Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems

Chapter 11Introduction To Latent Variable Models

11.1 Not Seen but Felt

Many interesting business concepts are not directly observable. We cannot directly touch, hear, or see the loyalty of a customer or the creditworthiness of a firm. Fortunately, we can observe a customer's purchase history and use that to understand loyalty. For creditworthiness we can examine assets, liabilities, and past repayments. The observed information helps us to reduce our uncertainty about these latent concepts. We may not know for sure whether a firm will repay a given debt or not, but intuitively we should have a better idea by considering the data, and the more data we consider, the more sure we may feel. This intuitive approach corresponds well with Bayesian inference where we use information to go from a broad prior distribution to a more concentrated and precise posterior distribution. We might feel that there are some clear distinctions between estimating model parameters (Chapters 2–9), imputing missing data (Section 10.3), or inferring latent data (this chapter). However, from a Bayesian perspective these different tasks are all handled similarly.

In the previous chapter, we examined data that was partially missing. This chapter covers the analysis of data which is, in a sense, “entirely” missing. Latent data models are models for data that are not observed directly. While we do not observe the latent data directly, we do observe other data. We can then use the values of the observed data ...