ANLY 505 - NYCFlightsDataModel
Week 3
Karoli Sakwa
2020-03-17
Summarize Data
daily <- flights %>%
mutate(date = make_date(year, month, day)) %>%
group_by(date) %>%
summarize(n = n())
ggplot(daily, aes(date, n)) +
geom_line()
Investigate Daily-Weekly Pattern
daily <- daily %>%
mutate(wday = wday(date, label = TRUE))
ggplot(daily, aes(wday,n)) +
geom_boxplot()
mod = lm(n ~ wday, data = daily, na.action = na.warn)
grid <- daily %>%
data_grid(wday) %>%
add_predictions(mod, "n")
ggplot(daily, aes(wday, n)) +
geom_boxplot() +
geom_point(data = grid, color = "orange", size = 4)
Investigate residuals
daily <- daily %>%
add_residuals(mod)
daily %>%
ggplot(aes(date, resid)) +
geom_ref_line(h = 0) +
geom_line()
ggplot(daily, aes(date, resid, color = wday)) +
geom_ref_line(h = 0, colour = "red") +
geom_line()
daily %>%
filter(resid < -100)## # A tibble: 11 x 4
## date n wday resid
## <date> <int> <ord> <dbl>
## 1 2013-01-01 842 Tue -109.
## 2 2013-01-20 786 Sun -105.
## 3 2013-05-26 729 Sun -162.
## 4 2013-07-04 737 Thu -229.
## 5 2013-07-05 822 Fri -145.
## 6 2013-09-01 718 Sun -173.
## 7 2013-11-28 634 Thu -332.
## 8 2013-11-29 661 Fri -306.
## 9 2013-12-24 761 Tue -190.
## 10 2013-12-25 719 Wed -244.
## 11 2013-12-31 776 Tue -175.daily %>%
ggplot(aes(date, resid)) +
geom_ref_line(h = 0, colour = "red", size = 1) +
geom_line(color = "grey50") +
geom_smooth(se = FALSE, span = 0.20)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Seasonal Saturday effect
daily %>%
filter(wday == "Sat") %>%
ggplot(aes(date, n)) +
geom_point()+
geom_line() +
scale_x_date(
NULL,
date_breaks = "1 month",
date_labels = "%b"
)
Add Seasonal Variable
term <- function(date) {
cut(date,
breaks = ymd(20130101, 20130605, 20130825, 20140101),
labels = c("spring", "summer", "fall")
)
}
daily <- daily %>%
mutate(term = term(date))
daily %>%
filter(wday == "Sat") %>%
ggplot(aes(date, n, color = term)) +
geom_point(alpha = 1/3)+
geom_line() +
scale_x_date(
NULL,
date_breaks = "1 month",
date_labels = "%b"
)
daily %>%
ggplot(aes(wday, n, color = term)) +
geom_boxplot()
mod1 <- lm(n ~ wday, data = daily, na.action = na.warn)
mod2 <- lm(n ~ wday * term, data = daily, na.action = na.warn)
daily %>%
gather_residuals(without_term = mod1, with_term = mod2) %>%
ggplot(aes(date, resid, color = model)) +
geom_line(alpha = 0.75)
grid <- daily %>%
data_grid(wday, term) %>%
add_predictions(mod2, "n")
ggplot(daily, aes(wday, n)) +
geom_boxplot() +
geom_point(data = grid, color = "red") +
facet_wrap(~ term)
Better model for outliers (Robust regression)
mod3 <- MASS::rlm(n ~ wday * term, data = daily, na.action = na.warn)
daily %>%
add_residuals(mod3, "resid") %>%
ggplot(aes(date, resid)) +
geom_hline(yintercept = 0, size = 2, color = "red") +
geom_line()
Computed Variables
# If you are creating variables it might be a good idea to bundle the creation of the variables up into a function
compute_vars <- function(data) {
data %>%
mutate(term = term(date),
wday = wday(date, label = TRUE)
)
}
# Another option would be to put the transformations directly in the model formula:
wday2 <- function(x) wday(x, label = TRUE)
mod3 <- lm(n ~ wday2(date) * term(date), data = daily, na.action = na.warn)Time of Year: An Alternative Approach
# We could use a more flexible model to capture the pattern of school term in the data
library(splines)
mod <- MASS::rlm(n ~ wday * ns(date, 5), data = daily, na.action = na.warn)
daily %>%
data_grid(wday, date = seq_range(date, n = 13)) %>%
add_predictions(mod) %>%
ggplot(aes(date, pred, color = wday)) +
geom_line() +
geom_point()
# We see a strong pattern in the numbers of Sat flights. This is reassuring, because we also saw that pattern in the raw data. It's a good sign when you get the same signal from different approaches.Question #1
Why are there fewer than expected flights on January 20, May 26 and September 1? (Hint: they all have the same explanation.) How would these days generalize into another year?
## This can be attributed to the fact that these days fall on before or after holidays. The holidays date vary from year to year.Question #2
What do the three days with high positive residuals represent? How would these days generalize to another year?
# Use this chunk to answer question 2
daily %>%
top_n(3, resid)## # A tibble: 3 x 5
## date n wday resid term
## <date> <int> <ord> <dbl> <fct>
## 1 2013-11-30 857 Sat 112. fall
## 2 2013-12-01 987 Sun 95.5 fall
## 3 2013-12-28 814 Sat 69.4 fall##This model is likely to underestimate the number of flight for Saturdays and Sundays. To make a generalisation we nmust factor that the dates vary yearly.Question #3
Create a new variable that splits the “wday” variable into terms, but only for Saturdays, i.e., it should have Thurs, Fri, but Sat-summer, Sat-spring, Sat-fall. How does this model compare with the model with every combination of “wday” and “term”?
# Use this chunk to answer question 3
daily <- daily %>%
mutate(term = term(date)) %>%
mutate(term2 = ifelse(wday == 'Sat',paste0(wday,"-",term),as.character(term) ))
mod3<- lm(n~ wday * term2, data = daily)
daily %>%
gather_residuals(mod3,mod2)%>%
arrange(date)%>%
ggplot(aes(date,resid,color = model))+
geom_line(alpha = 0.75)## Warning in predict.lm(model, data): prediction from a rank-deficient fit may be
## misleading
##The prediction result is did not change.Question #4
Create a new “wday” variable that combines the day of week, term(for Saturdays), and public holidays. What do the residuals of the model look like?
# Use this chunk to answer question 4
daily_holidays <-
daily %>%
mutate(holidays = case_when(date %in% ymd(c(20130101, # new years
20130121, # mlk
20130218, # presidents
20130527, # memorial
20130704, # independence
20130902, # labor
20131028, # columbus
20131111, # veterans
20131128, # thanksgiving
20131225)) ~ "holiday",
TRUE ~ "None")) %>%
unite(term, term2, holidays)
mod4 <- lm(n ~ term, data = daily_holidays)
daily_holidays %>%
add_residuals(mod4) %>%
ggplot(aes(date, resid)) +
geom_line()
##The residual and the model doesn't shows liitle variability from the unexplained variation.Question #5
What happens if you fit a day-of-week effect that varies by month (i.e.m n ~ wday*month)? Why is this not very helpful?
# Use this chunk to answer question 5
daily <- flights %>%
mutate(date = make_date(year, month, day)) %>%
group_by(date,month) %>%
summarise(n = n())
daily <- daily %>%
mutate(wday = wday(date, label = TRUE)) %>%
mutate(term = term(date))
mod2 <- lm(n ~ wday * term, data = daily)
mod5 <- lm(n~ wday * month, data = daily)
daily %>%
gather_residuals(mod5,mod2)%>%
arrange(date)%>%
ggplot(aes(date,resid,color = model))+
geom_line(alpha = 0.75)
##It is not effective because it is reducing the number of observations per bucket and increases the possibility of having outliers.Question #6
What would you expect the model n ~ wday + ns(date,5) to look like? Knowing what you know about the data, why would you expect it not to be particularly effective?
# Use this chunk to answer question 6
mod5 <- lm(n ~ wday + splines::ns(date, 5), data = daily)
daily %>%
gather_residuals(mod2,mod5)%>%
arrange(date)%>%
ggplot(aes(date,resid,color = model))+
geom_line(alpha = 0.75)
## The model would have significant residual errors because the days are not consistant in different years.Question #7
We hypothesized that people leaving on Sundays are more likely to be business travelers who need to be somewhere on Monday. Explore the hypothesis by seeing how if breaks down based on distance and time: if it’s true, you’d expect to see more Sunday evening flights to places that are far away.
# Use this chunk to answer question 7
week_relevel <- function(x) {
fct_relevel(x, "Sun", after = 7) # after 7 means night flights.
}
daily %>%
mutate(wday = week_relevel(wday)) %>%
ggplot(aes(wday, n)) + ggtitle("Sunday Night Flights") +
geom_boxplot()
##The boxplot shows no trend of preference to long distance night flights on Sundays.