We’re going to look at the structure of movie preferences: how people vary in which characteristics of movies they like and dislike.
Our first problem is that we have 1,128 tags describing movies, which is a bit much. These came from user-created tags that were filtered to retain the widely used, higher-quality ones, but even after this filtering, there’s still a lot of redundancy. For example, “vampire” and “vampires” are both tags, and they have a Pearson correlation of 0.99 across movies, making them basically duplicates. Having too many tags, especially when many are highly correlated with each other, can lead to problems. So, I use factor analysis with varimax rotation to reduce the tags to 115 underlying dimensions along which movies vary.
The interactive below lets you explore these dimensions and the tags most strongly associated with each one, giving an idea of what aspects of movies each dimension captures.
See which tags and films align with each dimension.
Most positively correlated tags · Pearson r
High-scoring movies
Low-scoring movies
Now that we have the movie dimensions, we can use them to predict people’s tastes in movies. The problem is that most people haven’t rated enough movies for ordinary linear regression to give reliable estimates of their preferences. Ridge regression helps with this by applying an L2 penalty to the coefficients, discouraging overly large estimates. In Bayesian terms, that’s equivalent to placing an isotropic Gaussian prior on the coefficients, that is, $\mathbf{\beta} \sim \mathcal{N}(\mathbf{0}, \tau^2 I)$.
In our case, though, we have reason to believe this isn’t the best prior. For example, one of our dimensions is “Awful Films,” and you’d expect that, on average, people don’t like awful films. So, rather than assuming all preference coefficients are centered on zero and have the same variance, we’d like a prior that reflects how people’s preferences actually vary. Sol has estimated such a prior for us.
The interactive below shows this estimated distribution of preferences across movie dimensions: which characteristics people tend to like or dislike on average, and how much people’s preferences differ from one another.
How preferences for each movie dimension vary across users.
Population distribution of preference coefficients
Coefficient units: change in a user's standardized rating per +1 SD on the movie dimension, holding the other dimensions fixed.
Still, 115 dimensions of movie preferences is kind of a lot. Many of these preferences are pretty correlated, for example Gore and Haunted House Horror (r = +0.54), or Sequels and Awful Films (r = +0.58). Perhaps there are a smaller number of underlying factors that explain how people’s preferences tend to covary? Let’s take a look.
The interactive below lets you explore the preference factors, see which movie dimensions contribute to each one, find movies that distinguish each factor, and examine how the factors correlate with one another.
How movie preferences vary together across users.
Preference-coefficient loadings
Standardized pattern loadings · click a dimension to explore it above
Movies that distinguish this factor
Change in predicted standardized rating for +1 SD on this preference factor, holding the others fixed
To see where your own ratings place you along these factors, go to Describing Your Movie Preferences.