The principal component is based on trying to explain the maximum level of variance in a certain set of variables, and oriented to elements located in the correlation matrix diagonal.There is another method, based on factor analysis aimed at implementing the approximation of the correlation matrix with a certain number of factors (less than the predetermined number of variables), but by the approximation method essentially differs from the first proposed method.
Thus, the method of factor analysis can explain the correlation between the variables themselves, and oriented on the elements of the correlation matrix type, beyond its diagonal.
Based on practical applications, try to understand the need to use a particular method.Factor analysis is used when there is the interest of the researchers in the study of the relationship between the variables, the principal components method is used in case of the need to reduce the dimension of the data and to a lesser extent their interpretation is required.
From our experience, we can see that the methods of factor analysis using a sufficiently large number of observations.This amount should be an order of magnitude higher than the number of identified factors.
The principal component is very popular in marketing research, because it can be used in the presence of multicollinearity source data.In the process of marketing research questionnaires contain similar questions, and the answers to them, and will conform to the principles of multicollinearity.
The principal component is appropriate to consider in the aggregate indicators, which should be a guide for the researcher in the preliminary choice of the number of components or factors.The most important of these are the eigenvalues of expressing the level of dispersion of the variables are explained by this factor.There is one important rule of thumb, which is very useful for estimating the number of factors (to be many factors as there are eigenvalues of more than one).This rule can explain a little bit easier - their own share of express normalized variances of variables that explains the factors in the case of exceeding his unit they should express those dispersions containing more than one variable.
necessary to clarify once again that the rule of "single eigenvalues" - thumb, and the need for its application can be resolved only by the researcher.For example, the proper number has a value less than unity, but it is due to the spread, distributed between variables.Those skilled in the field of marketing is very important that the segmentation of the identified factors were substantial sense.And those factors having eigenvalues over the unit, but do not have a meaningful interpretation, they are not taken into account.And the situation can arise quite the contrary.
Another important question regarding the practical application of factor analysis - the question of the rotation.It may consider such options for the rotation.The most popular of them - varimax method.It is based on achieving the maximum level of dispersion of variables on each individual factor.This method helps to find a rotation, in which some variables are high values, while others - low enough to each individual factor.
Another method of rotation - kvartimaks, it helps to find a particular turn in which the factors for each individual variable are both low and high loads.
ekvimaks rotation method is a compromise between the two methods discussed above.
All these methods are orthogonal with mutually perpendicular axes, their use can be traced no correlation between the individual factors.
