Structural equation models of change measurement.

We know from studies that variables like our salary or height are related to our health. These quantities can be seen directly or read off with a defined measurement, e.g. salary in euros or height in meters. However, many of the phenomena we are interested in are not directly visible, e.g. motivation to change behavior. Motivation cannot be measured in euros or in meters. 

Since there is no single tape measure for these latent variables, they must first be made "visible." This is done through measurable, observable indicators of the latent variable behind them, e.g. responses to items on a questionnaire measuring motivation. In a latent variable model, the latent variable is related to the observed indicators. Specifically, it is a multivariate regression model that describes the relationship between multiple observed dependent variables and one or more latent variables. In the model, the portion of the variance of the observed indicators that is not explained by the latent variable is the measurement error. The explicit consideration of measurement errors in latent variable models is not done in this form in usual analysis procedures and allows for 1) a better approximation of the true value of the construct being measured and 2) a measurement error-adjusted modeling of the relationships among the latent variables.