30 Assignment 4

Assignment 4 is be completed individually or with a partner (i.e., the maximum group size is two). Please submit the assignment as a single pdf or html file (one file per individual/group). Save the file as Yourlastname_Assignment4 (e.g., Hefley_Assignment4). Make sure to show your work in R to ensure that I can reproduce your results (e.g., figures, calculations, etc). Upload your complete answers to problems 1-5 to Canvas before 11:59 pm on Thursday 10/22/20.

30.1 Motivation

The purpose of this assignment is to give you practical experience with the analysis of spatio-temporal data. One common type of spatio-temporal data is trajectories. Trajectorie data are collected by recording the time and location (in two or three dimensions) of an object.

Since the discontinuation of selective avaiblitility in 2000, accurate trajectories have become easy and cheap to collect to due to the ubiquitous access to global positioning systems (GPS). As such, this assignment will used trajectory data collected from a GPS.

Although trajectory data is widely available in large quantities, turning these data into usable information to make inference and decisions in challenging. This is because trajectory data is a relatively new type of spatio-temporal data.

30.2 Data

Listed below are multiple trajectory data set you can use for this assignment. Please select one source of trajectory data for this assignment.

Most smartphones or smartwatches have onboard GPS. Typically these devices can be used with or without an app to collect trajectory data. The trajectory data can then be extracted from your smartphone or smartwatch as a .gpx file, which can be loaded in program R (see R code in lecture notes from Oct. 8). For this assignment, you may collect your own trajectory data set using your smartphone or smartwatch. If you choose to do this, be creative and have fun! Also, if you do not know how to use your smartphone or smartwatch to record your position and obtain a .gpx file, please spend a significant amount of time trying to figure out how to do it on your own before contacting me for help. Chances are, unless you have the exact same devices as me, that I won’t know exactly how to do it either and will have to also teach myself.
In 2019, two residents of two of Manhattan, KS, Joe Moore and Chirs Melgares qualified for the Olympic Trials in the marathon. The Olympic trials were held on January 22, 2020 in Atlanta. Chris Melgares finished 33rd with a time of 2 hours 16 min and 59 seconds. Chris Melgares has graciously shared his trajectory data from this event, which can be accessed with the R code below.

library(rgdal)
url <- "https://www.dropbox.com/s/ak8gwm9sl1xikas/Olympic_trials.gpx?dl=1"
# ogrListLayers(url) # See name of layers are included in gpx file
pt.marathon <- readOGR(url, "track_points")

# Change date/time to class 'POSIXct'
pt.marathon$time <- ymd_hms(pt.marathon$time, "%Y-%m-%d %H:%M:%S", tz = "America/Chicago")
# Drop all extra variables
pt.marathon <- pt.marathon[, 5]

3.Konza Prairie Biological Station is a long-term ecological research site located close to Manhattan, KS. Trajectory data were collected on 31 bison at this area resulting in 431,734 locations. More information about this data set is available at this website and the data set can be downloaded here. If you choose to use this data set, please use the data for only a single bison (i.e., use data for only a single unique Bison_ID).

4.You may have access to trajectory data that is closer to you’re area of study. If you have access to trajectory data and would like to use if for this assignment, please do so.

30.3 Goal

You will conduct a statistical analysis of the trajectory data of your choice. The goal of the analysis has three components. The first goal is to make predictions that show the location of the object, animal, or person at any given time between when the first location was recorded and when the last location was recorded. The second goal is to forecast where the object will be at some time point after the last location was recorded. The third goal is to uncover an interesting feature about the movement of the object, animal, or person (e.g., maximum velocity, maximum distance covered in one day. etc). All estimates, prediction, forecasts, and derived quantities must contain uncertainty quantification.

30.4 Problems

Please write 5-10 sentences describing the data. To help you understand your data you may want to plot your data in Google Earth Pro by using R to make a .kml file (see Oct. 8 lecture notes). Doing this may help you visualize and identify the measurement error (i.e., that your recorded location is different than your true location)
Determine the statistical approach that you will use to meet the three goals of the study. Please use words and mathematical notation to explain the exact model you have chosen to use. Make sure to define all relevant mathematical symbols.
Choose a time/date that you have no recorded location but that is between the time/date when the first location was recorded and the the last location. Using the statistical approach you chose from question 2, predict the location of the object, animal, or person at this time that you do not have data for. Please make sure to quantify the uncertainty associated with any estimated quantity.
Chose a time/date that is after the last recorded location. Using the statistical approach you chose from question 2, forecast the location of the object, animal, or person at this time. Please make sure to quantify the uncertainty associated with any estimated quantity.
Using the statistical approach you chose from question 2, define and then estimate an interesting feature. For example, if I collected trajectory data on myself using my smartphone, I might want to estimate my maximum velocity.