There are two basic approaches to factor analysis, and these are namely principal component analysis (PCA) and common factor analysis. Principal component analysis is an approach to factor analysis that considers the total variance in the data, which is unlike common factor analysis. The diagonal of the correlation matrix consists of unities and the full variance is brought into the factor matrix. The term factor matrix is the matrix that contains the factor loadings of all the variables on all the factors extracted. The term factor loadings are the simple correlation between the factors and the variables. Once it has been determined that it is the appropriate technique for the data, then the next task is choosing the appropriate approach. This is where principal component analysis comes into play.
Principal component analysis is recommended when the researcher’s primary concern is to determine the minimum number of factors that will account for the maximum variance in the data in use in the particular multivariate analysis. PCA is a useful statistical approach in factor analysis. It is a common technique for searching patterns in the data that consist of high dimensions. While conducting principal component analysis, the researcher can get well versed with standard deviation, covariance, eigenvectors and eigenvalues. The eigenvalues refer to the total variance explained by each factor. The standard deviation measures the variability of the data. The task of principal component analysis is to identify the patterns in the data and to direct the data by highlighting their similarities and differences.
In order to perform principal component analysis in an appropriate manner, the researcher needs to subtract the mean from each of the dimensions of the data. The mean subtracted is the average across each dimension. This task is called data adjustment. The next task is to calculate the covariance matrix. The covariance can be computed only if the data is two dimensional. If the dimension of data is more than two, then the covariance is calculated or measured more than once. If the data is two dimensional, then the covariance matrix in principal component analysis is a square matrix with non diagonal elements in this matrix as positive elements. As per the definition of eigenvalues, the calculation in PCA involves the extraction of the total variance from each factor. The role of eigenvalues, which are then formed into vectors, is to provide the researcher with information about the patterns in the data. The principal component is referred to as that eigenvector. This has the highest eigenvalue. Once the eigenvectors are found from the covariance matrix, the next task is to sort the eigenvalues from highest to lowest.
Thus, principal component analysis gives the original factors in terms of differences and similarities between the factors. For example, if the researcher wants to know the underlying benefits that a consumer seeks from toothpaste, then PCA will present the researchers with those principal components that are the most important factors or components that the consumers seek.
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