There are two basic approaches to factor analysis, and these are namely principal component analysis (PCA) and common factor analysis. Principal component analysis (PCA) is an approach to factor analysis that considers the total variance in the data, which is unlike common factor analysis. In principal component analysis (PCA), the diagonal of the correlation matrix consists of unities and the full variance is brought into the factor matrix. The term factor matrix in principal component analysis (PCA) is the matrix that contains the factor loadings of all the variables on all the factors extracted. The term factor loadings in principal component analysis (PCA) 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 (PCA) comes into play.
Principal component analysis (PCA) 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. Principal component analysis (PCA) is a useful statistical approach in factor analysis. Principal component analysis (PCA) is a common technique for searching patterns in the data that consist of high dimensions. While conducting principal component analysis (PCA), the researcher can get well versed with standard deviation, covariance, eigenvectors and eigenvalues. The eigenvalues in principal component analysis (PCA) refers to the total variance explained by each factor. The standard deviation in principal component analysis (PCA) measures the variability of the data. The task of principal component analysis (PCA) 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 (PCA) in an appropriate manner, the researcher needs to subtract the mean from each of the dimensions of the data. The mean subtracted in principal component analysis (PCA) is the average across each dimension. This task in principal component analysis (PCA) is called data adjustment. The next task is to calculate the covariance matrix in principal component analysis (PCA). The covariance in principal component analysis (PCA) can be computed only if the data is two dimensional. If the dimension of data in principal component analysis (PCA) 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 (PCA) is a square matrix with non diagonal elements in this matrix as positive elements. As per the definition of eigenvalues, the calculation in principal component analysis (PCA) involves the extraction of the total variance from each factor. The role of eigenvalues, which are then formed into vectors in principal component analysis (PCA), is to provide the researcher with information about the patterns in the data. In principal component analysis (PCA), the principal component is referred to as that eigenvector. This has the highest eigenvalue. Once the eigenvectors in principal component analysis (PCA) are found from the covariance matrix, the next task in principal component analysis (PCA) is to sort the eigenvalues from highest to lowest.
Thus, principal component analysis (PCA) 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 principal component analysis (PCA) will present the researchers with those principal components that are the most important factors or components that the consumers seek.
