Group D - Samuel J Stephen


Factor Analysis:

Factor analysis is a process that allows you to take a large set of attribute measures and convert them into a smaller set of interpretable common factors. In essence, the method of factor analysis allows you to simplify a complex set of data and variables. Factor analysis requires the user to complete three steps: Decide on the number of factors, find the factor solution and interpret the factors.

 

Steps in Factor Analysis:

1. Determine the number of factors. Perform principal component analysis on the data to obtain eigenvalues. Create a scree plot of the eigenvalues, with the variance explained on the y axis and the eigenvalue on the x axis. Find the "elbow," or the place where the values suddenly drop in the scree plot. The number of the eigenvalue closest to this elbow is the number of factors you should include in the factor analysis. For example, if after running a principle component analysis and graphing the scree plot you find that the variance explained by the principal components drops off sharply after the fourth eigenvalue, then the most suitable number of factors for your forthcoming factor analysis is four.
2. Run the common factor model. Set the squared multiple correlations as your initial estimates for the commonalities. The end result will be the solution in terms of the number of factors that you selected in the previous step. In the previous example, you had four factors, which means for the common factor model solution you have four as-of-yet unlabeled factors.

3. Interpret the solution. Because the common factor model only rarely produces interpretable solutions, you should apply a rotation to the solution. Try many forms of rotation to get a comparison. Choose a rotation that gives the solution the most interpretability. Interpret each factor in the solution with as few words as possible. In the example, after finding the four-factor solution, you can try rotation methods such as the varimax rotation and the quartimax rotation, comparing their results. Assume you are analyzing breakfast cereal on variables such as "filling," "energizing," "sweet," "fun" and other descriptions and you find the varimax rotation puts words that demonstrate the cereal being healthful such as "filling" and "energizing" together on one factor, then puts words that demonstrate kid-friendly marketing such as "sweet" and "fun" together on another factor. Then this result is easily interpretable, and you can let it be your final solution.

 Methods of Factor Analysis:

Geometrical 

Since the correlation coefficient is the basic statistic in factor analysis, you can perform factor analysis by using the geometrical method. The basic idea behind the geometrical method is to represent the correlation in a scattergram. A scattergram is a visual way of describing and checking the relationships between variables. This method is feasible for small factor analysis studies because each set of variables can be compared, yielding you a set of correlations. This method saves you the complication of dealing with correlation matrices and vectors.

Exploratory 

The main purpose of exploratory factor analysis is to assist the researcher in producing a hypothesis in his study. Exploratory factor analysis works by identifying variables, describing their interrelationships, and then classifying the variables into factor loadings. In this way, the researcher can analyze the complex web of variables and arrive at a hypothesis of how those variables relate to each other.

Confirmatory  

Confirmatory factor analysis works on the assumption that the researcher has already developed a theory from other sources, perhaps including other methods of factor analysis. From this standpoint, confirmatory factor analysis helps the researcher create models for her theory. This form of factor analysis begins with a set of relevant data and results in a factor structure. The researcher then uses the factor structure to validate, falsify or modify her model, depending on how well the data fit. 

 

We will also take a look at some of the terms that were mentioned in today's class:

Scree Plot:

-->

A plot in the descending order of magnitude, of the eigenvalues of a correlation matrix. In the context of factor analysis or principal components analysis a scree plot helps the analyst visualize the relative importance of the factors — a sharp drop in the plot signals that subsequent factors are ignorable.

-->

Thumb rules for Scree Plot:

1. One rule is to consider only those with eigenvalues over 1.
2. Plot all the eigenvalues in their decreasing order.

The Scree plot looks like the side of a mountain, and "scree" refers to the debris fallen from a mountain and lying at its base. So the sree test proposes to stop analysis at the point the mountain ends and the debris (error) begins.
BTW, Scree means 

1. Loose rock debris covering a slope.
2. A slope of loose rock debris at the base of a steep incline or cliff.

 Rotated Component Matrix:

The rotated component matrix helps you to determine what the components represent.