Towards Better Understanding Latent Structure Analysis: A Geometric Approach

Mikhail Kovtun, Duke University
Anatoliy I. Yashin, Duke University

Surveys and other similar data collection techniques are widely used in social sciences. In a survey, questions are not chosen arbitrarily, but to reflect the underlying latent structure, which cannot be observed directly. Latent structure analysis is a statistical technique for revealing such latent structures. We develop a geometric view on latent structure analysis, which allows us to describe in simple terms relation between different branches of LSA (including latent class models, latent trait models, and linear latent structure models), clearly formulate conditions of identifiability of models, and provide guidelines for practical applications of LSA. A special attention is paid to the role and applicability of "local independence" assumption. An extensive example, based on National Long Term Care Survey data, is discussed from this point of view.