Section 1
1.
536 children from Steubenville, Ohio were studied to understand the relationship between
maternal smoking and whether or not the child wheezed. The children participated in
the study for four years, from age 7 through age 10. At each age, children were assessed
to determine whether or not they wheezed and the researcher recorded whether or not
the child’s mother smoked.
Response Variable: Whether or not a child wheezes
What Type of Model: GLMM with a binomial response since each child is measured multiple times over 4 years.
What variable(s) would define the fixed effect(s): Age and mother's smoking status
What variable(s) would define the random effect(s): each child would receive a random effect
Describe the structure of the random effects if there is more than one random effect per observation: Longitudinal
2.
An experiment was conducted to determine the effect of recipe and baking temperature
on chocolate cake quality. Fifteen batches of cake mix for each recipe were prepared.
Each batch produced 6 cakes. Each of the six cakes was baked at a different temperature
(175, 185, 195, 205, 215, 225 degrees F), which was randomly assigned. Twenty taste
testers sampled each cake and rated it from 0 to 100 (0 is horrible, 100 is amazing). Each
taste tester sampled a single cake.
Response Variable: Rating
What Type of Model: GLMM w/ Poisson Response
What variable(s) would define the fixed effect(s): temperature, recipe
What variable(s) would define the random effect(s): batch, cake
Describe the structure of the random effects if there is more than one random effect per observation: The first level is the recipe, then each batch is nested w/in the recipe, then each cake is nested (repeated 6 times w/ a different treatment on each) w/in the batch, and the taste testers are nested (repeated 20 times) within the cakes.
3.
Pizza Hut is interested in the ounces of cheese on a large cheese pizza. Each pizza worker
is asked to produce ten large cheese pizzas. The number of ounces of cheese on each
pizza is then weighed. Assume that each pizza is constructed by a single worker and each
worker works at a single Pizza Hut. The Pizza Hut statisticians believe some workers
tend to be more generous with the cheese. The Pizza Hut statisticians also believe that
workers at the same store may influence each other and therefore produce similar pizzas.
Response Variable: ounces of cheese on a large cheese pizza
What Type of Model: LMM
What variable(s) would define the fixed effect(s): how much cheese you are ~supposed~ to put on the pizza... Grand Mean Model + two random effects
What variable(s) would define the random effect(s): worker, store location
Describe the structure of the random effects if there is more than one random effect per observation: the workers are nested in each location (spatial) and the pizzas are nested by each worker (repeated 10 times)
Section 2
4.
lmer(Time~Week+(1|Runner)+(1|Team))
5.
lmer(Score~CoachID + (1|AdvancedID))