Latent Class Cluster Models

Traditional clustering approaches utilize unsupervised classification algorithms that group cases together that are "near" each other according to an ad hoc definition of "distance". In the last decade interest has shifted towards model based approaches, especially mixture model clustering where each latent class represents a hidden cluster. Today's high-speed computers make these computationally intensive methods for model based approaches practical.

Latent GOLD's cluster module provides the state-of-the-art in cluster analysis based on latent class models. It is appropriate to include not only continuous variables, but also variables that are ordinal, nominal or counts, or any combination of these.

Latent GOLD improves over traditional approaches, using model based probabilities to classify cases into the appropriate cluster.

Covariates also can be included directly in the model for improved cluster description. In addition, the latent class cluster model can be used as a traditional latent class model, handling measurement and classification errors in categorical variables.

Discrete Factor (DFactor) Models

The factor model can also be used to deal with measurement and classification errors in categorical variables. It is actually equivalent to a latent trait (ITR) model without the requirement that the traits be normally distributed.

In addition, Latent GOLD's factor module remedies several problems inherent in traditional factor analysis.

Inherent Problems	Latent GOLD solution
1. To be interpretable, solutions require a rotation.	1. Solutions are immediately interpretable.
2. The factors are assumed to be continous.	2. The factors are assumed to be ordinal.
3. Factor scores must be estimated based on additional assumptions.	3. No additional assumptions are required to estimate factor scores.
4. The observed variables must be continous.	4. The observed variables can be nominal, ordinal, continous, or counts, or any combination of these.

Since the bi-plot is based on the latent class model, it represents an improvement over traditional biplots and traditional perceptual maps. See Magidson and Vermunt (2000), Bi-plots and Related Graphical Displays based on Latent Class Factor and Cluster Models".

Latent Class Regression Models

Traditional linear regression analysis makes two restrictive assumptions about data that are often violated in practice:

1. The dependent variable is continuous with prediction error normally distributed.
2. The population is homogeneous - one model holds for all cases.

The Latent GOLD regression module allows you to break out of this box.

1. Flexible model structure can accomodate dependent variables that are continuous, categorical (binary, nominal/polytomous, or ordinal), binomial counts, or Poisson counts - simply click on the dependent variable and select the desired scale type.
2. Population can be homogeneous or heterogeneous. Use informative diagnostic statistics to see whether multiple models are needed, in which case Latent GOLD will estimate a model for each latent class

Use both predictors and covariates. In addition to using predictors to estimate a regression model for each class, covariates can be specified to refine class descriptions and improve classification of cases into the appropriate latent classes. Follow the simple step-by-step procedure:

1. identify latent classes or hidden segments
2. use demographic and other covariates to predict class memberships, and
3. classify cases into the appropriate classes/segments