## Factor analysis

### Extract

Factor analysis is a technique for reducing the dimensionality of a dataset so that it is easier to interpret. Where variables in interval or ratio scale are implied.

### Article

Factor analysis is an interdependent technique because all variables have the same importance since no superiority relationship is established between them. The goal of factor analysis is to summarize the information to a few factors that can describe the dataset in a simpler way than with the initial variables.

Detailing more precisely the simple definition of factor analysis it is said that it is a technique that finds homogeneity within a set of variables that from the union of homogeneous variables form groups. Factor analysis is composed of dimensions or factors that are the variables. When a set of correlated variables is found, then there is a new dimension made up of scores.

It is about looking for similarities between the original dimensions (in principle they are not detectable given the high volume of data) to be able to summarize it in factors. A factor is a linear combination of the original variables of the dataset to be explored. Fi=A1X1 + A2X2+...+AkXk

F being the factor i of observation k. A represents the weight of each variable with respect to the factor. X are the original variables. The i is the factor number and k the variable number.

To carry out this analysis in principle, homoscedasticity must be given, data from populations with normal distribution, linear variables and, finally, the variables must be independent, but have a certain relationship between them. In short: normality, homogeneity, linearity and multicollinearity.

Once it is verified that the assumptions are fulfilled, then it is time to standardize the variables so that none of them has greater influence on another variable. Subsequently, the correlation matrix is constructed. Then you should consider what the method to follow will be: total or common variance. Finally, choose the number of factors as a solution. Choose the rotation of factors if necessary (oblique, orthogonal) and interpret the rotated factor matrix. In this way, decide if the model can be interpreted or remade.