Title: Monte Carlo likelihood approximation: accounting for "it's not you; it's me"
Abstract: Speed-dating rejection data can be modeled with a generalized linear mixed model. Each speed-dating participant receives decisions ("I would/wouldn't like to see you again.") from several potential love interests and each participant also makes this same decision for several potential love interests. Thus, the log odds of rejection can be modeled with crossed random effects: one for each decision-giver and one for each decision-recipient. A high random effect for a decision-giver would indicate that decision-giver is more likely than average to reject their suitors ("It's not you; it's me."). Similarly, a high random effect for a decision-recipient would indicate that person is more likely than average to be rejected ("It's you. Definitely you.") Though the data are relatively easy to collect and the model is easy to understand, conducting likelihood-based inference for this model is difficult because the likelihood is a high-dimensional integral. While some methods perform inference on an alternative function (e.g. penalized quasi likelihood), the method of Monte Carlo likelihood approximation (MCLA) enables likelihood-based inference by approximating the entire likelihood function. We will introduce MCLA, discuss MCLA theory, and examine the MCLA implementation in R package glmm.