Discrete Choice Analysis (DCA) sometimes called qualitative choice modeling, is an exciting new statistical technique sweeping the world of market research. DCM looks at choices that customers make between products (or services). By Identifying patterns in these choices, DCM models how different consumers respond to a marketplace filled with competing products. DCM allow marketers to examine the market-share impact of product configuration, service bundling, pricing and promotion on different classes of customers.

To some degree, all purchases involve choice. Shoppers choose among competing products or groups of products. They also choose to buy now, later, or not at all. Similarly, purchasing managers choose among suppliers, and companies choose among investment opportunities. The list of examples goes on and on. Each of these circumstances involves choice. In some cases, the set of alternatives and the cognitive process employed in choosing are complex.

Human behavior is especially complex. So much so that it is probably impossible to understand completely what lies behind a single individual's purchase decision. However, while it is impossible to say for sure what one person will do, one can draw inferences from many choices that groups of people make.

As an analogy, take a coin. If you flip a coin once, you cannot tell for certain whether it will turn up heads or tails; but if you flip it many times, you can be reasonably certain that the flips will be half heads and half tails. By observing many flips, one can infer a probability of 0.5 for heads and 0.5 for tails .Likewise, by observing many consumers' choices, one can infer the probability of purchasing a given product based on the product's characteristics, its price and the socio-demographic characteristics of the consumer.

see: Discrete Choice Sample Size

Latent class analysis (LCA) is a multivariate technique which can be applied to cluster analysis, factor analysis, or regression analysis. Latent constructs are created from indicator variables, as in structural equation modeling, and then used to construct clusters, factors, or to predict dependents in regression mode. Latent profile analysis is a variant on LCA for continuous variables. Log-linear modeling with latent variables is a form of analysis combining latent class analysis with log-linear analysis .Unlike traditional models, such latent class models support nominal and ordinal as well as continuous data.

The most common use of LCA is to discover case subtypes (or confirm hypothesized subtypes) based on multivariate categorical data. LCA is well suited to many health applications where one wishes to identify disease subtypes or diagnostic subcategories. Other common areas of application include marketing research, survey research, sociology, psychology, and education.

Another more-or-less distinctly medical LCA application is evaluation of diagnostic tests in the absence of a "gold standard." For example, if one has several tests for detecting presence/absence of a disease, but no comparison "gold standard" that indicates disease status with certainty, LCA can be used to provide estimates of diagnostic accuracy (sensitivity, specificity, proportion of correct diagnoses, etc.) of the different tests.

The finite mixture model can be adapted to OLS regression, logit, multinomial logit, and conditional logit models. Doing so is advantageous for the identification of latent segments, that may otherwise be unidentified.

Structural Equation Models (SEM) is a family of statistical techniques which incorporates and integrates path analysis and factor analysis. In fact, use of SEM software for a model in which each variable has only one indicator is a type of path analysis. Use of SEM software for a model in which each variable has multiple indicators but there are no direct effects (arrows) connecting the variables is a type of factor analysis. Usually, however, SEM refers to a hybrid model with both multiple indicators for each variable (called latent variables or factors), and paths specified connecting the latent variables. Synonyms for SEM are covariance structure analysis, covariance structure modeling, and analysis of covariance structures. Although these synonyms rightly indicate that analysis of covariance is the focus of SEM, be aware that SEM can also analyze the mean structure of a model.

In structural equation modeling, the key variables of interest are usually "latent constructs"--abstract psychological concepts such as "intelligence" or "attitude." We can observe the behavior of latent variables only indirectly, and imperfectly, through their effects on manifest variables.

SEM is used to test the directional relationship among variables in a customer satisfaction, loyalty, or retention model. The first step in the process is to develop a structural (conceptual) model that best represents your understanding of the underlying relationships and relative importance of the different variables. Factor analysis and multiple regression can be used to help you develop your model. The second step is then to test/examine the statistical relationship among the variables.
A finite mixture SEM model overcomes the assumption that the model can account for heterogeneity. Instead, heterogeneity is captured by a limited amount of homogenous segments.