factor analysis

Understanding of factor analysis describes us a method for investigating whether a number of variables of interest are linearly related to a smaller number of unobservable factors. It determines the strength of relationship between each factor and each observed measure. By the exercises to comprehend factor analysis we derive that it is a statistical tool to account for variability in a set of measured items in terms of a smaller numbers factors. There are several ways to conduct factor analysis and the choice of method depends on many things. We have the options pertaining to the retention of factors. The choice of either selexting factors with eigen values greater than a user- specified value or retaining a fixed number of factors. By looking at the scree plot and the Eigen values over 1 will lead us to retain the same number of factors then continue with analysis.
The objective of the factor analysis is to objectively detect natural groupings of variables. It also aims to extract quantitative information from large matrices using objective statistical criteria. It reduces the redundant data in the list.
The software uses the sample size from which communalities after extraction should probably be above 0.5. The system then finds a factor solution to a set of variables. When the first factor solution does not reveal the hypothesized structure of the loadings, it is customary to apply rotation in an effort to find another set of loadings that fit the observations equally well but can be more easily interpreted. The most widely used of these is the varimax criterion. It seeks the rotated loadings that maximize the variance of the squared loadings for each factor; the goal is to make some of these loadings as large as possible, and the rest as small as absolute value. It encourages the detection of factors each of which is related to few variables. It discourages the detection of factors influencing all variables.
The interpretability of factors can be improved through rotation. Rotation maximizes the loading of each variable on one of the extracted factors whilst minimizing the loading on all other factors. Rotation works through changing the absolute values of the variables whilst keeping their differential values constant.

The scores factor allows one to save factor scores for each subject in the data editor. It reates new column for each factor extracted and then places the factor score for each subject within that column. These scores can then be used for further analysis, or simply to identify groups of subjects who score highly on particular factors. Another feature provided by SPSS is options which helps use to list variables by size.
To analysis the output in SPSS software, the R matrix shows the Pearson correlation coefficient between all pairs of questions whereas the bottom half contains the one tailed significance of these coefficients. We can use this matrix to check the pattern of relations. The significance values details provides the confidence level or the reliability of the data. If any data of significance value more than 0.9 is found, then one should be aware that a problem could arise because of singularity in the data which demands for the check of determinants of the correlation matrix and if necessary eliminate one of the two variables causing the problem. Generally, the data is considered based on the null hypothesis proven right or wrong. Based on the acceptance or rejection of null hypothesis, further analysis is done on the information obtained.

SPSS lists the Eigen values associated with each linear component before extraction, after extraction and after rotation. The eigen values associated with each factor represent the variance explained by that particular linear component and it also displays the eigen values in terms of the percentage of variance explained.

Another output table displays the communalities before and after extraction. The principal component analysis works on the initial assumption that all variance are common, therefore before extraction he communalities are 1. Another way to look at these is in terms of the proportion of variance explained by the underlying factors. The output also explains the component matrix before rotation. This matrix contains loadings of each variable onto each factor.
Another important output is the rotated component matrix which provides with loads of information. It is the matrix that contains same information as the component matrix except that it is calculated after rotation. Before rotation most variables loaded highly onto first factor and the remaining factors didn’t really get a look in.
Therefore, the detailed analysis report explains that SPSS as a tool is every exploratory and is it should be used to guide the researcher to make various decisions. The conclusions derived out of the SPSS analysis can help the leaders to take strategic decisions and build strategies to achieve them.

Regards,
Nisha

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