# Factor Analysis

If we make the assumption that a set of underlying (or latent) variables is responsible for a large part of the dynamics in the target dataset, then we can use a set of techniques that seek to identify and quantify those underlying variables. While many such techniques exist, one such very widely used one is called Factor Analysis.

Rotation Options:

- None
- Equamax
- Orthomax
- Parsimax
- Promax
- Quartimax
- Varimax

Scoring:

- WLS
- Regression

N : Number of Components

### Description

The factor analysis model can be described as
$$ Y = \Lambda F + E $$
where

$ \Lambda $ are the factor weights

$ F $ are the factor scores

$ E $ is the error term

Clearly, a reconstructed approximation of the target dataset can be carried out by $ \Lambda * F $. For example, in a single factor model:

$$ \begin{matrix} y_1 = \lambda_{1} f_{1} + \epsilon_{1} \\ y_2 = \lambda_{2} f_{1} + \epsilon_{2} \\ y_3 = \lambda_{3} f_{1} + \epsilon_{3} \end{matrix} $$

### Returns

**GoF:**Chi-square, p-value, log-likelihood**Factor Loadings:**$ \Lambda\ $ i.e. weights**Rotation Matrix****Factor Scores:**$ F $**MLE Variances:**