Latent Structure Analysis (LSA) by Lazarsfeld is primarily introduced for the important special case of Latent Class Analysis (LCA). The goal of LSA is to identify unobserved latent variables that explain the relationship between manifest variables. This approach is similar to factor analysis but can also be seen as a non-metric cluster analysis. The model parameters of LCA represent probabilities. Some estimation methods can produce invalid estimates, and a sufficient number of cases is required for meaningful application of maximum likelihood (ML) estimators. However, a large number of cases can lead to significance issues during model testing. Comparing current estimation methods, a modified Chi-Square Minimum Estimation procedure by Mooij et al. is highlighted for its good properties. This method considers only marginal frequencies up to a certain order. The chapter concludes with an interpretation of an LCA result using Mooij et al.'s method and provides insights into emerging research on applying LCA in larger studies. LSA, as an exploratory method, has gained increasing interest in recent years. While it is a highly specialized technique, many areas require further experience in its application. The chapter focuses on relatively simple models, referring to more generalizations in the cited literature. The core idea of LSA, as proposed by Lazarsfeld, is to treat manifest variables as indicators or "symptoms" of a latent property. The relationship between the latent variable and manifest characteristics is assumed to be non-deterministic. For example, a doctor diagnoses a patient based on the presence of specific symptoms, even though not all symptoms are present in every patient with a particular disease. Similarly, a latent structure model can estimate the probability that a patient with a specific disease has certain symptoms or that the presence of certain symptoms indicates a specific disease. For non-metric manifest variables and metric latent variables, Latent Polynomial Models are crucial. These models assume the probability that a person with a specific value on the latent continuum exhibits certain manifestations of manifest variables as a polynomial. In Latent Profile Analysis, the manifest variables are metric.Latent Structure Analysis (LSA) by Lazarsfeld is primarily introduced for the important special case of Latent Class Analysis (LCA). The goal of LSA is to identify unobserved latent variables that explain the relationship between manifest variables. This approach is similar to factor analysis but can also be seen as a non-metric cluster analysis. The model parameters of LCA represent probabilities. Some estimation methods can produce invalid estimates, and a sufficient number of cases is required for meaningful application of maximum likelihood (ML) estimators. However, a large number of cases can lead to significance issues during model testing. Comparing current estimation methods, a modified Chi-Square Minimum Estimation procedure by Mooij et al. is highlighted for its good properties. This method considers only marginal frequencies up to a certain order. The chapter concludes with an interpretation of an LCA result using Mooij et al.'s method and provides insights into emerging research on applying LCA in larger studies. LSA, as an exploratory method, has gained increasing interest in recent years. While it is a highly specialized technique, many areas require further experience in its application. The chapter focuses on relatively simple models, referring to more generalizations in the cited literature. The core idea of LSA, as proposed by Lazarsfeld, is to treat manifest variables as indicators or "symptoms" of a latent property. The relationship between the latent variable and manifest characteristics is assumed to be non-deterministic. For example, a doctor diagnoses a patient based on the presence of specific symptoms, even though not all symptoms are present in every patient with a particular disease. Similarly, a latent structure model can estimate the probability that a patient with a specific disease has certain symptoms or that the presence of certain symptoms indicates a specific disease. For non-metric manifest variables and metric latent variables, Latent Polynomial Models are crucial. These models assume the probability that a person with a specific value on the latent continuum exhibits certain manifestations of manifest variables as a polynomial. In Latent Profile Analysis, the manifest variables are metric.