ANLY 505 - NYCFlightsDataModel
Week 3
Qian Yao
2020-03-16
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?
# Jan 21 is Martin Luther King Jr. Day, May 26 is Trinity Sunday, and Sep 2 is the labor day, which indicate all 3 dates are around a holiday. However, it's hard to generalize into another year because they might end up into different days into another year, since the holiday is not on a fixed calendar date, it is based on the week number. 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# It means that the model is underestimating the number of flight for Saturdays and Sundays. Howerer,these specific dates in another year might be different like the previous question, so these days also can not generalize well to another year.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”?
daily_1 <-
daily %>%
mutate(wday = as.character(wday),
term_sat = ifelse(wday == "Sat", paste0(wday, "-", term), wday))
mod1 <- MASS::rlm(n ~ term_sat, data = daily_1)
daily_1 %>%
add_residuals(mod1) %>%
ggplot(aes(date, resid)) +
geom_line()
# The graph shows that both the Jan-March are underestimated and the outliers from summer and winter are obvious.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 <-
daily_1 %>%
mutate(holidays = case_when(date %in% ymd(c(20130101, # New Year's Day
20130121, # MLK
20130218, # President's Day
20130527, # Memorial Day
20130704, # July 4th
20130902, # Labor Day
20131028, # Columbus Day
20131111, # veterans Day
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()
#The residual and the model doesn't change too much on 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?
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)
mod4 <- lm(n~ wday * month, data = daily)
daily %>%
gather_residuals(mod4,mod2)%>%
arrange(date)%>%
ggplot(aes(date,resid,color = model))+
geom_line(alpha = 0.9)
# It is not helpful. The model changes by month has larger residuals than by date. There’s more outlier in this graph. This is becaue the interaction term leaves less observations in each cell, making the predictions less accurateQuestion #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 expect model should work for the specific year(this year). However, since the days various by each year, so it would not be particularly effective into generalizing to another 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()
##The boxplot indicates there’s no trend that people tend to do long distance night flights on Sundays. Saturday flights are the longest on average.