I am studying Structural Equations Modeling and we saw that there are "latent variables", usually extracted using factorial analysis, which we do not observe but that explain the covariance structure of the observed variables. My question is: is the error (in any statistical model) a latent variable?
My intuition is yes, because 1. we do not directly observe the error and 2. We assume that what we observe is a function of the error (among other things)
Latent variable is a random variable, so the error is "included" by default. The idea of an error comes from models like linear regression, where the distribution is conditionally Gaussian so you can write
$$ y = \mu + \varepsilon, \qquad \varepsilon \sim \mathcal{N}(0, \sigma^2) $$
as
$$ y \sim \mathcal{N}(\mu, \sigma^2) $$
But not every random variable can be decomposed like this. The notion of an error is about something being a random variable and the same applies to latent variables. In statistical models, the data is assumed to be realizations of the random variables, while latent variables are just not observed (or not observable), the results we obtain have "error" because they are functions of random variables, so they are random variables themselves (they also vary).
