In R, there is a package called "lme4" that holds the function "lmer," which is used to fit random effects model. The attached data set has four movie critics rating the same four movies. We are not interested in the particular differences between the individual critics, but rather how the variable "critic" affects the score of the movie in general. That means we will treat the variable "critic" as a random effect and not a fixed one.

1. Import the movie critic data below. In R, to add a random effect x, use the syntax (1|x). So a line of R code may look something like:

model = lmer(score ~ (critic|1), data = data)

Use a model of this sort to fit the critic data, thinking of "critic" as a random effect. Repeat this model fitting using "critic" as a fixed effect. What is the major theoretical difference?

Movie Rating (out of 100) Critic

1 84 87

1 78 81

1 75 73

1 65 63

2 82 91

2 76 83

2 68 59

2 58 62

3 45 61

3 49 47

3 62 70

3 65 81

4 89 83

4 87 87

4 75 62

4 72 78