Stat 414 – Day 22

Last Time – Pseudo R2 “The literature does not seem to have converged on this topic.” Comparison of total variation to null model Change in variance components when add variables

Day 20 handout What are the following 4 equations for na vs. mpqnem: Orch = 0, Large performance Orch = 1, Large performance Orch = 0, Smaller performance Orch = 1, Smaller performance

Multilevel Data (Table 2.2) Teachers Families Employees Teeth Children Animals Patients Measurements Respondents Suspects Schools Neighborhoods, States Firms Jawbones Families Litters Doctors, Hospitals Subjects Interviewees Judges

Other examples Level 1 Level 2 Yelp reviews Airbnb (prices) Voter (why voted for T) Year (financial aid) Year (corruption index) Year (happiness index) Restaurant Neighborhoods Census tract, State College Country

Common applications Multistage sample Growth models Random sample of clusters Random sample of individuals within each cluster Growth models Community health survey stratified by neighborhood California Cancer Registry within HMO

Typically Number of (level 2) groups is large Level 2 units are considered random sample of larger population (come from a distribution)

Possibilities? Level 1 Level 2 Movie theater Movie patron Free agent Revenue of Halloween Movie patron Movie rating Free agent Salary Playoff game Points scored Price bottle of wine City Number theaters, distances Theater College town Agent Years experience, # clients Year TV market Region

Possibilities? Level 1 Level 2 Olympic athletes Body fat percentages Finishing time Body fat percentages Movie revenue, rating Country (over time) Time – athlete – country Clinic Location, SES Genre, Year

Sports? JSM 2018: Hierarchical or multilevel models can play an important role in player evaluation in team sports. In American football, Yurko et al (2018) present a hierarchical model for estimating wins above replacement (WAR) for offensive skill positions, complete with a full treatment of uncertainty similar to that of Baumer et al (2015), but for football and using a drive-based resampling approach. In hockey, Thomas et al (2013) present a hierarchical competing process model for offensive and defensive player ratings. We discuss these two papers and their extensions, including how National Football League (NFL) teams can use this approach to calculate WAR for players of all positions, and how subsequent improvements can potentially be made in player evaluation and strategy at the NFL Draft. We present results on the 2017 NFL season and provide a definitive answer, once and for all, to the question: "Is Joe Flacco elite?"

Possibilities? IPEDS – education data Census.gov FDA clinical trials Data on individual schools but in different regions/counties/states Census.gov American Community Survey PUMS FDA clinical trials Repeated measures NCAA reference Randomly sample by college