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Latent class analysis:

Latent Class Analysis (LCA) is a statistical method for identifying unmeasured class

membership among subjects using categorical and/or continuous observed variables. For

example, you may wish to categorize people based on their drinking behaviors (observations)

into different types of drinkers (latent classes). This could lead to finding categories such as

abstainers, social drinkers, and alcohol abusers. You could try to create models to predict why

one falls into particular class memberships (why do people become alcohol abusers), and you

can also seek to explore the consequences of such class memberships (does being an alcohol

abuser/not abuser predict other variables). You can even combine latent class analysis with other

techniques. For example, you might use survival analysis to model time to first use of alcohol

and find that latent class analysis identifies a class of long term abstainers and whose survival is

modeled separately from non-abstainers. Or if you were using latent growth curve modeling of

alchohol use over time, you could apply latent class analysis to the trajectories of alcohol use to

identify classes such as abstainers, early drinkers who taper off, and chronic alcohol abusers.

LCA can be used in many disciplines such as Health Sciences, Psychology, Education, and the

Social Sciences. Examples will be shown using Mplus version 3.

Latent class analysis (wiki):

In statistics, a latent class model (LCM) relates a set of observed (usually

discrete)multivariatevariables to a set oflatent variables. It is a type oflatent variable model. It

is called a latent class model because the latent variable is discrete. A class is characterized by a

pattern ofconditional probabilitiesthat indicate the chance that variables take on certain values.

Latent Class Analysis (LCA) is a subset ofstructural equation modeling, used to find groups or

subtypes of cases in multivariate categorical data. These subtypes are called "latent classes".[1]

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.

http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Multivariate_random_variablehttp://en.wikipedia.org/wiki/Multivariate_random_variablehttp://en.wikipedia.org/wiki/Multivariate_random_variablehttp://en.wikipedia.org/wiki/Latent_variablehttp://en.wikipedia.org/wiki/Latent_variablehttp://en.wikipedia.org/wiki/Latent_variablehttp://en.wikipedia.org/wiki/Latent_variable_modelhttp://en.wikipedia.org/wiki/Latent_variable_modelhttp://en.wikipedia.org/wiki/Latent_variable_modelhttp://en.wikipedia.org/wiki/Conditional_probabilitieshttp://en.wikipedia.org/wiki/Conditional_probabilitieshttp://en.wikipedia.org/wiki/Conditional_probabilitieshttp://en.wikipedia.org/wiki/Structural_equation_modelinghttp://en.wikipedia.org/wiki/Structural_equation_modelinghttp://en.wikipedia.org/wiki/Structural_equation_modelinghttp://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Structural_equation_modelinghttp://en.wikipedia.org/wiki/Conditional_probabilitieshttp://en.wikipedia.org/wiki/Latent_variable_modelhttp://en.wikipedia.org/wiki/Latent_variablehttp://en.wikipedia.org/wiki/Multivariate_random_variablehttp://en.wikipedia.org/wiki/Statistics

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The LCA will attempt to detect the presence of latent classes (the disease entities), creating

patterns of association in the symptoms. As in factor analysis, the LCA can also be used to

classify case according to theirmaximum likelihoodclass membership.[1]

Because the criterion for solving the LCA is to achieve latent classes within which there is nolonger any association of one symptom with another (because the class is the disease which

causes their association, and the set of diseases a patient has (or class a case is a member of)

causes the symptom association, the symptoms will be "conditionally independent", i.e.,

conditional on class membership, they are no longer related.

http://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Latent_class_model#cite_note-Lazarsfeld-1http://en.wikipedia.org/wiki/Maximum_likelihood