Latent variable measurement models and path analysis

What is a latent variable? • A variable that is not observable or is not directly measurable. • A variable that is measured with error or can only be measured with error. • A latent variable can be used to represent a 'true' variable which is measured with error, OR a single conceptual variable, OR a construct which is a summarization of a complex concept. Examples of 'true' variables that are measured with error: calcium intake measured by a Food Frequency, physical activity measured by self-report, self-reported weight, sleep latency recorded with sleep diaries, lung capacity measured by FEV1 (Forced Expiratory Volume in 1 second) Examples of conceptual variables and constructs that are desirable to measure: lib-• Our goal is to use statistical models to measure latent variables by relating them with things that can be observed (e.g. questionnaire items, test results, any observable tool) • Philosophical debates about the fundamental existence or non-existence of conceptual latent variables will be avoided and a more pragmatic point of view will be taken focused on obtaining useful information and explanations for relationships from data using statistical modeling. • This course will focus more on latent variables representing concepts or constructus. Latent variables are also used in different statistical modeling techniques as a mathematical convenience where they often are not of primary interest, i.e. the goal is not to " measure " them per se: • Unobserved heterogeneity (e.g. frailties in survival analysis, random effects in longitudinal data or clustered data)