FACTOR ANALYSIS

Factor Analysis



Factor Analysis

Introduction

Factor analysis is a multivariate statistical technique for a large number of observed variables identifies a smaller number of underlying variables. These unobserved, underlying variables called factors. Importantly, the factors almost as much of the variation explained if the observed variables. Factor Analysis is used for data reduction and to understand the structure of the dataset. A good factor solution provides a relatively small number of factors that a major proportion of the variance in the original variables are present, explain. Matrix Algebra is an essential part of factor analysis. The factor solution is obtained by manipulation of the correlation matrix (Bryant and Yarnold (1994), 1994).

Factor Analysis is a technique that is to summarize the information in a data matrix with V variables. This will identify a small number of factors F, the number of factors being less than the number of variables. The factors represent the original variables with minimum loss of information (Bryant and Yarnold (1994), 1994).

The mathematical model of factor analysis is similar to multiple regression. Each variable is expressed as a linear combination of factors not directly observable.

X ij = F 1i + F 2i to i1 to i2 +....+ F ki ik + V i

Where:

X ij the score of individual i on variable j

F ij are the input coefficients.

a ij are the factor scores.

V i is the unique factor of each variable.

It is assumed that the unique factors are uncorrelated among themselves or with the common factors. We may distinguish between exploratory factor analysis where factors are not known a priori but are determined by factor analysis and on the other side would Confirmatory Analysis which proposes "a priori" model, whereby there are factors that represent the original variables, and the number of these higher than those, and is tested for the model (Sheppard, 1996).

For the factor analysis makes sense to be fulfilled two basic conditions: Parsimony and interpreted according to the principle of parsimony the phenomena to be explained with the fewest possible elements. Therefore, compared to factor analysis, the number of factors must be as small as possible and they must be amenable to substantive interpretation. A good factor solution is one that is simple and interpretable (Sheppard, 1996).

Discussion

The data reduction used to find homogeneous groups variable gene from a large group of variables. These homogeneous groups formed with the variables that correlate much with each other and trying, initially, that some groups are independent of others. Factor analysis responses of the subjects we find groups of variables with common meaning and get thus reduce the number of dimensions needed to explain the subjects' responses. Factor analysis is therefore a technique for reducing the dimensionality of the data. Its ultimate purpose is to find the minimum number of dimensions capable of explain the maximum amount of information contained in the data. Unlike what happens in other techniques such as analysis of variance or the regression, in the factor analysis all variables in the analysis fulfilled the same role: they ...