Hw_8: Multilevel Analysis of APR
Kat Rodriguez
April 7, 2019
Academic Progress Rate: How does progress vary when looking at schools versus individual sports?
Universities, educators, and parents are concerned about the academic track of student atheletes. The National Collegiate Athletic Association designed the Academic Progress Rate (APR) that creates a score for athletes of which informs them of their likelihood to graduate school. The academic progress report is a compilation of several rates: their academic eligibility (did they earn passing marks to compete in championships), retention (were they retained as athletes in the following semester/year), and if they are on track for graduation. For my research, I am using the “Academic Scores for NCAA Athletic Programs” dataset that I downloaded from Kaggle.
I chose to conduct a multilevel analysis using academic progress rate as my continuous dependent variable. I will be looking at academic progress rate according to two levels: the schools and the individual sports teams. I will also determine how gender and conference-region impacts academic progress rate.
Packages Used
library(readr)
library(nlme)
library(lme4)## Loading required package: Matrix##
## Attaching package: 'lme4'## The following object is masked from 'package:nlme':
##
## lmListlibrary(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:nlme':
##
## collapse## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(lmerTest)##
## Attaching package: 'lmerTest'## The following object is masked from 'package:lme4':
##
## lmer## The following object is masked from 'package:stats':
##
## steplibrary(ggplot2)Importing Dataset
apr <-read_csv("C:/Users/Skippz/Desktop/database.csv", col_names = TRUE)## Parsed with column specification:
## cols(
## .default = col_double(),
## SCHOOL_NAME = col_character(),
## SPORT_NAME = col_character(),
## NCAA_CONFERENCE = col_character()
## )## See spec(...) for full column specifications.apr1<-apr%>%
select(SCHOOL_NAME, SPORT_NAME, SCHOOL_TYPE, FOURYEAR_SCORE, FOURYEAR_ATHLETES, FOURYEAR_ELIGIBILITY, FOURYEAR_RETENTION)%>%
filter(!is.na(FOURYEAR_SCORE), !is.na(FOURYEAR_ATHLETES), !is.na(FOURYEAR_ELIGIBILITY), !is.na(FOURYEAR_RETENTION))
head(apr1)## # A tibble: 6 x 7
## SCHOOL_NAME SPORT_NAME SCHOOL_TYPE FOURYEAR_SCORE FOURYEAR_ATHLET~
## <chr> <chr> <dbl> <dbl> <dbl>
## 1 Alabama A&~ Baseball 0 931 80
## 2 Alabama A&~ Football 0 932 321
## 3 Alabama A&~ Men's Bas~ 0 964 43
## 4 Alabama A&~ Men's Golf 0 898 22
## 5 Alabama A&~ Men's Ten~ 0 988 12
## 6 Alabama A&~ Men's Tra~ 0 932 62
## # ... with 2 more variables: FOURYEAR_ELIGIBILITY <dbl>,
## # FOURYEAR_RETENTION <dbl>Analysis by School Type (Complete Pooling)
There are 2 different types of schools: public and private. According to complete pooling, public school has an average APR score of 975.4496 and private school has a 6.1180 increase in APR score beyond that.This suggests that private schools are more successful at keeping student-athletes on a strong academic track.
length(unique(apr1$SCHOOL_TYPE))## [1] 2cpool <- lm(FOURYEAR_SCORE ~ SCHOOL_TYPE, data = apr1)
summary(cpool)##
## Call:
## lm(formula = FOURYEAR_SCORE ~ SCHOOL_TYPE, data = apr1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1080.57 -8.45 6.55 16.43 24.55
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 975.4496 0.7424 1313.935 < 2e-16 ***
## SCHOOL_TYPE 6.1180 1.2507 4.892 1.02e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 48.21 on 6509 degrees of freedom
## Multiple R-squared: 0.003663, Adjusted R-squared: 0.00351
## F-statistic: 23.93 on 1 and 6509 DF, p-value: 1.024e-06Analysis by School Level (Ecological Regression)
The ecological regression below states that an increase in the mean of private schools has an increase in the mean of APR scores by 7.0996. This data continues to support the idea that private schools have higher APR scores than their public counterparts.
length(unique(apr1$SCHOOL_NAME))## [1] 385aprmean <- apr1 %>%
group_by(SCHOOL_NAME) %>%
summarise(m_score = mean(FOURYEAR_SCORE, na.rm=TRUE), m_schooltype = mean(SCHOOL_TYPE, na.rm = TRUE))
head(aprmean)## # A tibble: 6 x 3
## SCHOOL_NAME m_score m_schooltype
## <chr> <dbl> <dbl>
## 1 Abilene Christian University 978. 1
## 2 Alabama A&M University 956. 0
## 3 Alabama State University 950. 0
## 4 Alcorn State University 956. 0
## 5 American International College 993 1
## 6 American University 986. 1er <- lm(m_score ~ m_schooltype, data=aprmean)
summary(er)##
## Call:
## lm(formula = m_score ~ m_schooltype, data = aprmean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -79.983 -3.441 3.288 8.348 22.725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 974.2746 0.9141 1065.819 < 2e-16 ***
## m_schooltype 7.0996 1.5437 4.599 5.77e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.45 on 383 degrees of freedom
## Multiple R-squared: 0.05234, Adjusted R-squared: 0.04986
## F-statistic: 21.15 on 1 and 383 DF, p-value: 5.774e-06No Pooling Model
Private schools always have a significantly higher APR score than public schools.
dcoef <- apr1 %>%
group_by(SCHOOL_NAME) %>%
do(mod = lm(FOURYEAR_SCORE ~ SCHOOL_TYPE, data = .))
coef <- dcoef %>% do(data.frame(SCHOOL_TYPE = coef(.$mod)[1]))
ggplot(coef, aes(x = SCHOOL_TYPE)) + geom_histogram(fill = "#3366ff")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(coef, aes(x = SCHOOL_TYPE)) + geom_density(fill="#ffcc33")+xlab("APR Scores Across 385 Schools ")
#Finding the Slope There does not seem to be a significant difference between individual sports by public and private and their impact on APR scores.
dcoef <- apr1%>%
group_by(SPORT_NAME) %>%
do(mod = lm(FOURYEAR_SCORE ~ SCHOOL_TYPE, data = .))
coef <- dcoef %>% do(data.frame(SCHOOL_TYPE= coef(.$mod)[2.]))
ggplot(coef, aes(x = SCHOOL_TYPE)) + geom_histogram(fill="#34d000")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Random Intercept Model
According to this random intercept model, public schools had a standard deviation of 8.783339 and APR on average is 975.112. However, the standard deviation for private schools is 47.3848 and on average, they will score higher on APR than public schools by 6.1426.
random_i <- lme(FOURYEAR_SCORE ~ SCHOOL_TYPE, data = apr1, random = ~1|SCHOOL_NAME, method = "ML")
summary(random_i)## Linear mixed-effects model fit by maximum likelihood
## Data: apr1
## AIC BIC logLik
## 68900.87 68927.99 -34446.43
##
## Random effects:
## Formula: ~1 | SCHOOL_NAME
## (Intercept) Residual
## StdDev: 8.783339 47.3848
##
## Fixed effects: FOURYEAR_SCORE ~ SCHOOL_TYPE
## Value Std.Error DF t-value p-value
## (Intercept) 975.1120 0.9299801 6126 1048.5300 0e+00
## SCHOOL_TYPE 6.1426 1.5819439 383 3.8829 1e-04
## Correlation:
## (Intr)
## SCHOOL_TYPE -0.588
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -22.4330095 -0.1632614 0.1193379 0.2902233 1.1395799
##
## Number of Observations: 6511
## Number of Groups: 385Random Slope Model
random_s <- lme(FOURYEAR_SCORE ~ SCHOOL_TYPE, data = apr1, random = ~1|SCHOOL_NAME, method = "ML")
summary(random_s)## Linear mixed-effects model fit by maximum likelihood
## Data: apr1
## AIC BIC logLik
## 68900.87 68927.99 -34446.43
##
## Random effects:
## Formula: ~1 | SCHOOL_NAME
## (Intercept) Residual
## StdDev: 8.783339 47.3848
##
## Fixed effects: FOURYEAR_SCORE ~ SCHOOL_TYPE
## Value Std.Error DF t-value p-value
## (Intercept) 975.1120 0.9299801 6126 1048.5300 0e+00
## SCHOOL_TYPE 6.1426 1.5819439 383 3.8829 1e-04
## Correlation:
## (Intr)
## SCHOOL_TYPE -0.588
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -22.4330095 -0.1632614 0.1193379 0.2902233 1.1395799
##
## Number of Observations: 6511
## Number of Groups: 385Findings & Results
Private schools have significantly higher academic progress rates than public schools. These findings suggest that public schools may need more gudiance and programming on how to better motivate and train their athletes to do well both as an athlete and as an academic. Its extremely important to ensure that athletes have a solid educational background in case they do not go on a professional career track or are unable to grab attention of scouts for teams. There is no guarantee that an student athlete will have a successful sports career. College education should be giving them more opportunities in their careers and to improve their livelihood.