Final Project

Lucy D’Agostino McGowan

The data

  • Data was obtained from IPEDS
  • Includes:
    • US 4 year public or not-for-profit private institions that are degree-granting, primarily baccalaureate or above with between 1,000-9,999 students (N = 1,002)
    • 157 observations were dropped due to missing data, leaving N = 845 observations in the final data set

Application Exercise

  1. Copy the following template into RStudio Pro:
https://github.com/sta-112-f22/final-project.git

  1. Open the file labeled data-exploration.qmd

  2. Read in the data set into an object called dat

  3. Examine the data, how many observations are there? How many variables? Add the description to your file.

  4. Examine the data dictionary by opening the file called data-dictionary.csv

  5. Find the outcome variable (the retention rate) and your variable of interest specific to your group. Create a plot to visualize the relationship between these variables. Add a description to your file

  6. Does the data look like it needs a transformation? If so, apply one and examine the plot again. Describe this in your file.

08:00

Examine the distribution of the other variables

We can build a table to examine the distribution of our variables.

library(gtsummary)
mtcars %>%
  tbl_summary()
Characteristic N = 321
mpg 19.2 (15.4, 22.8)
cyl
4 11 (34%)
6 7 (22%)
8 14 (44%)
disp 196 (121, 326)
hp 123 (96, 180)
drat 3.70 (3.08, 3.92)
wt 3.33 (2.58, 3.61)
qsec 17.71 (16.89, 18.90)
vs 14 (44%)
am 13 (41%)
gear
3 15 (47%)
4 12 (38%)
5 5 (16%)
carb
1 7 (22%)
2 10 (31%)
3 3 (9.4%)
4 10 (31%)
6 1 (3.1%)
8 1 (3.1%)
1 Median (IQR); n (%)

Application Exercise

  1. In the Console in RStudio Pro run:
install.packages("gtsummary")
  1. Edit the code in the table-one chunk to examine a Table of your variables. Move your variable of interest to the top of the list so that it is the first rendered in the table.
03:00

Building your causal framework

The ggdag package can help us display our causal assumptions you drew last week. There are three steps:

  1. Write out the models (like the ones you are submitting in homework 2) in a function called dagify
  2. Pass this to the ggdag function to plot them
  3. Pass this to the ggdag_adjustment_set function to determine what you need to add to your final model.

ggdag

library(ggdag)

dag <- dagify(
  exposure ~ variable1 + variable2 + variable3 + variable4,
  outcome ~ exposure + variable1,
  variable1 ~ variable3,
  variable2 ~ variable3
)

ggdag

library(ggdag)

dag <- dagify(
  exposure ~ variable1 + variable2 + variable3 + variable4,
  outcome ~ exposure + variable1,
  variable1 ~ variable3,
  variable2 ~ variable3,
  exposure = "exposure",
  outcome = "outcome",
  latent = "variable3",
  labels = c(variable1 = "Variable 1",
             variable2 = "Variable 2",
             variable3 = "Variable 3",
             variable4 = "Variable 4",
             exposure = "Exposure",
             outcome = "Outcome")
)

ggdag

dag %>%
  ggdag()
Code 
dag %>%
  tidy_dagitty() %>%
  node_status() %>%
  ggplot(
    aes(x, y, xend = xend, yend = yend, color = status)
  ) +
  geom_dag_edges() +
  geom_dag_point() +
  geom_dag_label_repel() +
  scale_color_okabe_ito(na.value = "grey90") +
  theme_dag() +
  theme(legend.position = "none") +
  coord_cartesian(clip = "off")

ggdag

dag %>%
  ggdag_adjustment_set(text_col = "black")

Final model

lm(outcome ~ exposure + variable1)

🎉

Application Exercise

  1. Open the data-dictionary.csv file and map the available variables to the names in the equations you developed for homework 2.
  2. Rewrite the formulas using these equations; if something is not available in this dataset, you can make up a variable name for it
  3. Open causal-assumptions.qmd
  4. Add your equations to the dagify code chunk after deleting the # add your equations here comment. Make sure to separate each equation with a comma
  5. Update the “exposure” with your variable of interest
  6. Run the ggdag chunk to create the causal diagram
  7. Run the adjustment_set chunk to see what variables you need to adjust for
  8. Write out your final model based on this adjustment set
20:00

Loose ends

  1. Click the blue, down arrow in the Git Panel on the top right to pull in new data. Raise your hand if this doesn’t work.
  2. Open data-exploration.qmd Render the document. Do you see a figure of your variable on the x-axis and the outcome on the y-axis? If not, create that figure and re-render the document
  3. Is all of the example text “filled in” in data-exploration.qmd? If not, fill it in.
  4. Open causal-assumptions.qmd Render the document. Do you see two figures, one with the Causal Diagram and one showing the adjustment set? If not, be sure that you have set eval: true in all of the chunks Note: if you are getting an error, raise your hand so I can come help out
05:00

Application Exercise

  1. Open data-dictionary.csv and examine the available variables. Are there any that you didn’t include in your causal diagram that maybe should be included? Add them now
  2. Pair up with another group and present your causal diagram. Exchange thoughts on what other variables might be important to include. Add them now

Pairs:

  • student services – endowment
  • percent admitted – total cost
  • student/faculty ratio – average instructor salary
  1. Re-render your causal-assumptions.qmd file with these changes and observe your final adjustment set.
20:00

Putting it all together

  • Ultimately, we are interested in the effect of changing your variable of interest on first-year retention rates.
  • After fitting your final model, extract the coefficient and confidence interval for this effect. Consider adjusting the effect to be on a “useful” scale (for example rather than dollars, perhaps $1,000 is easier to interpret)
  • Based on the evidence presented decide whether you think Wake Forest should invest in changing your variable of interest in order to increase first-year retention
  • Report a predicted change in retention based on a change in your variable for a school with Wake Forest’s same characteristics

Application Exercise

  1. Open final-model.qmd
  2. Fit your final model – be sure to use any transformations that you determined in your first step and include all variables determined necessary by your “adjustment set” analysis
  3. Check the assumptions for linear regression – were they met?
  4. Extract the coefficient and 95% confidence interval for your effect of interest – is this significantly related to first-year retention?
  5. Give a one sentence recommendation to Wake Forest based on what you have found.
20:00

Application Exercise

  1. Open the sensitivity-data.qmd file. This is a sensitivity analysis for including athletic data and US News Ranking data
  2. Read in the athletics_dat. How many observations are there? Fill in the explanation with this number.
  3. Refit your “final model” adding in the bball_power_rating. Does this change your result? Add an explanation of what you see.
  4. Read in the usnews_dat. How many observations are there? Fill in the explanation with this number.
  5. Refit your “final model” adding in the usnews_ranking. Does this change your result? Add an explanation of what you see.
10:00

Application Exercise

Let’s put this all together!

  1. Open index.qmd
  2. Write one or two sentences describing your recommendation to Wake Forest University based on your findings. This can include information from your sensitivity analysis.
  3. Render the document. Click on all of the links on the top, make sure they are rendered as well.
10:00

Dr. Lucy D’Agostino McGowan