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|Table of Contents Multivariate Data Modeling Introduction
|See also: classification vs. calibration, modeling - example
In many cases, we often suspect some relationships among the data when acquiring the data. However, in order to make more precise statements, draw conclusions, or predict from the measured data, we have to set up a model which represents the nature of the underlying relationship.
Another aspect to discriminate between models is their (non)linearity. Depending on the circumstances we may either try to linearize non-linear models, or apply non-linear models. Using non-linear models generally requires much more caution than linear models, since non-linear models are much more likely to adapt to noise in the data than linear models.
A third aspect is the type of the dependent (response) variable, which
may be either qualitative or quantitative. Qualitative variables will result
in classification models, quantitative variables will result in
models. In general, there are several terms which have been developed historically
to describe some aspects of a model:
|Additive models are linear models. The predictor variables show an additive effect on the response variable.
|Biased models are models which are based on estimators which show a non-zero difference between the expected value of the estimator and its corresponding true value (biased estimator).
|Models with a causal relationship between predictor and response variables.
|Does not contain any random parts (cf. to stochastic model).
|Linear models are models which are linear in their parameters. Linear models must not necessarily estimate plane relationships.
|A non-linear model is non-linear in the parameters to be estimated (see also the discussion about linearity for more details).
|A parsimonious model is a model with as few parameters as possible for a given quality of a model.
|A soft model relies on intermediary (latent) variables, which are often formed by eigenanalysis of the data. A predictor variable of soft models cannot be assigned to a single measured variables, but is rather some combination of several measured variables.
|A stochastic model contains random elements (in contrast to the deterministic model)
Methods for modeling cover a wide range. The following is a short list of the more important ones:
LISREL (linear structural relationship)
partial least squares (PLS)
principal component regression (PCR)
Last Update: 2006-Jšn-17