# Chapter 2: Factor Analysis

### Terminology

In factor analysis, the latent constructs are referred to as *factors* or *latent variables*, and the observable variables which are treated as measures of the factors are called *indicators, items,* or *observed variables*. The survey questions in our examples are regarded as such indicators.

An indicator is not assumed to measure the corresponding factor perfectly but with some *measurement error*. For instance, the question "to what extent is it your duty to back the decisions made by the police even when you disagree with them?" is conceptually narrower than the factor "obligation to obey". This specific question provides information about the factor, but not enough on its own for reliable inference on the factor. For better measurement, several items are used to measure the same factor, and information from them is combined through factor analysis.

### The notation used here

We will denote a latent factor by the Greek letter *η*. Different factors are denoted with subscripts, so that for example *η*_{1} and *η*_{2} are two distinct factors. Indicators are denoted with *y* and their measurement errors with *ε*, with subscripts for different indicators and errors. In later sections the models will also involve observed variables which are treated as explanatory variables rather than measures of the factors; notation for them will be introduced later.