# Statistical Advisor, Searching for Factors or Dimensions

Use one of the following to explore data and search for structure/patterns/factors/clusters.

## Factor Analysis

The Factor Analysis chapter discusses techniques for performing factor and principal components analysis. In general, the goal of these analyses is to detect underlying dimensions that explain relations between multiple variables. For example, if one would factor analyze four different measures of size (e.g., height, weight, shoe-size, arm length) taken in a sample of 100 people, then factor analysis would most likely return one dimension. One might appropriately label that dimension as 'size.' Computationally, factor analysis is based on the correlation matrix; the program will attempt to find the minimum number of factors necessary to reproduce the observed correlations.

## Correspondence Analysis

Correspondence analysis is a descriptive/exploratory technique designed to analyze two-way and multi-way tables containing some measure of correspondence between the rows and columns. The results provide information which is similar in nature to those produced by factor analysis techniques, and they allow one to explore the structure of categorical variables included in the table. The most common kind of table of this type is the two-way frequency crosstabulation table (see for example the Basic Statistics or Log-Linear chapter).

## Multidimensional Scaling

Multidimensional Scaling chapter discusses non-metric multidimensional scaling, based on similarities or dissimilarities. Like factor analysis, the goal of multidimensional scaling is to detect underlying dimensions for a set of multiple input variables. However, unlike factor analysis which is based on the correlation matrix of variables, multidimensional scaling begins with a similarity or dissimilarity matrix. These dis/similarities can be actual ratings, or derived in other ways (e.g., geographic distances). It is not necessary for these dis/similarities to be precise measurements; it is only required that the dis/similarity values contain rank order information (for example, that greater similarity values indeed indicate greater similarity).

## Partial Least Squares (PLS)

Partial Least Squares (PLS) chapter discusses an implementation of partial least squares (PLS). PLS allows you to extract factors (components) from a data set that includes one or more predictor variables, and one or more dependent (response) variables.