POLS 503, Spring 2016: Assignment 1

Due: Thurs, April 14, 16:30 PDT.

Instructions

1. Fork this repository to your GitHub account.
2. Write your solutions in R Markdown in a file named solutions.Rmd.
3. When you are ready to submit your assignment, initiate a pull request. Title your pull request "Submission".

To update your fork from the upstream repository:

1. On your fork, e.g. https://github.com/jrnold/Assignment_01 click on "New Pull reqest"
2. Set your fork jrnold/Assignment_01 as the base fork on the left, and UW-POLS503/Assignment_01 as the head fork on the right. In both cases the branch will be master. This means, compare any chanes in the head fork that are not in the base fork. You will see differences between the US-POLS503 repo and your fork. Click on "Create Pull Request", and if there are no issues, "Click Merge" A quick way is to use this link, but change the jrnold to your own username: https://github.com/jrnold/Assignment_01/compare/master...UW-POLS503:master.

Problem 1: Data Wrangling and Viz Refresher

The file democracy.csv contains data from Przeworski et. al, Demoracy and Deveolpment: Political Institutions and Well-Being in the Worlds, 1950-1990 ¹. The data have been slightly recoded, to make higher values indicate higher levels of political liberty and democracy.

Variable	Description
COUNTRY	numerical code for each country
CTYNAME	name of each country
REGION	name of region containing country
YEAR	year of observation
GDPW	GDP per capita in real international prices
EDT	average years of education
ELF60	ethnolinguistic fractionalization
MOSLEM	percentage of Muslims in country
CATH	percentage of Catholics in country
OIL	whether oil accounts for 50+% of exports
STRA	count of recent regime transitions
NEWC	whether county was created after 1945
BRITCOL	whether country was a British colony
POLLIB	degree of political liberty (1--7 scale, rising in political liberty)
CIVLIB	degree of civil liberties (1--7 scale, rising in civil liberties)
REG	presence of democracy (0=non-democracy, 1=democracy)

For these questions use ggplot2 for plotting, and dplyr and tidyr for the data manipulation.

a. Load the democracy data frame

democracy <- read.csv(file = "democracy.csv", stringsAsFactors = FALSE)

When you run this, you will notice that POLLIB and CIVLIB, which should be integer variables with values 1--7, are character variables. There is a problem with how read.csv reads missing values. Figure out how this dataset indicates missing values, and add the correct argument to read.csv to fix this problem.

b. Create a data frame with statistics (minimum, mean, sd, and maximum) for all variables but COUNTRY, CTYNAME, REGION, and YEAR. Instead of doing this with summary, use dplyr and tidyr as shown in this example.

dem_summary_stats <-
  ... %>% 
  group_by(...) %>%
  summarize(...) %>%
  gather(...) %>%
  ungroup(...) %>%
  unite(...) %>%
  spread

Print this table using the function `kable` in the **knitr** package, an the code chunk option `results='asis`. See the [R Markdown Help](http://rmarkdown.rstudio.com/authoring_rcodechunks.html).

d. Create a histogram for political liberties in which each unique value of the variable is in its own bin.

e. Create a histogram for GDP per capita.

f. Create a histogram for log GDP per capita. How is this histogram different than the one for GDP per capita when it was not logged.

g. Plot political liberties against GDP per capita. If you use a scatterplot, there will be overlap. Figure out a way to plot these two variables so that the pattern (if any) between them is clear. There could be multiple ways to do this, and not necessarily a scatterplot.

i. Plot political liberties against log GDP per capita, using the same method as the previous question. How is the relationship different than when GDP per capita was not logged?

j. Create a boxplot of GDP per capita for oil producing and non-oil producing nations. Use ggplot2. This should be one plot, not two separate plots.

k. Calculate the mean GDP per capita in countries with at least 40 percent Catholics. How does it compare to mean GDP per capita for all countries? Remember to check the units of Catholic.

l. Calculate the average GDP per capita in countries with greater than 60% ethnolinguistic fractionalization, less than 60%, and missing ethnolinguistic fractionalization. Hint: you can calculate this with the dplyr verbs: mutate, group_by and summarize.

m. For all years, calculate the median average years of education. Return this as a data-frame. Hint: use dplyr functions: group_by, filter, summarize. Plot the median of the years of education for all years using a line. Also show the original data.

o. Repeat the previous question but group by both year and democracy. Plot separate lines for democracies and non-democries and the original data. Use color to differentiate democracies and non-democracies.

n. Which country was (or countries were) closest to the median years of education in 1985 among all countries? Hint: use dplyr functions: filter, mutate, arrange, and slice.

q. What were the 25th and 75th percentiles of ethnolinguistic fractionalization for new and old countries? Return this as a data frame with columns NEWC, ELF60_p25, and ELF60_p75. Print it as a nicely formatted table with kable.

Problem 2: Plotting data and regressions

This question will use a dataset included with R

data("anscombe")

The dataset consists of 4 seperate datasets each with an $x$ and $y$ variable.² The original dataset is not a tidy dataset. The following code creates a tidy dataset of the anscombe data that is easier to analyze than the

library("dplyr")
library("tidyr")
anscombe2 <- anscombe %>%
	mutate(obs = row_number()) %>%
	gather(variable_dataset, value, - obs) %>%
	separate(variable_dataset, c("variable", "dataset"), sep = 1L) %>%
	spread(variable, value) %>%
	arrange(dataset, obs)

a. For each dataset: calculate the mean and standard deviations of x and y, and correlation between x and y, and run a linear regression between x and y for each dataset. How similar do you think that these datasets will look?

b. Create a scatter plot of each dataset and its linear regression fit. Hint: you can do this easily with facet_wrap.

Problem 3: Predicting Sprint Times

In a 2004 paper in Nature, Tatem et al. estimate the trend lines of sprint times for men and women using the winning times of the 100-meters in the Olympics.³ They report that using current trends, in the 2156 Olympics, the women's 100-meter will have a faster time.⁴

The dataset includes the winning times from the 100-meter dash for both men and women for all Olympics 1900-2012 and Track & Field World Championships finals 1976-2015.

Variable	Description
year	Year of the Olympics or World Championships
time	Winning time
women	1 if women's race; 0 if men's race
olympics	1 if in the olympics; 0 if in the World Championships

Load the data into R from the csv file:

sprinters <- read.csv("sprinters.csv")

a. The referenced paper only used data from the Olympics 2004 and before. Create a new dataset named sprinters_orig with only those observations.

sprinters_orig <-
  filter(sprinters,
         year <= 2004,
         olympics == 1)

b. Run the regressions

library("dplyr")
mod1 <- lm(time ~ year + women, data = sprinters_orig)
mod2 <- lm(time ~ year * women, data = sprinters_orig)
mod3 <- lm(time ~ year, data = filter(sprinters_orig, women == 1))
mod4 <- lm(time ~ year, data = filter(sprinters_orig, women == 0))

Interpret each regression. How are they similar or different in their slopes? Plot each of these using the texreg package.

library("texreg")
htmlreg(list(mod1, mod2, mod3, mod4), stars = numeric(),
        caption = "Trends in Winning Times in the Olympic 100-meter dash, 1896-2004")

Trends in Winning Times in the Olympic 100-meter dash, 1896-2004

	Model 1	Model 2	Model 3	Model 4
(Intercept)	34.96	31.83	44.35	31.83
	(1.96)	(2.13)	(4.28)	(1.68)
year	-0.01	-0.01	-0.02	-0.01
	(0.00)	(0.00)	(0.00)	(0.00)
women	1.09	12.52
	(0.06)	(4.08)
year:women		-0.01
		(0.00)
R2	0.91	0.93	0.79	0.88
Adj. R2	0.91	0.92	0.78	0.88
Num. obs.	42	42	18	24
RMSE	0.19	0.17	0.21	0.13

c. Plot the fitted values of the first regression (mod1) against the original values. The function augment in the broom package is useful for this. See examples here or here for examples.

Extra Credit: Do the same not only for one but for all four regressions. Create a new datasets with 3 variables (actual, fitted, and model) containing the information from all the models. Then, use ggplot and the facet_wrap to create the 4 plots (2 by 2) in only 1 command.

d. Use the function predict to predict the times of men and women in the 2156 Olympics. Is this plausible?

e. Calculate the square root of the mean of the squared residuals (root mean squared error or RMSE) for the regression time ~ year * women. Predict the values for the years after 2004 for both Olympics and World Championships. What are the root mean squared residuals for these predictions? Is it surprising that the RMSE for the predictions out of the sample are lower than those in the sample?

Footnotes

1. Przeworski, Adam, Michael E. Alvarez, Jose Antonio Cheibub, and Fernando Limongi. 2000. Democracy and Development: Political Institutions and Well-Being in the World, 1950-1990. Cambridge University Press. ↩

2. These data are from: Anscombe, F. J. (1973). "Graphs in Statistical Analysis". American Statistician 27 (1): 17–21. ↩

3. Andrew J. Tatem, Carlos A. Guerra, Peter M. Atkinson & Simon I. Hay. 2004. "Athletics: Momentous sprint at the 2156 Olympics?" Nature. https://dx.doi.org/10.1038/431525 ↩

4. I've read the short article several times. I still can't tell whether it is tongue in cheek. ↩