# Factor Analysis

## Factor Analysis

(Statistical Analysis > Factor Analysis)

Description
Factor Analysis is a technique to reduce the number of variables into a smaller number of unobservable factors. Factor Analysis can be performed using maximum-likelihood solution on a covariance matrix or data matrix.

## Inputs

Factor Analysis Dataset Input – select a dataset that contains the variables of interest.
Factor Analysis Variable Names – a set of independent variables.
Factor Analysis Number of Factors – number of factors to extract. Default is 1.
Factor Analysis Rotate – “none”, “varimax” and “promax” are possible functions to be used to rotate the factors: it will be called with first argument the loadings matrix and should return a list with component loadings giving the rotated loadings, or just the rotated loadings.
Factor Analysis Scores – type of scores to produce, if any. The default is none, “regression” gives Thompson’s scores, “Bartlett” given Bartlett’s weighted least-squares scores. Partial matching allows these names to be abbreviated.
Factor Analysis The number of starting values – the number of starting values to be tried. Default 1.
Factor Analysis Lower bound for uniquenesses – the lower bound for uniquenesses during optimization. Should be > 0. Default 0.005.

## Outputs

Output includes the following:
Converged: Rotation converged (TRUE or FALSE)
Loadings : a matrix of loadings, one column for each factor. The factors are ordered in decreasing order of sums of squares of loadings, and given the sign that will make the sum of the loadings positive.
Uniquenesses : the uniqueness of each variable is computed as the noise left over after the factors are ﬁtted.
Correlation: a measurement of how two variables are related.
Criteria : the results of the optimization: the value of the negative log-likelihood and information on the iterations used, including objective and counts.function and counts.gradient.
Factors : the number of factors.
Dof : the number of degrees of freedom of the factor analysis model.
The Chi square statistic : the significance-test statistic
The p-value: p value, if it can be computed.
N.obs : the number of observations.

## Advanced

Because of the complexity of FA formula, no formula is provided in this section. Please refer to the following references for the FA.

References
(1) An Introduction to R (3.1.0 (2014-04-10)).
(2) Jöreskog, K. G. (1963) Statistical Estimation in Factor Analysis: A New Technique and Its Foundation, Almqvist and Wiksell, Stockholm,
(3) Kim, J-O. and C. W. Mueller (1978) Factor Analysis: Statistical Methods and Practical Issues, SAGE Publications, Inc, Beverly Hills.
(4) Lawley, D. N. and A. E. Maxwell (1971) Factor Analysis as a Statistical Method (Second Edition), Butterworths, London.
(5) Rossiter, D. G. (2014) Tutorial: An example of statistical data analysis using the R environment for statistical computing, ITC, The Netherlands.