NYCFlightsDataModel
Arun Kumar
2019-10-02
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)
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)
mod2 <- lm(n ~ wday * term, data = daily)
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)
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)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)
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?
Jan 21: Martin Luther King Jr Day May 26: Trinity Sunday Sep 2: Labor day
Since every year the holidays will not be on the exact same day but will fall in a range. Hence we can assume that the drop in flights is due to passengers not travelling on the specific holiday or having already travelled for their holiday before and after the specific dates.
holiday <- c("0121", "0526", "0902")
years <- 2013:2019
map(years, ~ wday(ymd(paste0(.x, holiday, sep = "")), label = TRUE))## [[1]]
## [1] Mon Sun Mon
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[2]]
## [1] Tue Mon Tue
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[3]]
## [1] Wed Tue Wed
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[4]]
## [1] Thu Thu Fri
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[5]]
## [1] Sat Fri Sat
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[6]]
## [1] Sun Sat Sun
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < Sat
##
## [[7]]
## [1] Mon Sun Mon
## Levels: Sun < Mon < Tue < Wed < Thu < Fri < SatQuestion #2
What do the three days with high positive residuals represent? How would these days generalize to another year?
In Saturdays and Sundays, the model under estimates the number of flights. Since the specific days of week might varies for another year based on the test we did in question 1, Hence we need make sure that the variation is a weekend effect or a date effect.
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 fallQuestion #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”?
daily <-
flights %>%
mutate(date = make_date(year, month, day)) %>%
group_by(date) %>%
summarize(n = n()) %>%
mutate(wday = wday(date, label = TRUE))
mod <- lm(n ~ wday, data = daily)
daily <- add_residuals(daily, mod)
term <- function(date) {
cut(date,
breaks = ymd(20130101, 20130605, 20130825, 20140101),
labels = c("spring", "summer", "fall")
)
}
daily <-
daily %>%
mutate(term = term(date))
###
new_daily <-
daily %>%
mutate(wday = as.character(wday),
term_sat = ifelse(wday == "Sat", paste0(wday, "-", term), wday))
mod1 <- MASS::rlm(n ~ term_sat, data = new_daily)
new_daily %>%
add_residuals(mod1) %>%
ggplot(aes(date, resid)) +
geom_line()
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?
daily_holidays <-
new_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(new_term, term_sat, holidays)
mod2 <- lm(n ~ new_term, data = daily_holidays)
daily_holidays %>%
add_residuals(mod2) %>%
ggplot(aes(date, resid)) +
geom_line()
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?
Predictions are uncertain due to less observations owing to interaction term. The Outliers are high in this graph.
mod2 <- lm(n ~ wday * month(date), data = daily_holidays)
daily_holidays %>%
add_residuals(mod2) %>%
ggplot(aes(date, resid)) +
geom_line()
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?
The model is effective for the specific current year. However, this model will not be scalable for any other year since the Holidays mentioned will have varied dates for each year.
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.
week_relevel <- function(x) {
fct_relevel(x, "Sun", after = 7)
}
daily %>%
mutate(wday = week_relevel(wday)) %>%
ggplot(aes(wday, n)) +
geom_boxplot()