# What is factor analysis?

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### 1.0 DEFINITION OF FACTOR ANALYSIS

Factor analysis (FA) refers to a latent structure approach that can be used to analyze interrelationships among a large number of variables by explaining the underlying unobservable variables (latent variables) that are reflected in the observed variables (manifest variables) known as factors. With FA, the researcher can first identify the separate dimensions of the structure and then determine the extent to which each variable is explained by each dimension.Â  Once these dimensions and the explanation of each variable are determined, the summarization and reduction of data can be achieved. In summarizing the data, FA describes the underlying dimensions of data in a much smaller number of items than the original variables.

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It examines the pattern of correlations (or covariances) between the observed measures. Data reduction can be achieved by calculating scores for each underlying dimension and substituting them for the original variables. FA is an interdependence technique where variates (factors) are formed to maximize their explanation of the entire variable set. These groups of variable would represent dimensions within the data which the researcher needs to label them. Basically, there are two types of FA, exploratory and confirmatory. The first analysis is used to discover the nature of the construct that influence a set of response and latter, test a specified set of constructs is influencing responses in a predicted way.

### Data summarization

The goal of data summarization is achieved by defining a small number of factors that adequately represent the original set of variables.

### Data reduction

Data reduction is achieved by identifying representative variables from a much larger set of variables for use in subsequent multivariate analyses or creating an entirely new set of variables whilst retaining the nature and character of the original variables. Data reduction relies on the factor loadings and uses them a s a basis for either identifying variables for subsequent analysis with other techniques or making estimates of the factor themselves (factor scores or summated scales), which then replace the original variables in subsequent analysis.Â Factor analytic technique is run according to their purpose either an exploratory or confirmatory perspective. Many researchers consider using the Exploratory Factor Analysis (EFA) when they are searching for structure among a set of variables or as a data reduction technique. EFA technique does not set any a priori constraints on the estimation of the components or the number of components to be extracted compared to the Confirmatory Factor Analysis (CFA). CFA is used to confirm what is expected on the basis of pre-established theory.

### 2.0 PURPOSE OF FACTOR ANALYSIS

The primary purpose of FA is to discover simple patterns in the pattern of relationships amongst variables by defining the underlying structure in a data matrix.

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