A brief description of the various multivariate techniques named above (with special emphasis on factor analysis) is as under:
Factor analysis: Factor analysis is by far the most often used multivariate technique of research studies, specially pertaining to social and behavioural sciences. It is a technique applicable when there is a systematic interdependence among a set of observed or manifest variables and the researcher is interested in finding out something more fundamental or latent which creates this commonality.For instance, we might have data, say, about an individual’s income, education, occupation and dwelling area and want to infer from these some factor (such as social class) which summarises the commonality of all the said four variables. The technique used for such purpose is generally described as factor analysis. Factor analysis, thus, seeks to resolve a large set of measured variables in terms of relatively few categories, known as factors. This technique allows the researcher to group variables into factors (based on correlation between variables) and the factors so derived may be treated as new variables (often termed as latent variables) and their value derived by summing the values of the original variables which have been grouped into the factor. The meaning and name of such new variable is subjectively determined by the researcher. Since the factors happen to be linear combinations of data, the coordinates of each observation or variable is measured to obtain what are called factor loadings. Such factor loadings represent the correlation between the particular variable and the factor, and are usually place in a matrix of correlations between the variable and the factors.
The mathematical basis of factor analysis concerns a data matrix* (also termed as score matrix), symbolized as S. The matrix contains the scores of N persons of k measures. Thus a1 is the score of person 1 on measure a, a2 is the score of person 2 on measure a, and kN is the score of person N on measure k. The score matrix then take the form as shown following:
SCORE MATRIX (or Matrix S)
It is assumed that scores on each measure are standardized [i.e., xi = (X - Xi )2 /si ] . This being so, the sum of scores in any column of the matrix, S, is zero and the variance of scores in any column is 1.0. Then factors (a factor is any linear combination of the variables in a data matrix and can be stated in a general way like: A = Waa + Wbb + … + Wkk) are obtained (by any method of factoring). After this, we work out factor loadings (i.e., factor-variable correlations). Then communality, symbolized as h2, the eigen value and the total sum of squares are obtained and the results interpreted. For realistic results, we resort to the technique of rotation, because such rotations reveal different structures in the data. Finally, factor scores are obtained which help in explaining what the factors mean. They also facilitate comparison among groups of items as groups. With factor scores, one can also perform several other multivariate analyses such as multiple regression, cluster analysis, multiple discriminant analysis, etc.
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Research Methodology Tutorial
Research Methodology: An Introduction
Defining The Research Problem
Measurement And Scaling Techniques
Methods Of Data Collection
Processing And Analysis Of Data
Testing Of Hypotheses I (parametric Or Standard Tests Of Hypotheses)
Analysis Of Variance And Co-variance
Testing Of Hypotheses-ii (nonparametric Or Distribution-free Tests)
Multivariate Analysis Techniques
Interpretation And Report Writing
The Computer: Its Role In Research
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