Instructions to Students

This assignment is designed to simulate a scenario where you are given a dataset, and taking over someone’s existing work, and continuing with it to draw some further insights. This aspect of it is similar to Assignment 1, but it will provide less scaffolding, and ask you to draw more insights, as well as do more communication.

Your previous submission of crime data was well received!

You’ve now been given a different next task to work on. Your colleague at your consulting firm, Amelia (in the text treatment below) has written some helpful hints throughout the assignment to help guide you.

Questions that are worth marks are indicated with “Q” at the start and end of the question, as well as the number of marks in parenthesis. For example

## Q1A some text (0.5 marks)

Is question one, part A, worth 0.5 marks

Marking + Grades

This assignment will be worth 10% of your total grade, and is marked out of 58 marks total.

9 Marks for grammar and clarity. You must write in complete sentences and do a spell check.
9 Marks for presentation of the data visualisations
40 marks for the questions
- Part 1: 7 Marks
- Park 2: 17 Marks
- Park 3: 16 Marks
Your marks will be weighted according to peer evaluation.

A Note on skills

As of week 6, you have seen most of the code for parts 1 - 2 that needs to be used here, and Week 7 will give you the skills to complete part 3. I do not expect you to know immediately what the code below does - this is a challenge for you! We will be covering skills on modelling in the next weeks, but this assignment is designed to simulate a real life work situation - this means that there are some things where you need to “learn on the job”. But the vast majority of the assignment will cover things that you will have seen in class, or the readings.

Remember, you can look up the help file for functions by typing ?function_name. For example, ?mean. Feel free to google questions you have about how to do other kinds of plots, and post on the ED if you have any questions about the assignment.

How to complete this assignment.

To complete the assignment you will need to fill in the blanks for function names, arguments, or other names. These sections are marked with *** or ___. At a minimum, your assignment should be able to be “knitted” using the knit button for your Rmarkdown document.

If you want to look at what the assignment looks like in progress, but you do not have valid R code in all the R code chunks, remember that you can set the chunk options to eval = FALSE like so:

```{r this-chunk-will-not-run, eval = FALSE}`r''`
ggplot()
```

If you do this, please remember to ensure that you remove this chunk option or set it to eval = TRUE when you submit the assignment, to ensure all your R code runs.

You will be completing this assignment in your assigned groups. A reminder regarding our recommendations for completing group assignments:

Each member of the group completes the entire assignment, as best they can.
Group members compare answers and combine it into one document for the final submission.

Your assignments will be peer reviewed, and results checked for reproducibility. This means:

25% of the assignment grade will come from peer evaluation.
Peer evaluation is an important learning tool.

Each student will be randomly assigned another team’s submission to provide feedback on three things:

Could you reproduce the analysis?
Did you learn something new from the other team’s approach?
What would you suggest to improve their work?

Due Date

This assignment is due in by 6pm on Wednesday 20th May. You will submit the assignment via ED. Please change the file name to include your teams name. For example, if you are team dplyr, your assignment file name could read: “assignment-2-2020-s1-team-dplyr.Rmd”

Treatment

You work as a data scientist in the well named consulting company, “Consulting for You”.

On your second day at the company, you impressed the team with your work on crime data. Your boss says to you:

Amelia has managed to find yet another treasure trove of data - get this: pedestrian count data in inner city Melbourne! Amelia is still in New Zealand, and now won’t be back now for a while. They discovered this dataset the afternoon before they left on holiday, and got started on doing some data analysis.

We’ve got a meeting coming up soon where we need to discuss some new directions for the company, and we want you to tell us about this dataset and what we can do with it.

Most Importantly, can you get this to me by Wednesday 20th May, COB (COB = Close of Business at 6pm).

I’ve given this dataset to some of the other new hire data scientists as well, you’ll all be working as a team on this dataset. I’d like you to all try and work on the questions separately, and then combine your answers together to provide the best results.

From here, you are handed a USB stick. You load this into your computer, and you see a folder called “melbourne-walk”. In it is a folder called “data-raw”, and an Rmarkdown file. It contains the start of a data analysis. Your job is to explore the data and answer the questions in the document.

Note that the text that is written was originally written by Amelia, and you need to make sure that their name is kept up top, and to pay attention to what they have to say in the document!

Overview

The City of Melbourne has sensors set up in strategic locations across the inner city to keep hourly tallies of pedestrians. The data is updated on a monthly basis and available for download from Melbourne Open Data Portal. The rwalkr package provides an API in R to easily access sensor counts and geographic locations.

There are three parts to this work:

Data wrangling and data visualisation of the pedestrian data
Joining data together weather data
Performing preliminary modelling

Part 1: Data wrangling and data visualisation of the pedestrian data

Amelia: I’ve downloaded a map chunk of Melbourne. Can you take the map I made, and plot the location of the sensors on top of it? We want to be able to see all of the sensors, but we also want to create different shapes for the following sensors:

“Southern Cross Station”
“Melbourne Central”
“Flinders Street Station Underpass”
“Birrarung Marr”

First we download the data on the pedestrian sensor locations around Melbourne.

And now we draw a plot on a map tile of the pedestrian sensor locations

Q1A Tell me what this map shows us? (0.5 Mark)

!> Answer: This map specifies the locations where all the metro stations are in the City of Melbourne. are labelled as triangle while rest of the stations are labelled as blue dots.

Q1B Create a markdown table of the number of sensors installed each year (0.5 Mark)

ped_loc %>% 
  # calculate the year from the date information
  mutate(year = year(installation_date)) %>%
  # count up the number of sensors
  count(year) %>%
  # then use `kable()` to create a markdown table
  kable()

year	n
2009	13
2013	12
2014	2
2015	7
2016	1
2017	9
2018	5
2019	6
2020	4

Additionally, how many sensors were added in 2016, and in 2017?

!> Answer: There were 1 and 9 sensors newly installed in 2016 and 2017, respectively.

Q1C Filter the data down to just look at the selected four sensors (1 mark)

We would like you to focus on the foot traffic at 4 sensors:

“Southern Cross Station”
“Melbourne Central”
“Flinders Street Station Underpass”
“Birrarung Marr”

Your task is to:

Extract the data for the year 2018 from Jan 1 to April 30 using rwalkr (you might want to cache this so it doesn’t run every time you knit)
Filter the data down to include only the four sensors above, note that you could do this directly with rwalkr
add variables that contain the day of the month, month, year, and day in the year.

walk_2018 <- walk_2018 %>% 
  # Filter the data down to include only the four sensors above
  filter(Sensor %in% selected_sensors) %>%
# now add four columns, containing month day, month, year, and day of the year
  # using functions from lubridate.
  mutate(mday = mday(Date),
         mon = month(Date),
         year = year(Date),
         yday = yday(Date))

Now we can plot the pedestrian count information for January - April in 2018

ggplot(walk_2018,
       aes(x = Date_Time, 
           y = Count)) +
  geom_line(size = 0.3) +
  facet_grid(Sensor ~ ., 
             # this code presents the facets ina  nice way
             labeller = labeller(Sensor = label_wrap_gen(20))) +
  # this code mades the x axis a bit nicer to read
  scale_x_datetime(date_labels = "%d %b %Y", 
                   date_minor_breaks = "1 month") +
  labs(x = "Date Time")

We can see that there are quite different patterns in each of the sensors. Let’s explore this further.

Q1D How many types of activities might this capture at the four selected places? (0.5 marks)

!> Answer: Three types of activities are captured. Flinders Street Station Underpass and Southern Cross Station have similar type of activities. Melbourne Central and Birrarung Marr have unique types.

Q1E Create a plot of the counts of each sensor over the day (2 Marks)

We’re primarily interested in exploiting pedestrian patterns at various time resolutions and across different locations. In light of people’s daily schedules, let’s plot the counts against time of day for each sensor.

ggplot(walk_2018,
       aes(x = Time,
           y = Count,
           group = yday,
           colour = Sensor)) +
  geom_line() +
  facet_wrap(~Sensor ,
             labeller = labeller(Sensor = label_wrap_gen(20))) +
  scale_colour_brewer(palette = "Dark2",
                      name = "Sensor") +
  theme(legend.position = "none")

Write a short paragraph that describe what the plot shows:

What is plotted on the graph? What does each line represent?
Is the data in these sensors similar, or different?
Does each panel show the same trend within it, or is there variation?
What do you learn?

!> Answer: This plot shows the type of daily activities in the four selected stations. Each line represent activity in each day. Flinders Street Station Underpass and Southern Cross Station have similar type of activities. They both have two peaks at same times during a day. And they both have big variations. Melbourne Central has similar trends each day and does not have big variation. Birrarung Marr has similar trend every day with only a few outliers.

The lines with peaks in Flinders Street Station Underpass must stand for weekdays. The rest of the lines should be public holiday and weekends. Melbourne Central is where people go shopping and sightseeing, thus, the count starts to increase after 10am when most of the stores open. Birrarung Marr locates at the corner of the city; not many people would go there except some special events are nearby.

Q1F Exploring non work days (2 marks)

Use the data inside the hols_2018 data to identify weekdays and weekends, and holidays.

hols_2018 <- tsibble::holiday_aus(year = 2018, state = "VIC")

walk_2018_hols <- walk_2018 %>% 
  mutate(weekday = wday(Date, label = TRUE, week_start = 1),
         workday = if_else(
           condition = Date %in% hols_2018$date |weekday %in% c("Sat", "Sun"),
           true = "holiday",
           false = "yes"
           ))

Now create a plot to compare the workdays to the non workdays.

ggplot(walk_2018_hols,
       aes(x= Time, y = Count, group = yday, color = Sensor)) +
  geom_line(size = 0.3,
            alpha = 0.3) +
  facet_grid(workday ~ Sensor,
             labeller = labeller(Sensor = label_wrap_gen(20))) +
  scale_colour_brewer(palette = "Dark2", name = "Sensor") +
  theme(legend.position = "none")

Write a short paragraph that describe what the plot shows, and helps us answer these questions:

What is plotted on the graph? What does each line represent?
How are the data in these sensors similar or different?
Does each panel show the same trend within it, or is there variation?
What do you learn?

!> Answer: This plot specifies pedestrian movement during each day in four selected stations. Each line represents each day between 2018-Jan-01 and 2018-Apr-30.

Flinders Street Station and Southern Cross Station are important transfer stations because the peaks are at the rush hours. People barely go to Southern Cross Station in holiday because there is no scenic spots nearby. Unlike Southern Cross Station, Flinder Street Station is a landmark of the City of Melbourne, thus, there are still many people in holiday going here in holidays.
Birrarung Marr is at the vicinity of a park. People usually go there in holidays. That is why pedestrian movements of holidays in this station are more than those of working days.
There is no big variation in the pedestrian movements in Melbourne Central. The reason may be there are many shopping centres, so people go there mostly for shopping and entertainment, so there won’t be peak flow at a certain point in time. At the same time, it can be seen that there will be more people on weekends than on working days.

Q1G Calendar plot (0.5 mark)

To locate those unusual moments, Flinders Street Station data is calendarised on the canvas, using the sugrrants package. We can spot the unusual weekday patterns on public holidays using their color. Using the calendar plot, try to spot another unusual pattern, do a google search to try to explain the change in foot traffic. (Hint: Look at the plot carefully, does a particular day show a different daily pattern? Is there a specific event or festival happening on that day?)

# filter to just look at flinders st station
flinders <- walk_2018_hols %>% filter(Sensor =="Flinders Street Station Underpass")

flinders_cal <- flinders %>% 
  frame_calendar(x = Time, y = Count, date = Date)
gg_cal <- flinders_cal %>% 
  ggplot(aes(x = .Time, y = .Count, colour = workday, group = Date)) +
  geom_line()
prettify(gg_cal) +
  theme(legend.position = "bottom")

!> Answer: On 17-Feb-2018 and 18-Feb-2018, angry taxi drivers gathered outside Melbourne’s Flinders Street station [source: ABC news] (https://www.abc.net.au/news/2018-02-17/angry-taxi-drivers-gather-outside-melbournes/9458046?nw=0), people nearby must have opt to take trains because they couldn’t take taxi or Uber. This was the main reason of unusual pattern of pedestrian movements for that weekend.

Part Two: Combining data sources

Q2A Extract the pedestrian count data for 2020 from the Jan 1 to April 30, can you add that to the data? (2 marks)

You’ll need to ensure that you follow the steps we did earlier to filter the data and add the holiday information.

walk_2020 <- walk_2020 %>% 
  filter(Sensor %in% selected_sensors)  %>% 
# now add four using `mutate` columns which contain the day of the month, month, and year, and day of the year using functions from lubridate.
  mutate(mday = mday(Date),
         mon = month(Date),
         year = year(Date),
         yday = yday(Date))

Now add the holiday data

# also the steps for adding in the holiday info
hols_2020 <- tsibble::holiday_aus(year = 2020, state = "VIC")

walk_2020_hols <- walk_2020 %>% 
  mutate(weekday = wday(Date, label = TRUE, week_start = 1),
         workday = if_else(
           condition = Date %in% hols_2020$date | weekday %in% c("Sat", "Sun"),
           true = "holiday",
           false = "yes"
           ))

melb_walk_hols <- bind_rows(walk_2018_hols, walk_2020_hols)

Q2B There is some repetition in the code above from previous, describe two (or more) ways to limit that repetition, and demonstrate the use of this as a function (1 Mark)

filter_sensor <- function(data, sensors){
  data %>% filter(Sensor %in% selected_sensors)
}

add_day_info <- function(data){
# now add four using `mutate` columns which contain the day of the month, month, and year, and day of the year using functions from lubridate.
  data %>% 
  mutate(mday = mday(Date),
         mon = month(Date),
         year = year(Date),
         yday = yday(Date))
}

add_working_day <- function(data){
  
  walk_years <- unique(data$year)
  
  hols <- tsibble::holiday_aus(year = walk_years, state = "VIC")
  
  data %>% 
    mutate(weekday = wday(Date, label = TRUE, week_start = 1),
           workday = if_else(
            condition = Date %in% hols$date | weekday %in% c("Sat", "Sun"),
            true = "holiday",
            false = "yes"
             ))
}

# Step one, combine the walking data
bind_rows(walk_2018, walk_2020) %>%
  # Step two, filter the sensors
  filter_sensor(Sensor %in% selected_sensors) %>%
  # step three, add the info on day of the year, month, etc
  add_day_info() %>%
  # strep four, add info on working days.
  add_working_day()

## # A tibble: 23,136 x 11
##    Sensor Date_Time           Date        Time Count  mday   mon  year  yday
##    <chr>  <dttm>              <date>     <int> <int> <int> <dbl> <dbl> <dbl>
##  1 Melbo~ 2018-01-01 00:00:00 2018-01-01     0  2996     1     1  2018     1
##  2 Flind~ 2018-01-01 00:00:00 2018-01-01     0  3443     1     1  2018     1
##  3 Birra~ 2018-01-01 00:00:00 2018-01-01     0  1828     1     1  2018     1
##  4 South~ 2018-01-01 00:00:00 2018-01-01     0  1411     1     1  2018     1
##  5 Melbo~ 2018-01-01 01:00:00 2018-01-01     1  3481     1     1  2018     1
##  6 Flind~ 2018-01-01 01:00:00 2018-01-01     1  3579     1     1  2018     1
##  7 Birra~ 2018-01-01 01:00:00 2018-01-01     1  1143     1     1  2018     1
##  8 South~ 2018-01-01 01:00:00 2018-01-01     1   436     1     1  2018     1
##  9 Melbo~ 2018-01-01 02:00:00 2018-01-01     2  1721     1     1  2018     1
## 10 Flind~ 2018-01-01 02:00:00 2018-01-01     2  3157     1     1  2018     1
## # ... with 23,126 more rows, and 2 more variables: weekday <ord>, workday <chr>

Q2C For Flinders st, in the month of April, can you compare 2018 to 2020? (2 Marks)

Write a paragraph that describe what you learn from these plots. Can you describe any similarities, and differences amongst the plots, and why they might be similar or different? (You might need to play with the plot output size to clearly see the pattern)

melb_walk_hols_flinders_april <- melb_walk_hols %>%
  filter(Sensor == "Flinders Street Station Underpass",
         mon == "4")

ggplot(melb_walk_hols_flinders_april,
       aes(x = Time, y = Count, group = yday,
           colour = as.factor(year))) +
  geom_line() +
  facet_wrap(~ mday, ncol = 5) +
  theme(legend.position = "bottom") +
  labs(colour = "Year")

!> Answer: In 2018, as mentioned before, the pattern of weekdays is similar, comparing to the lines on weekends are relatively smooth. For example, April 7, 2018 was Saturday, so its pattern is a smooth curve, while April 9 was Monday, so its pattern has small peaks.

In 2020, due to COVID-19, most people stay at home, thus, the pedestrian movement level is low in April.

In 12th April 2018, the broken line specifies the sensor stopped working for a few hours.

Q2D Produce a similar plot (to 2C) that will also allow us to contrast the patterns across the four sensors. (2 marks)

What do you learn? Which Sensors seem the most similar? Or the most different?

melb_walk_hols_april <- melb_walk_hols %>%  filter(mon == "4")

ggplot(melb_walk_hols_april,
       aes(x = Time, 
           y = Count, 
           group = yday,
           colour = as.factor(year))) +
  geom_line() +
  facet_grid(Sensor~weekday) +
  theme(legend.position = "bottom") +
  labs(colour = "Year")

!> Answer: In 2020, due to COVID-19, all stations have similar patterns, which shows that few people take trains.

The sensors of Melbourne Central seem the most similar, because the plot depicts similar pettern from Monday to Friday. From Monday to Friday, Flinders Street Station and Southern Cross Station have similar patterns; but on weekends, they have different patterns. Birrarung Marr has different patterns every day.

It can be explained from this plot that Flinders Street Station and Southern Cross Station are transfer stations that people usually pass in working days.Unlike Southern Cross Station, Flinders Street Station can also attract tourists on weekends. What’s more, as there are several shopping centres near Melbourne Central, people go there every day for shopping and working. And that’s why its pattern doesn’t differ significantly on weekends or weekdays.

Combining weather data with pedestrian counts

One question we want to answer is: “Does the weather make a difference to the number of people walking out?”

Time of day and day of week are the predominant driving force of the number of pedestrian, depicted in the previous data plots. Apart from these temporal factors, the weather condition could possibly affect how many people are walking in the city. In particular, people are likely to stay indoors, when the day is too hot or too cold, or raining hard.

Daily meteorological data as a separate source, available on National Climatic Data Center, is used and joined to the main pedestrian data table using common dates.

Binary variables are created to serve as the tipping points

We have pulled information on weather stations for the Melbourne area - can you combine it together into one dataset?

Q2E Read in and add flagging variables to the weather data (2 marks)

high_prcp if prcp > 5 (if yes, “rain”, if no, “none”)
high_temp if tmax > 33 (if yes, “hot”, if no, “not”)
low_temp if tmin < 6 (if yes, “cold”, if no, “not”)

# Now create some flag variables 
melb_weather_2018 <- read_csv(
  here::here("data-raw/melb_ncdc_2018.csv")
  ) %>% 
  mutate(
  high_prcp = if_else(condition = prcp > 5,
                          true = "rain",
                          false = "none"),
    high_temp = if_else(condition = tmax > 33,
                        true = "hot",
                        false = "not"),
    low_temp = if_else(condition = tmin < 6,
                       true = "cold",
                       false = "not")
  )

Q2F summarise the pedestrian count data and join it to the weather data (2 marks)

The weather data is per day, and the pedestrian count data is every hour. One way to explore this data is to collapse the pedestrian count data down to the total daily counts, so we can compare the total number of people each day to the weather for each day. This means each row is the total number of counts at each sensor, for each day.

Depending on how you do this, you will likely need to merge the pedestrian count data back with the weather data. Remember that we want to look at the data for 2018 only

melb_daily_walk_2018 <- melb_walk_hols %>%
  filter(year == "2018") %>%
  group_by(Sensor, Date) %>%
  summarise(Count = mean(Count)) %>%
  ungroup()

melb_daily_walk_weather_2018 <- melb_daily_walk_2018 %>%
  left_join(melb_weather_2018, by = c("Date"="date"))

melb_daily_walk_weather_2018

## # A tibble: 480 x 10
##    Sensor Date       Count station  tmax  tmin  prcp high_prcp high_temp
##    <chr>  <date>     <dbl> <chr>   <dbl> <dbl> <dbl> <chr>     <chr>    
##  1 Birra~ 2018-01-01 349.  ASN000~  26.2  14       0 none      not      
##  2 Birra~ 2018-01-02 410.  ASN000~  23.6  15.5     0 none      not      
##  3 Birra~ 2018-01-03  NA   ASN000~  22.3  11.2     0 none      not      
##  4 Birra~ 2018-01-04  NA   ASN000~  25.5  11.5     0 none      not      
##  5 Birra~ 2018-01-05  43.8 ASN000~  30.5  12.2     0 none      not      
##  6 Birra~ 2018-01-06 278   ASN000~  41.5  16.6     0 none      hot      
##  7 Birra~ 2018-01-07  65.3 ASN000~  22    15.7     0 none      not      
##  8 Birra~ 2018-01-08 258.  ASN000~  23.6  15.9     0 none      not      
##  9 Birra~ 2018-01-09 350.  ASN000~  22.8  13.9     0 none      not      
## 10 Birra~ 2018-01-10 508.  ASN000~  25.5  12.1     0 none      not      
## # ... with 470 more rows, and 1 more variable: low_temp <chr>

Q2H Exploring sensor count against weather flagging variables (4 marks)

Create a few plots that look at the spread of the daily totals for each of the sensors, according to the weather flagging variables (high_prcp, high_temp, and low_temp). Write a paragraph that tells us what you learn from these plots, how you think weather might be impacting how people go outside. Make sure to discuss the strengths and limitations of the plots summarised like this, what assumption do they make?

# Plot of count for each sensor against high rain
ggplot(melb_daily_walk_weather_2018,
       aes(y = Count,
           x = Sensor,
           colour = high_prcp)) +
  geom_boxplot() +
  theme(legend.position = "bottom")+
  labs(color = "Rain")

# Plot against high temperature
ggplot(melb_daily_walk_weather_2018,
       aes(y = Count,
           x = Sensor,
           colour = high_temp)) +
  geom_boxplot()+
  theme(legend.position = "bottom")+
  labs(color = "High temp")

# Plot of low temperature
ggplot(melb_daily_walk_weather_2018,
       aes(y = Count,
           x = Sensor,
           colour = low_temp)) +
  geom_boxplot()+
  theme(legend.position = "bottom")+
  labs(color = "Low temp")

!> Answer: People prefer to take trains in normal whether. If the day was rainy, hot or cold, people are reluctant to take trains.

Q2F Combine the weather data with the pedestrian count data (2 marks)

The visualisations tell us something interesting about the data, but to really understand the data, we need to perform some modelling. To do this, you need to combine the weather data with the pedestrian data. We have provided the weather data for 2018 and 2020, combine with the pedestrian data for 2018 and 2020.

melb_weather_2018 <- read_csv(here::here("data-raw/melb_ncdc_2018.csv"))
melb_weather_2020 <- read_csv(here::here("data-raw/melb_ncdc_2020.csv"))

# task: combine the weather data together into an object, `melb_weather`
melb_weather <- bind_rows(melb_weather_2018,
                          melb_weather_2020) %>%
# remember to add info about high precipitation, high temperature, + low temps
  mutate(
  high_prcp = if_else(condition = prcp > 5,
                          true = "rain",
                          false = "none"),
    high_temp = if_else(condition = tmax > 33,
                        true = "hot",
                        false = "not"),
    low_temp = if_else(condition = tmin < 6,
                       true = "cold",
                       false = "not")
  )

# now combine this weather data with the walking data
melb_walk_weather <- melb_walk_hols %>% 
  left_join(melb_weather, by = c("Date"="date"))

Part 3: Modelling Count data

We have been able to start answering the question, “Does the weather make a difference to the number of people walking out?” by looking at a few exploratory plots. However, we want to get a bit more definitive answer by performing some statistical modelling.

We are going to process the data somewhat so we can fit a linear model to the data. First, let’s take a set relevant variables to be factors. This ensures that the linear model interprets them appropriately.

We also add one to count and then take the natural log of it. The reasons for this are a bit complex, but essentially a linear model is not the most ideal model to fit for this data, and we can help it be more ideal by taking the log of the counts, which helps stabilise the residuals (predictions - observed) when we fit the model.

melb_walk_weather_prep_lm <- melb_walk_weather %>% 
  mutate_at(.vars = vars(Sensor, 
                         Time,
                         mon,
                         year,
                         workday,
                         high_prcp,
                         high_temp,
                         low_temp),
            as_factor) %>% 
  mutate(log_count = log1p(Count))

Q3A: Fit a linear model (1 mark)

Now we fit a linear model, predicting logCount using Time, Month, weekday and the weather flag variables (high_prcp, high_temp, and low_temp)

walk_fit_lm <- lm (
  formula = log_count ~ Time + mon + weekday + high_prcp + high_temp + low_temp,
  data = melb_walk_weather_prep_lm
)

Q3B: Evaluate the model fit statistics (1 mark)

Provide some summary statistics on how well this model fits the data? What do you see? What statistics tell us about our model fit?

glance(walk_fit_lm)

## # A tibble: 1 x 11
##   r.squared adj.r.squared sigma statistic p.value    df  logLik    AIC    BIC
##       <dbl>         <dbl> <dbl>     <dbl>   <dbl> <int>   <dbl>  <dbl>  <dbl>
## 1     0.524         0.524  1.21      669.       0    36 -34259. 68592. 68887.
## # ... with 2 more variables: deviance <dbl>, df.residual <int>

!> Answer: \(R^2\) is 0.524, which means only 52.4% of variation in log_count that is explained by the linear model. This turns out to be not a very ideal model.

Q3C: Look at the model predictions (1 mark)

We have had one look at the model fit statistics, but let’s now look at the fitted and observed (log_count) values, for each sensor:

peds_aug_lm <- augment(walk_fit_lm, data = melb_walk_weather_prep_lm)

ggplot(peds_aug_lm,
       aes(y = log_count,
       x = .fitted)) +
  geom_point(alpha = 0.2) +
  facet_wrap(~Sensor)

There is actually a lot of variation. Looking at this, you might assume that the model does a bad job of fitting the residuals. However, we must remember that there is an inherent time structure to the data. A better way to explore this is to look directly at the temporal components. We can do this directly with a calendar plot.

Q3D: Arrange the data so we can examine predictions (1 Mark)

Before we can get the data into the right format for analysis, we need to pivot the data into a longer format, so that we have columns of Date, Time, Count, Model, and log_count.

flinders_lm <- peds_aug_lm %>% 
  # filter the data to only look at flinder st
  filter(Sensor == "Flinders Street Station Underpass") %>%
  # Select the Date, Time, Count, .fitted, and log_count
  select(Date, Time, Count, .fitted, log_count) %>%
  # Now pivot the log count and fitted columns into a column called "model"
  # data so we have columns of Date, Time, Count, Model, 
  # and log_count. 
  pivot_longer(c(".fitted","log_count"), names_to = "model",values_to = "log_count") %>%
  # Now we're going to undo the intiial data transformation
  mutate(Count = expm1(log_count))

Q3F: Plot the observed and fitted values in a calendar plot (3 Marks)

flinders_lm_cal <- flinders_lm %>% 
# Let's just look at 2020 to make it a bit easier
  filter(year(Date) == "2020") %>% 
  frame_calendar(x = Time, y = Count, date = Date)

gg_cal <- ggplot(flinders_lm_cal) +
  # Part of the interface to overlaying multiple lines in a calendar plot
  # is drawing two separate `geom_line`s -
  # See https://pkg.earo.me/sugrrants/articles/frame-calendar.html#use-in-conjunction-with-group_by
  # for details
  geom_line(data = filter(flinders_lm_cal,  model == ".fitted"),
         aes(x = .Time, 
             y = .Count, 
             colour = model, 
             group = Date)) +  
  geom_line(data = filter(flinders_lm_cal, model == "log_count"),
         aes(x = .Time, 
             y = .Count, 
             colour = model, 
             group = Date)) 

prettify(gg_cal) + theme(legend.position = "bottom")

Write a paragraph answering these questions:

What do you see in the difference between the fitted and the observed (log_count)?
What is a difference between 2020 and 2018?
Is there a difference across sensors?
What other variables might you consider adding to the model, and why?

!> Answer: It can be seen that nearly half of daily log_count data is not fitting the predicted data.

Compared to Birrarung Marr, other three stations have relatively lower variance. We are considering to add tmax, tmin, prcp and sensor into the model because they may be the variables into which passengers may take consideration.

Q3G: Fit one more (or more!) models to explore and compare (2 marks)

What sort of improvements do you think you could make to the model? Fit two more models, Try adding more variables to the linear model.

walk_fit_lm_Sensor <- lm(log_count ~  Time + mon + weekday + high_prcp + high_temp + low_temp + Sensor + workday + prcp + tmin + tmax,
                           data = melb_walk_weather_prep_lm)

walk_fit_lm_year <- lm(log_count ~ Time + mon + weekday + high_prcp + high_temp + low_temp + Sensor + workday + prcp + tmin + tmax + year,
                           data = melb_walk_weather_prep_lm)

Why did you add those variables?

!> Answer: The reason for adding those variables is that they may be the variables which passengers may take into consideration.

Q3H Compare the model fit statistics (2 marks)

bind_rows(
  first = glance(walk_fit_lm),
  sensor = glance(walk_fit_lm_Sensor),
  year = glance(walk_fit_lm_year),
  .id = "type"
)

## # A tibble: 3 x 12
##   type  r.squared adj.r.squared sigma statistic p.value    df  logLik    AIC
##   <chr>     <dbl>         <dbl> <dbl>     <dbl>   <dbl> <int>   <dbl>  <dbl>
## 1 first     0.524         0.524 1.21       669.       0    36 -34259. 68592.
## 2 sens~     0.697         0.696 0.970     1159.       0    43 -29487. 59062.
## 3 year      0.722         0.722 0.928     1283.       0    44 -28542. 57175.
## # ... with 3 more variables: BIC <dbl>, deviance <dbl>, df.residual <int>

Which model does the best? Why do you think that is? What statistics are you basing this decision off?

!> Answer:

The highest \(R^2\) is 0.722, which means 72.2% of variation in log_count that is explained by the linear model year. This is deemed to be an ideal model.

Q3I Recreate the same calendar plot for your best model and explore the model fit. (2 Marks)

(Suggestion - Perhaps write this as a function to speed up comparison)

peds_aug_lm_sensor_fit <- augment(walk_fit_lm_year, melb_walk_weather_prep_lm)

pivot_sensor <- function(lm_fit, sensor = "Flinders Street Station Underpass"){
  lm_fit %>% 
  filter(Sensor == sensor) %>%
  select(Date, Time, Count, .fitted, log_count) %>%
  pivot_longer(c(".fitted","log_count"), 
               names_to = "model",
               values_to = "log_count") %>%
  mutate(Count = expm1(log_count))
}

calendar_fit_obs <- function(lm_fit_aug){
  
  data_cal <- lm_fit_aug %>% 
    frame_calendar(x = Time, y = Count, date = Date)

gg_cal <-
  ggplot(data_cal) +
  geom_line(data = filter(data_cal, model == ".fitted"),
         aes(x = .Time, 
             y = .Count, 
             colour = model, 
             group = Date)) +
  geom_line(data = filter(data_cal, model == "log_count"),
         aes(x = .Time, 
             y = .Count, 
             colour = model, 
             group = Date))

prettify(gg_cal) + theme(legend.position = "bottom")

}

pivot_sensor(peds_aug_lm_sensor_fit) %>%
filter(year(Date) == "2020") %>%
  calendar_fit_obs()

What do you see? How does it compare to the previous model?

!> Answer:

There are more fits than the previous model. And thus, this supports our viewpoint which figures out that the year model is the best in this case.

Q3J Compare model residuals against the fit (3 marks)

Compare the fitted against the residuals, perhaps write a function to help you do this in a more readable way.

walk_fit_lm_fit <- augment(walk_fit_lm, data = melb_walk_weather_prep_lm)
walk_fit_lm_fit_Sensor <- augment(walk_fit_lm_Sensor, data = melb_walk_weather_prep_lm)
walk_fit_lm_fit_year <- augment(walk_fit_lm_year, data = melb_walk_weather_prep_lm)

plot_fit_resid <- function(data){
  ggplot(data,
         aes(x = .fitted,
             y = .resid)) +
  geom_point(alpha = 0.2) +
  facet_wrap(~Sensor)
}

plot_fit_resid(walk_fit_lm_fit)

plot_fit_resid(walk_fit_lm_fit_Sensor)

plot_fit_resid(walk_fit_lm_fit_year)

We’ve looked at all these models, now pick your best one, and compare the predicted values against the actual observed values. What do you see? Is the model good? Is it bad? Do you have any thoughts on why it is good or bad?

!> Answer:

This is a good model. As we all know, the closer the residuals approaches to zero, the more arrurate the fitted model is. And looking into te figure above, it’s obvious that the residuals is scattered around the line parallel to the x-axis with a value of 0, so this is a good model.

References

Make sure to reference all of the R packages that you used here, along with any links or blog posts that you used to help you answer these questions

The following packages are used in this report:

broom
ggmap
knitr
lubridate
rwalkr
sugrrants
timeDate
tsibble
here
readr
tidyverse

Extra code

This code below here is what was used to retrieve the data in the data-raw folder.

# melb_bbox <- c(min(ped_loc$longitude) - .001,
#                min(ped_loc$latitude) - 0.001,
#                max(ped_loc$longitude) + .001,
#                max(ped_loc$latitude) + 0.001)
# 
# melb_map <- get_map(location = melb_bbox, source = "osm")
# write_rds(melb_map,
#           path = here::here("2020/assignment-2/data-raw/melb-map.rds"),
#           compress = "xz")

# code to download the stations around the airport and the weather times
# this is purely here so you can see how we downloaded this data
# it is not needed for you to complete the assignment, so it is commented out
# melb_stns <- read_table(
#   file = "https://www1.ncdc.noaa.gov/pub/data/ghcn/daily/ghcnd-stations.txt",
#   col_names = c("ID",
#                 "lat",
#                 "lon",
#                 "elev",
#                 "state",
#                 "name",
#                 "v1",
#                 "v2",
#                 "v3"),
#   skip = 353,
#   n_max = 17081
#   ) %>%
#   filter(state == "MELBOURNE AIRPORT")
# # 
# get_ncdc <- function(year){
#   vroom::vroom(
#     glue::glue(
#       "https://www1.ncdc.noaa.gov/pub/data/ghcn/daily/by_year/{year}.csv.gz"
#     ),
#     col_names = FALSE,
#     col_select = 1:4
#     )
# }
# 
# clean_ncdc <- function(x){
#   x %>%
#   filter(X1 == melb_stns$ID, X3 %in% c("PRCP", "TMAX", "TMIN")) %>%
#   rename_all(~ c("station", "date", "variable", "value")) %>%
#   mutate(date = ymd(date), value = value / 10) %>%
#   pivot_wider(names_from = variable, values_from = value) %>%
#   rename_all(tolower)
#   }

# ncdc_2018 <- get_ncdc(2018)
# melb_ncdc_2018 <- clean_ncdc(ncdc_2018)
# write_csv(melb_ncdc_2018,
#           path = here::here("2020/assignment-2/data-raw/melb_ncdc_2018.csv"))
# 
# ncdc_2020 <- get_ncdc(2020)
# beepr::beep(sound = 4)
# melb_ncdc_2020 <- clean_ncdc(ncdc_2020)
# beepr::beep(sound = 4)
# write_csv(melb_ncdc_2020,
#           path = here::here("2020/assignment-2/data-raw/melb_ncdc_2020.csv"))

ETC5510 Assignment 2

Siddhant Tirodkar, Yiwen Zhang, Aryan Jain, Yuheng Cui

19/05/2020

Instructions to Students

Marking + Grades

A Note on skills

How to complete this assignment.

Due Date

Treatment

Overview

Part 1: Data wrangling and data visualisation of the pedestrian data

Q1A Tell me what this map shows us? (0.5 Mark)

Q1B Create a markdown table of the number of sensors installed each year (0.5 Mark)

Q1C Filter the data down to just look at the selected four sensors (1 mark)

Q1D How many types of activities might this capture at the four selected places? (0.5 marks)

Q1E Create a plot of the counts of each sensor over the day (2 Marks)

Q1F Exploring non work days (2 marks)

Q1G Calendar plot (0.5 mark)

Part Two: Combining data sources

Q2A Extract the pedestrian count data for 2020 from the Jan 1 to April 30, can you add that to the data? (2 marks)

Q2B There is some repetition in the code above from previous, describe two (or more) ways to limit that repetition, and demonstrate the use of this as a function (1 Mark)

Q2C For Flinders st, in the month of April, can you compare 2018 to 2020? (2 Marks)

Q2D Produce a similar plot (to 2C) that will also allow us to contrast the patterns across the four sensors. (2 marks)

Q2E Read in and add flagging variables to the weather data (2 marks)

Q2F summarise the pedestrian count data and join it to the weather data (2 marks)

Q2H Exploring sensor count against weather flagging variables (4 marks)

Q2F Combine the weather data with the pedestrian count data (2 marks)

Part 3: Modelling Count data

Q3A: Fit a linear model (1 mark)

Q3B: Evaluate the model fit statistics (1 mark)

Q3C: Look at the model predictions (1 mark)

Q3D: Arrange the data so we can examine predictions (1 Mark)

Q3F: Plot the observed and fitted values in a calendar plot (3 Marks)

Q3G: Fit one more (or more!) models to explore and compare (2 marks)

Q3H Compare the model fit statistics (2 marks)

Q3I Recreate the same calendar plot for your best model and explore the model fit. (2 Marks)

Q3J Compare model residuals against the fit (3 marks)

References

Extra code