
100	:	23868	(	11.8%	)
200	:	3312	(	1.6%	)
300	:	1172	(	0.6%	)
600	:	1937	(	1.0%	)
610	:	7031	(	3.5%	)

202634 (100.0%)

0 (0.0%)

EMPSTAT [numeric]

Mean (sd) : 14.9 (13.1)

min ≤ med ≤ max:

0 ≤ 10 ≤ 36

IQR (CV) : 22 (0.9)

0	:	46883	(	23.1%	)
1	:	654	(	0.3%	)
10	:	88359	(	43.6%	)
12	:	3012	(	1.5%	)
21	:	6579	(	3.2%	)
22	:	785	(	0.4%	)
32	:	7806	(	3.9%	)
34	:	26890	(	13.3%	)
36	:	21666	(	10.7%	)

202634 (100.0%)

0 (0.0%)

LABFORCE [numeric]

Mean (sd) : 1.3 (0.8)

min ≤ med ≤ max:

0 ≤ 1 ≤ 2

IQR (CV) : 1 (0.6)

0	:	47537	(	23.5%	)
1	:	56362	(	27.8%	)
2	:	98735	(	48.7%	)

202634 (100.0%)

0 (0.0%)

EDUC99 [numeric]

Mean (sd) : 8.7 (5.6)

min ≤ med ≤ max:

0 ≤ 10 ≤ 18

IQR (CV) : 8 (0.6)

16 distinct values

202634 (100.0%)

0 (0.0%)

SCHLCOLL [numeric]

Mean (sd) : 2.4 (2.4)

min ≤ med ≤ max:

0 ≤ 1 ≤ 5

IQR (CV) : 5 (1)

0	:	96504	(	47.6%	)
1	:	8358	(	4.1%	)
2	:	195	(	0.1%	)
3	:	8255	(	4.1%	)
4	:	2781	(	1.4%	)
5	:	86541	(	42.7%	)

202634 (100.0%)

0 (0.0%)

FTOTVAL [numeric]

Mean (sd) : 76965.6 (90026.2)

min ≤ med ≤ max:

-19998 ≤ 56000 ≤ 2742997

IQR (CV) : 73036 (1.2)

37560 distinct values

202634 (100.0%)

0 (0.0%)

OFFPOV [numeric]

Mean (sd) : 2 (4.1)

min ≤ med ≤ max:

1 ≤ 2 ≤ 99

IQR (CV) : 0 (2)

1	:	29865	(	14.7%	)
2	:	172404	(	85.1%	)
99	:	365	(	0.2%	)

202634 (100.0%)

0 (0.0%)

POVERTY [numeric]

Mean (sd) : 20.9 (4.6)

min ≤ med ≤ max:

10 ≤ 23 ≤ 23

IQR (CV) : 0 (0.2)

10	:	30237	(	14.9%	)
21	:	9658	(	4.8%	)
22	:	9990	(	4.9%	)
23	:	152749	(	75.4%	)

202634 (100.0%)

0 (0.0%)

GOTWIC [numeric]

Mean (sd) : 0.2 (0.4)

min ≤ med ≤ max:

0 ≤ 0 ≤ 2

IQR (CV) : 0 (2.4)

0	:	171493	(	84.6%	)
1	:	28588	(	14.1%	)
2	:	2553	(	1.3%	)

202634 (100.0%)

0 (0.0%)

HOURWAGE [numeric]

Mean (sd) : 962.5 (188.4)

min ≤ med ≤ max:

1 ≤ 1000 ≤ 1000

IQR (CV) : 0 (0.2)

1032 distinct values

202634 (100.0%)

0 (0.0%)

SEX_HEAD [numeric]

Min : 1

Mean : 1.5

Max : 2

1	:	103725	(	51.2%	)
2	:	98812	(	48.8%	)

202537 (100.0%)

97 (0.0%)

RACE_HEAD [numeric]

Mean (sd) : 160.5 (158.8)

min ≤ med ≤ max:

100 ≤ 100 ≤ 830

IQR (CV) : 0 (1)

24 distinct values

202537 (100.0%)

97 (0.0%)

MARST_HEAD [numeric]

Mean (sd) : 2.4 (2)

min ≤ med ≤ max:

1 ≤ 1 ≤ 6

IQR (CV) : 3 (0.8)

1	:	128602	(	63.5%	)
2	:	2856	(	1.4%	)
3	:	5678	(	2.8%	)
4	:	22621	(	11.2%	)
5	:	9902	(	4.9%	)
6	:	32878	(	16.2%	)

202537 (100.0%)

97 (0.0%)

BPL_HEAD [numeric]

Mean (sd) : 14577.2 (11814.4)

min ≤ med ≤ max:

9900 ≤ 9900 ≤ 96000

IQR (CV) : 0 (0.8)

161 distinct values

202537 (100.0%)

97 (0.0%)

CITIZEN_HEAD [numeric]

Mean (sd) : 1.7 (1.4)

min ≤ med ≤ max:

1 ≤ 1 ≤ 5

IQR (CV) : 0 (0.8)

1	:	162456	(	80.2%	)
2	:	1535	(	0.8%	)
3	:	1930	(	1.0%	)
4	:	17417	(	8.6%	)
5	:	19199	(	9.5%	)

202537 (100.0%)

97 (0.0%)

NATIVITY_HEAD [numeric]

Mean (sd) : 2 (1.6)

min ≤ med ≤ max:

0 ≤ 1 ≤ 5

IQR (CV) : 2 (0.8)

0	:	224	(	0.1%	)
1	:	147234	(	72.7%	)
2	:	3915	(	1.9%	)
3	:	3375	(	1.7%	)
4	:	7868	(	3.9%	)
5	:	39921	(	19.7%	)

202537 (100.0%)

97 (0.0%)

HISPAN_HEAD [numeric]

Mean (sd) : 42.1 (127.9)

min ≤ med ≤ max:

0 ≤ 0 ≤ 610

IQR (CV) : 0 (3)

0	:	166837	(	82.4%	)
100	:	22756	(	11.2%	)
200	:	3052	(	1.5%	)
300	:	1178	(	0.6%	)
600	:	1906	(	0.9%	)
610	:	6808	(	3.4%	)

202537 (100.0%)

97 (0.0%)

LABFORCE_HEAD [numeric]

Mean (sd) : 1.7 (0.5)

min ≤ med ≤ max:

0 ≤ 2 ≤ 2

IQR (CV) : 1 (0.3)

0	:	1200	(	0.6%	)
1	:	56257	(	27.8%	)
2	:	145080	(	71.6%	)

202537 (100.0%)

97 (0.0%)

EDUC99_HEAD [numeric]

Mean (sd) : 11.9 (3.2)

min ≤ med ≤ max:

1 ≤ 11 ≤ 18

IQR (CV) : 5 (0.3)

15 distinct values

202537 (100.0%)

97 (0.0%)

FTOTVAL_HEAD [numeric]

Mean (sd) : 79686.1 (90713.3)

min ≤ med ≤ max:

-19998 ≤ 59488 ≤ 2742997

IQR (CV) : 72484 (1.1)

36025 distinct values

202537 (100.0%)

97 (0.0%)

OFFPOV_HEAD [numeric]

Min : 1

Mean : 1.9

Max : 2

1	:	29002	(	14.3%	)
2	:	173535	(	85.7%	)

202537 (100.0%)

97 (0.0%)

POVERTY_HEAD [numeric]

Mean (sd) : 21 (4.5)

min ≤ med ≤ max:

10 ≤ 23 ≤ 23

IQR (CV) : 0 (0.2)

10	:	29009	(	14.3%	)
21	:	9643	(	4.8%	)
22	:	9974	(	4.9%	)
23	:	153911	(	76.0%	)

202537 (100.0%)

97 (0.0%)

GOTWIC_HEAD [numeric]

Mean (sd) : 0.2 (0.5)

min ≤ med ≤ max:

0 ≤ 0 ≤ 2

IQR (CV) : 0 (2.3)

0	:	167379	(	82.6%	)
1	:	29486	(	14.6%	)
2	:	5672	(	2.8%	)

202537 (100.0%)

97 (0.0%)

Generated by summarytools 1.0.1 (R version 4.2.1)
2023-02-11

3. Data Wrangling

In this section, I clean the data to get it ready for modelling.

3.1. Create New Variables

The first thing I do is create new variables out of the existing ones. It involves breaking up categorical variables with multiple levels into binary variables that will be used in the regression. Some of the dummy variables created include AFRICAN_HEAD, CARRIBEAN_HEAD.

3.2. Remove Unwanted Observations

Some of the main variables used in this work have observations that fall outside the scope of the analysis. I remove them from the data.

AGE: The analysis focuses on respondents of college-going age and their families. Hence, I set the age criteria to 18 and 25 years, excluding repondents who fall outside of that age range.
FTOTVAL: Some respondents reported income levels of $0 or less (see summary table in Section 3). Since the analyses focuses on working families, I treat those with no incomes as outliers and remove them from our analysis.

Now, let’s execute the cleaning listed above.

After removing the unwanted age groups and those with no income, we are left with 18994 total number of observations.

3.3. Remove Unwanted Variables

I keep only variables needed for the analysis - there are about 12 of them. The rest are excluded from this work.

3.4. Convert Binary Variables from `numeric` to `factor`

All the categorical variables have been classified as character variables in R. I change them to factors, as this matters for the regression analysis.

Current Data Types

Binary Variables Changed to Factors

3.5. Check for Missing Values

The summary table indicated that some of the columns had missing values. Let’s check to see if there are still present even after doing some cleaning.

From the chart above, there are no missing values in our data. It seems removing respondents outside the age group we need and those with no incomes took care of the missing values.

3.6. Check for Duplicated Rows

The summary table above showed that there were duplicated rows. Let’s check to see if they are still present and consolidate them.

Number of Duplicated Rows
419

Now, let’s keep only unique rows and confirm that all the duplicates have been delt with.

Number of Duplicated Rows
0

4. Exploratory Data Analysis

Now that we have our final data for the analysis, let’s do some EDA.

4.1. Check for Multicollinearity

One of the main assumptions for logistic regressions is that there be no collinearity/multicollinearity among the explanatory variables. This means that the predictor variables must not have a high correlation or association. Hence, I check the correlation among all the variables I intend to use as predictor variables in the logistic regression model.

From the plot, there appear to be strong positive correlation between some pair of variables. RACE_OTHER and HISPANICS are highly correlated. This makes sense since most Hispanics probably identify as “other” when it comes to race.

There is also high correlation between the birth place of heads of household (BPL_HEAD) and their status as a foreigner (FOREIGN_HEAD). Again, this makes sense as most non-U.S. born heads of households are from other continents besides Africa and Caribbean.

It is important to keep track of which two or more variables are highly correlated. Using them as explanatory variables in the same model would cause multicollinearity issues, affecting the overall validity of the model.

5. Modeling: Logistic Regression

Using logit regression models, I attempt to answer the main question: is there a difference in college enrollment rates between Native-born Blacks household children and African immigrants household children?.

But before modeling enrollment rates among Black people, I look at college enrollment rates in the overall population with emphasis on the differences in enrollment rates between whites and other races and Hispanics. I also look at college enrollment rates in California to determine if the State’s ban on affirmative action in 1996 has had any impact on college enrollment rates.

The dependent variable for the regression is COLL_ATT.

5.1. Overall Enrollment Odds

Let’s start with enrollment rates in the overall sample and compare enrollment rates among other races to that of whites.

## 
## Call:
## glm(formula = COLL_ATT ~ AGE + SEX + FTOTVAL + BACHELORS_HEAD + 
##     STABLEMARRIAGE + RACE + HISPANIC, family = binomial(link = "logit"), 
##     data = IPUMS)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8336  -0.9200  -0.7477   1.2642   2.1406  
## 
## Coefficients:
##                       Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          1.609e+00  1.536e-01  10.473  < 2e-16 ***
## AGE                 -1.299e-01  6.977e-03 -18.617  < 2e-16 ***
## SEXFEMALE            3.842e-01  3.169e-02  12.124  < 2e-16 ***
## FTOTVAL              2.425e-06  2.340e-07  10.360  < 2e-16 ***
## BACHELORS_HEADYES    5.072e-01  3.770e-02  13.452  < 2e-16 ***
## STABLEMARRIAGEYES    4.818e-02  3.476e-02   1.386 0.165766    
## RACEASIAN            6.363e-01  6.732e-02   9.451  < 2e-16 ***
## RACEBLACK           -3.225e-02  5.096e-02  -0.633 0.526796    
## RACEMIXED RACE       8.942e-02  9.618e-02   0.930 0.352523    
## RACENATIVEAMERICAN  -7.125e-01  1.891e-01  -3.768 0.000164 ***
## RACEOTHER           -1.853e-01  2.618e-01  -0.708 0.479014    
## RACEPACIFICISLANDER -2.047e-01  2.232e-01  -0.917 0.359057    
## HISPANICYES          1.294e-01  2.589e-01   0.500 0.617016    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 24410  on 18777  degrees of freedom
## Residual deviance: 23203  on 18765  degrees of freedom
## AIC: 23229
## 
## Number of Fisher Scoring iterations: 4

From the regression, the following variables are statistically significant at 95% confidence interval: AGE, SEX(FEMALE), FTOTVAL, BACHELORS_HEAD, and RACE (ASIAN & NATIVE AMERICAN). The aforementiond variable influence college enrollment odds - some positively, others negatively.

Odds Ratio

##         (Intercept)                 AGE           SEXFEMALE             FTOTVAL 
##           4.9980399           0.8781926           1.4684601           1.0000024 
##   BACHELORS_HEADYES   STABLEMARRIAGEYES           RACEASIAN           RACEBLACK 
##           1.6605527           1.0493574           1.8894788           0.9682623 
##      RACEMIXED RACE  RACENATIVEAMERICAN           RACEOTHER RACEPACIFICISLANDER 
##           1.0935369           0.4903964           0.8308155           0.8149197 
##         HISPANICYES 
##           1.1382000

Interpreting the Regression Results

Assuming all else are equal, we can make the following inferences from the model:

A one unit in age (in this case year) reduces a person’s odds of enrolling in college by approximately 12.1%.
Females have 47.2% higher odds of enrolling in college compared to males.
A one unit increase in total family income (FTOTVAL) barely raises a person’s college enrollment odds (0.0002%). This is expected as the availability of student loans make it easier for people from poor backgrounds to attend.
Having a head of household with at least a bachelors degree increases a person’s odds of college enrollment by about 66.6%.
Compared to White people, Asians have 66.6% higher odds of enrolling in college, while Native Americans have 51.3% lower odds.

Note: Because they are not statistically significant, we cannot make any inferences about enrollment rates when comparing college enrollment among Blacks, Pacific Islanders, Hispanics, Mixed Race and Other races to that among Whites. We also cannot make any conclusion about the odds of enrollment for people coming from statble homes.

5.2. College Enrollment Among Californians

In 1996, the State of California banned the use of affirmative action. To test the effects of the ban on college enrollment rates, let’s restrict our sample in this regression to the state of California.

The size of the sample for our analysis is 2200.

## 
## Call:
## glm(formula = COLL_ATT ~ AGE + SEX + FTOTVAL + RACE + HISPANIC + 
##     BACHELORS_HEAD + STABLEMARRIAGE, family = binomial(link = "logit"), 
##     data = IPUMS_CALI)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.1869  -1.0429  -0.8291   1.2146   1.8320  
## 
## Coefficients:
##                       Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          2.437e+00  4.392e-01   5.548 2.88e-08 ***
## AGE                 -1.388e-01  1.983e-02  -6.998 2.60e-12 ***
## SEXFEMALE            3.151e-01  8.853e-02   3.559 0.000372 ***
## FTOTVAL              1.122e-06  5.940e-07   1.888 0.059002 .  
## RACEASIAN            3.831e-01  1.538e-01   2.492 0.012702 *  
## RACEBLACK           -3.668e-02  2.037e-01  -0.180 0.857068    
## RACEMIXED RACE       7.578e-01  2.893e-01   2.619 0.008808 ** 
## RACENATIVEAMERICAN  -1.082e+00  8.128e-01  -1.331 0.183221    
## RACEOTHER            4.795e-01  5.753e-01   0.834 0.404559    
## RACEPACIFICISLANDER -3.203e-01  5.343e-01  -0.599 0.548919    
## HISPANICYES         -7.269e-01  5.659e-01  -1.285 0.198933    
## BACHELORS_HEADYES    1.554e-01  1.167e-01   1.332 0.182824    
## STABLEMARRIAGEYES    1.350e-01  9.417e-02   1.433 0.151754    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 3015.6  on 2199  degrees of freedom
## Residual deviance: 2899.6  on 2187  degrees of freedom
## AIC: 2925.6
## 
## Number of Fisher Scoring iterations: 4

Odds Ratio

##         (Intercept)                 AGE           SEXFEMALE             FTOTVAL 
##          11.4365513           0.8704066           1.3704233           1.0000011 
##           RACEASIAN           RACEBLACK      RACEMIXED RACE  RACENATIVEAMERICAN 
##           1.4668978           0.9639843           2.1335949           0.3389883 
##           RACEOTHER RACEPACIFICISLANDER         HISPANICYES   BACHELORS_HEADYES 
##           1.6152338           0.7259535           0.4834042           1.1681600 
##   STABLEMARRIAGEYES 
##           1.1445206

Interpreting the Regression Results

A one unit in age reduces college enrollment odds by approximately 12.9%.
Females have 36.9% higher enrollment odds compared to males.
Compared to White people, college enrollment odds are 52.7% higher for Asians enrolling in college and 114.9% higher for mixed race individuals.
College enrollment odds among Blacks, Hispanics, Native Americans, Pacific Islanders and other races are not statistically compared to white enrollment. Hence, no meaningful inferences can be about the effects of the of California’s affirmative action ban on enrollment odds among those groups.

5.3. College Enrollment Rates Among Black People

In the second part of this analysis, I take at college enrollment rates among black people only. To begin, let’s pull a subset respondents who identify solely as black and nothing else.

5.3.1. Baseline Regression: Enrollment Rates Among Black People

First, I look at college enrollment odds among all black people.

## 
## Call:
## glm(formula = COLL_ATT ~ AGE + SEX + FTOTVAL + BACHELORS_HEAD + 
##     STABLEMARRIAGE, family = binomial(link = "logit"), data = IPUMS_BLK)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7263  -0.8697  -0.7178   1.2398   1.9768  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        2.891e-01  4.458e-01   0.649   0.5166    
## AGE               -8.413e-02  2.060e-02  -4.084 4.44e-05 ***
## SEXFEMALE          6.071e-01  9.318e-02   6.515 7.27e-11 ***
## FTOTVAL            4.518e-06  9.421e-07   4.795 1.63e-06 ***
## BACHELORS_HEADYES  6.212e-01  1.202e-01   5.170 2.34e-07 ***
## STABLEMARRIAGEYES  2.286e-01  1.061e-01   2.154   0.0312 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2926.2  on 2325  degrees of freedom
## Residual deviance: 2764.2  on 2320  degrees of freedom
## AIC: 2776.2
## 
## Number of Fisher Scoring iterations: 4

Odds Ratio

##       (Intercept)               AGE         SEXFEMALE           FTOTVAL 
##         1.3352525         0.9193131         1.8350230         1.0000045 
## BACHELORS_HEADYES STABLEMARRIAGEYES 
##         1.8612173         1.2568511

Interpreting the Regression Results

All variables included are statistically significant when it comes to college enrollment rates among black people. From the odds ratios, we can make following conclusions about the effects of each variable on black college enrollment rates.

A unit increase in age reduces a black person’s college enrollment odds by about 8%.
Black females have 82.8% higher odds of enrolling in college compared to black males.
Blacks from high income households have marginally higher odds of enrolling in college - similar to the overall population.
The head of households having at least a bachelors degree raises a black person’s odds of college enrollment by about 88.8%.
Lastly, black people from stable homes, with two parents present, have 27.2% higher odds of enrollment compared those from non-stable homes.

5.3.2. Black Households with Foreigners as Head

What if the head of a black household is a foreigner, meaning they are not from the U.S. or any of its territories? Does that affect the odds of college enrollment for a black person from such a household?

## 
## Call:
## glm(formula = COLL_ATT ~ AGE + SEX + FTOTVAL + BACHELORS_HEAD + 
##     STABLEMARRIAGE + FOREIGN_HEAD, family = binomial(link = "logit"), 
##     data = IPUMS_BLK)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -2.599  -0.866  -0.706   1.206   1.999  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        2.059e-01  4.479e-01   0.460   0.6458    
## AGE               -8.279e-02  2.067e-02  -4.005 6.20e-05 ***
## SEXFEMALE          6.179e-01  9.360e-02   6.601 4.07e-11 ***
## FTOTVAL            4.266e-06  9.427e-07   4.526 6.02e-06 ***
## BACHELORS_HEADYES  5.957e-01  1.207e-01   4.936 7.97e-07 ***
## STABLEMARRIAGEYES  2.052e-01  1.066e-01   1.925   0.0542 .  
## FOREIGN_HEADYES    5.634e-01  1.342e-01   4.197 2.70e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2926.2  on 2325  degrees of freedom
## Residual deviance: 2746.9  on 2319  degrees of freedom
## AIC: 2760.9
## 
## Number of Fisher Scoring iterations: 4

Odds Ratio

##       (Intercept)               AGE         SEXFEMALE           FTOTVAL 
##         1.2285950         0.9205414         1.8550405         1.0000043 
## BACHELORS_HEADYES STABLEMARRIAGEYES   FOREIGN_HEADYES 
##         1.8142718         1.2278002         1.7565551

Interpreting the Regression Results

The odds of a black person enrolling in college is 77.1% higher if they come from a home where the head of household has at least a bachelors degree.
The other variables in the regression have the same effects on black college enrollment as described in Section 3.3.1.

5.3.3. Does Citizenship matter for Black Enrollment Rates?

Let’s look citizenship status of the respondents. Does citizenship affect a black person’s chances of enrolling in college?

## 
## Call:
## glm(formula = COLL_ATT ~ AGE + SEX + FTOTVAL + BACHELORS_HEAD + 
##     STABLEMARRIAGE + FOREIGN_HEAD + CITIZEN, family = binomial(link = "logit"), 
##     data = IPUMS_BLK)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -2.599  -0.866  -0.706   1.206   1.999  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        2.091e-01  5.306e-01   0.394 0.693493    
## AGE               -8.280e-02  2.068e-02  -4.003 6.25e-05 ***
## SEXFEMALE          6.179e-01  9.360e-02   6.601 4.07e-11 ***
## FTOTVAL            4.266e-06  9.429e-07   4.524 6.06e-06 ***
## BACHELORS_HEADYES  5.956e-01  1.207e-01   4.934 8.07e-07 ***
## STABLEMARRIAGEYES  2.052e-01  1.066e-01   1.925 0.054222 .  
## FOREIGN_HEADYES    5.627e-01  1.472e-01   3.822 0.000132 ***
## CITIZENYES        -3.061e-03  2.689e-01  -0.011 0.990918    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2926.2  on 2325  degrees of freedom
## Residual deviance: 2746.9  on 2318  degrees of freedom
## AIC: 2762.9
## 
## Number of Fisher Scoring iterations: 4

Odds Ratio

##       (Intercept)               AGE         SEXFEMALE           FTOTVAL 
##         1.2325786         0.9205343         1.8550375         1.0000043 
## BACHELORS_HEADYES STABLEMARRIAGEYES   FOREIGN_HEADYES        CITIZENYES 
##         1.8141966         1.2277773         1.7553466         0.9969437

Interpreting the Regression Results

From the regression, citizenship status of the respondent is not statistically significant. Hence, we cannot make any meaningful inference about its effects on college enrollment odds for black people.
The other variables in the regression have the same effects on black college enrollment as described in sections.

5.3.4. What if the Head of Household is an Immigrant?

In this section, I assess how college enrollment odds differ for black children with an immigrant as head of household compared to those with non-immigrant head of household. I pay particular to those with African or Caribbeans as head of household since majority of the black immigrant population come from African and Caribbean countries.

## 
## Call:
## glm(formula = COLL_ATT ~ AGE + SEX + FTOTVAL + BACHELORS_HEAD + 
##     STABLEMARRIAGE + BPL_HEAD, family = binomial(link = "logit"), 
##     data = IPUMS_BLK)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.5933  -0.8649  -0.7047   1.2064   2.0007  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        2.051e-01  4.481e-01   0.458  0.64715    
## AGE               -8.295e-02  2.068e-02  -4.011 6.06e-05 ***
## SEXFEMALE          6.188e-01  9.370e-02   6.604 4.00e-11 ***
## FTOTVAL            4.257e-06  9.429e-07   4.515 6.32e-06 ***
## BACHELORS_HEADYES  5.954e-01  1.208e-01   4.931 8.20e-07 ***
## STABLEMARRIAGEYES  2.062e-01  1.067e-01   1.931  0.05344 .  
## BPL_HEADAFRICA     5.807e-01  1.885e-01   3.080  0.00207 ** 
## BPL_HEADCARIBBEAN  5.701e-01  1.985e-01   2.873  0.00407 ** 
## BPL_HEADOTHER      6.646e-01  3.545e-01   1.875  0.06084 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2926.2  on 2325  degrees of freedom
## Residual deviance: 2745.2  on 2317  degrees of freedom
## AIC: 2763.2
## 
## Number of Fisher Scoring iterations: 4

Odds Ratio

##       (Intercept)               AGE         SEXFEMALE           FTOTVAL 
##         1.2276315         0.9204001         1.8566887         1.0000043 
## BACHELORS_HEADYES STABLEMARRIAGEYES    BPL_HEADAFRICA BPL_HEADCARIBBEAN 
##         1.8137854         1.2289504         1.7872992         1.7684728 
##     BPL_HEADOTHER 
##         1.9437560

Interpreting the Regression Results

Compared to black respondents with non-immigrant head of household, those from homes with African or Caribbean heads of household have 82.6% and 75.6% higher odds of college enrollment, respectively.

Literature (Bennett and Lutz, 2009) suggests that immigrant parents have higher educational attainments compared to parents of native blacks and that perhaps has an effect on the differences in college enrollment odds between their children.

College Enrollment Odds Among Black Students: A Logit Model

William Kyeremateng

May 05, 2019

1. Introduction

2. Data

Head

Tail

Data Frame Summary

IPUMS

3. Data Wrangling

3.1. Create New Variables

3.2. Remove Unwanted Observations

3.3. Remove Unwanted Variables

3.4. Convert Binary Variables from `numeric` to `factor`

Current Data Types

Binary Variables Changed to Factors

3.5. Check for Missing Values

3.6. Check for Duplicated Rows

4. Exploratory Data Analysis

4.1. Check for Multicollinearity

5. Modeling: Logistic Regression

5.1. Overall Enrollment Odds

5.2. College Enrollment Among Californians

5.3. College Enrollment Rates Among Black People

5.3.1. Baseline Regression: Enrollment Rates Among Black People

5.3.2. Black Households with Foreigners as Head

5.3.3. Does Citizenship matter for Black Enrollment Rates?

5.3.4. What if the Head of Household is an Immigrant?

College Enrollment Odds Among Black Students: A Logit Model

William Kyeremateng

May 05, 2019

1. Introduction

2. Data

Head

Tail

Data Frame Summary

IPUMS

3. Data Wrangling

3.1. Create New Variables

3.2. Remove Unwanted Observations

3.3. Remove Unwanted Variables

3.4. Convert Binary Variables from numeric to factor

Current Data Types

Binary Variables Changed to Factors

3.5. Check for Missing Values

3.6. Check for Duplicated Rows

4. Exploratory Data Analysis

4.1. Check for Multicollinearity

5. Modeling: Logistic Regression

5.1. Overall Enrollment Odds

5.2. College Enrollment Among Californians

5.3. College Enrollment Rates Among Black People

5.3.1. Baseline Regression: Enrollment Rates Among Black People

5.3.2. Black Households with Foreigners as Head

5.3.3. Does Citizenship matter for Black Enrollment Rates?

5.3.4. What if the Head of Household is an Immigrant?

3.4. Convert Binary Variables from `numeric` to `factor`