library(vinereg)
library(quantreg)
library(ggplot2)
library(dplyr)
library(purrr)
library(scales)
plot_marginal_effects <- function(covs, preds) {
cbind(covs, preds) %>%
tidyr::gather(alpha, prediction, -seq_len(NCOL(covs))) %>%
dplyr::mutate(prediction = as.numeric(prediction)) %>%
tidyr::gather(variable, value, -(alpha:prediction)) %>%
dplyr::mutate(value = as.numeric(value)) %>%
ggplot(aes(value, prediction, color = alpha)) +
geom_point(alpha = 0.15) +
geom_smooth(span = 0.5, se = FALSE) +
facet_wrap(~ variable, scale = "free_x") +
theme(legend.position = "none") +
theme(plot.margin = unit(c(0, 0, 0, 0), "mm")) +
xlab("")
}
bikedata <- read.csv("day.csv")
bikedata[, 2] <- as.Date(bikedata[, 2])
head(bikedata)
## instant dteday season yr mnth holiday weekday workingday weathersit
## 1 1 2011-01-01 1 0 1 0 6 0 2
## 2 2 2011-01-02 1 0 1 0 0 0 2
## 3 3 2011-01-03 1 0 1 0 1 1 1
## 4 4 2011-01-04 1 0 1 0 2 1 1
## 5 5 2011-01-05 1 0 1 0 3 1 1
## 6 6 2011-01-06 1 0 1 0 4 1 1
## temp atemp hum windspeed casual registered cnt
## 1 0.344167 0.363625 0.805833 0.1604460 331 654 985
## 2 0.363478 0.353739 0.696087 0.2485390 131 670 801
## 3 0.196364 0.189405 0.437273 0.2483090 120 1229 1349
## 4 0.200000 0.212122 0.590435 0.1602960 108 1454 1562
## 5 0.226957 0.229270 0.436957 0.1869000 82 1518 1600
## 6 0.204348 0.233209 0.518261 0.0895652 88 1518 1606
bikedata <- bikedata %>%
rename(
temperature = atemp,
month = mnth,
weathersituation = weathersit,
humidity = hum,
count = cnt
)
See variable description on UCI web page.
bikedata <- bikedata %>%
mutate(
temperature = 66 * temperature + 16,
windspeed = 67 * windspeed,
humidity = 100 * humidity
)
ggplot(bikedata, aes(dteday, count)) +
geom_line() +
scale_x_date(labels = scales::date_format("%b %y")) +
xlab("date") +
ylab("rental count") +
stat_smooth(method = "lm", se = FALSE, linetype = "dashed") +
theme(plot.title = element_text(lineheight = 0.8, face = "bold", size = 20)) +
theme(text = element_text(size = 18))
lm_trend <- lm(count ~ instant, data = bikedata)
trend <- predict(lm_trend)
bikedata <- mutate(bikedata, count = count / trend)
ggplot(bikedata, aes(dteday, count)) +
geom_line() +
scale_x_date(labels = scales::date_format("%b %y")) +
xlab("date") +
ylab("detrended rental count") +
theme(plot.title = element_text(lineheight = 0.8, face = "bold", size = 20)) +
theme(text = element_text(size = 18))
bikedata <- bikedata %>%
select(-instant, -dteday, -yr) %>% # time indices
select(-casual, -registered) %>% # casual + registered = count
select(-holiday) %>% # we use 'workingday' instead
select(-temp) # we use 'temperature' (feeling temperature)
ordereddisc_vars <- c("season", "month", "weekday", "workingday", "weathersituation")
bikedata <- bikedata %>%
mutate(weekday = ifelse(weekday == 0, 7, weekday)) %>% # sun at end of week
purrr::modify_at(disc_vars, as.ordered)
fit <- vinereg(
count ~ .,
data = bikedata,
family = c("onepar", "tll"),
selcrit = "aic"
)
fit
## D-vine regression model: count | temperature, humidity, windspeed, month, season, weathersituation, weekday, workingday
## nobs = 731, edf = 71.06, cll = 438.54, caic = -734.97, cbic = -408.5
summary(fit)
## var edf cll caic cbic
## 1 count 9.59683 -198.076002 415.34567 459.43747
## 2 temperature 21.96537 415.808987 -787.68724 -686.76925
## 3 humidity 17.92558 118.991497 -202.13184 -119.77432
## 4 windspeed 1.00000 22.861612 -43.72322 -39.12881
## 5 month 1.00000 12.460300 -22.92060 -18.32619
## 6 season 1.00000 14.230519 -26.46104 -21.86662
## 7 weathersituation 1.00000 12.499591 -22.99918 -18.40477
## 8 weekday 16.56942 29.790776 -26.44271 49.68404
## 9 workingday 1.00000 9.973117 -17.94623 -13.35182
## p_value
## 1 NA
## 2 1.067790e-161
## 3 2.034176e-40
## 4 1.361984e-11
## 5 5.974065e-07
## 6 9.560314e-08
## 7 5.735465e-07
## 8 9.172812e-07
## 9 7.965070e-06
alpha_vec <- c(0.1, 0.5, 0.9)
pred <- fitted(fit, alpha_vec)
plot_marginal_effects(
covs = select(bikedata, temperature),
preds = pred
)
plot_marginal_effects(covs = select(bikedata, humidity), preds = pred) +
xlim(c(25, 100))
plot_marginal_effects(covs = select(bikedata, windspeed), preds = pred)
month_labs <- c("Jan","", "Mar", "", "May", "", "Jul", "", "Sep", "", "Nov", "")
plot_marginal_effects(covs = select(bikedata, month), preds = pred) +
scale_x_discrete(limits = 1:12, labels = month_labs)
plot_marginal_effects(covs = select(bikedata, weathersituation),
preds = pred) +
scale_x_discrete(limits = 1:3,labels = c("good", "medium", "bad"))
weekday_labs <- c("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun")
plot_marginal_effects(covs = select(bikedata, weekday), preds = pred) +
scale_x_discrete(limits = 1:7, labels = weekday_labs)
plot_marginal_effects(covs = select(bikedata, workingday), preds = pred) +
scale_x_discrete(limits = 0:1, labels = c("no", "yes")) +
geom_smooth(method = "lm", se = FALSE) +
xlim(c(0, 1))
season_labs <- c("spring", "summer", "fall", "winter")
plot_marginal_effects(covs = select(bikedata, season), preds = pred) +
scale_x_discrete(limits = 1:4, labels = season_labs)
