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In statisticsa latent class model LCM relates a set of observed usually discrete multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a lca and binary outcome variable class model because the latent variable is discrete. A class is characterized by a pattern of conditional probabilities that indicate the chance that variables take on certain values.

Latent class analysis LCA is a subset of structural equation modelingused to find groups or subtypes of cases in multivariate categorical data. These subtypes are called "latent classes". Confronted with a situation as follows, a researcher might choose to use LCA to understand the data: Imagine that symptoms a-d have been measured in a range of patients with diseases X Y and Z, and that disease X is associated with the presence of symptoms a, b, and c, disease Y with symptoms b, c, d, and disease Z with symptoms a, c and d.

The LCA will attempt to detect the presence of latent classes the disease entitiescreating patterns of association in the symptoms. As in factor analysis, the LCA can lca and binary outcome variable be used to classify case according to their maximum likelihood class membership. Because the criterion for solving the LCA is to achieve latent classes within which there is no longer any association of one symptom with another because the class is the disease which causes their association lca and binary outcome variable, and the set of diseases a patient has or class a case is a member of causes lca and binary outcome variable symptom association, the symptoms will be "conditionally independent", i.

Within each latent class, the observed variables are statistically independent. This is lca and binary outcome variable important aspect.

Usually the observed variables are statistically dependent. By introducing the latent variable, independence is restored in the sense that within classes variables are independent local independence. We then say that the association between the observed variables is explained by the classes of the latent variable McCutcheon, This two-way model is related to probabilistic latent semantic analysis and non-negative matrix factorization.

As in much of statistics, there is a large number of methods with distinct names and uses, which share a common relationship. Cluster analysis is, like LCA, used to discover taxon-like groups of cases in data. Multivariate mixture estimation MME is applicable to continuous data, and assumes that such data arise from a mixture of distributions: If a multivariate mixture estimation is constrained so that measures must be uncorrelated within each distribution it is termed latent profile analysis.

Modified to handle discrete data, this constrained analysis is known as LCA. Discrete latent trait models further constrain the classes to form from segments of a single dimension: As a practical instance, the variables could be multiple choice items of a political questionnaire. The data in this case consists of a N-way contingency table with answers to the items for a number of respondents. In this example, the latent variable refers to political lca and binary outcome variable and the latent classes to political groups.

Given group membership, the conditional probabilities specify the chance certain answers are chosen. LCA may be used in many fields, such as: From Wikipedia, the free encyclopedia. Introduction to theory and application]. Retrieved from " https: Classification algorithms Latent variable models Market research Market segmentation.