Homework 4

Data

data<-read.csv("data_assignment5.csv")

Models - One Exposure (one row per student)

Random Intercept Only

\[\hat{y}\sim\log(\beta_{0j}+\beta_{2} Treatement_{1i}+\beta_2 PriorAccuracy_{2j}+e_ij)\] \[\beta_0 = \gamma_{00} + \gamma_{02} ProblemDifficulty_{j} + \mu_{0i} \] I’m not sure that the Problem Difficulty is in the right place.

glmer code

# m1 <- glmer(
#   next_problem_correctness_complete ~
#       treatment +
#         prior_accuracy + 
#         problem_avg_accuracy +
#   (1|problem_id) ,
#   data = data,
#   family = binomial)
# summary(m1)

Note that problem_avg_accuracy is a measure of problem difficulty.

STAN CODE

data {
  
}

parameters {
  
}

transformed parameters {
  
}


model {
 
}

Random Intercept and Random Effect Treatment

\[\hat{y}\sim\log(\beta_{0j}+\beta_{2} Treatement_{1i}+\beta_2 PriorAccuracy_{2j}+e_ij)\] \[\beta_0 = \gamma_{00} + \gamma_{02} ProblemDifficulty_{j} + \mu_{0i} \] \[\beta_1 = \gamma_{10} + \mu_{1i} \]

glmer code

# m1 <- glmer(
#   next_problem_correctness_complete ~
#       treatment +
#         prior_accuracy + 
#         problem_avg_accuracy +
#   (1+treatment|problem_id) ,
#   data = data,
#   family = binomial)
# summary(m1)

Note that problem_avg_accuracy is a measure of problem difficulty.

STAN CODE

data {
  
}

parameters {
  
}

transformed parameters {
  
}


model {
 
}

Random Intercept and Random Effect Treatment with cross Level Interaction

\[\hat{y}\sim\log(\beta_{0j}+\beta_{2} Treatement_{1i}+\beta_2 PriorAccuracy_{2j}+e_ij)\] \[\beta_0 = \gamma_{00} + \gamma_{02} ProblemDifficulty_{j} + \mu_{0i} \] \[\beta_1 = \gamma_{10} + \gamma_{12} ProblemDifficulty_{j} + \mu_{1i} \]

glmer code

# m1 <- glmer(
#   next_problem_correctness_complete ~
#       treatment +
#         prior_accuracy + 
#         problem_avg_accuracy +
#         problem_avg_accuracy*treatment +
#   (1+treatment|problem_id) ,
#   data = data,
#   family = binomial)
# summary(m1)

Note that problem_avg_accuracy is a measure of problem difficulty.

STAN CODE

data {
  
}

parameters {
  
}

transformed parameters {
  
}


model {
 
}