# Method of main components

The method of the main components is based on attemptsexplain the maximum level of variance in a certain set of variables, and focuses on the elements located in the correlation matrix along the diagonal. There is another method based on factor analysis aimed at approximating the correlation matrix using a certain number of factors (less than a given number of variables), but the methods of approximation differ substantially from the first proposed method.

So, the method of factor analysis allows us to explain the correlation between the variables themselves, and is oriented on the elements of a correlation matrix that are outside its diagonal.

Based on practical application, we will tryto understand the need to apply this or that method. Factor analysis is used when there is an interest of the researcher in studying the relationship between variables, the method of the main components is used in the case of the need to reduce the dimensionality of the data and to a lesser extent requires an interpretation of them.

Based on practice, we can see that methodsFactor analysis uses a fairly large number of observations. At the same time, this quantity must be higher by an order of magnitude than the number of detected factors.

The method of the main components is very popularin marketing research, since it can be used in the presence of multicollinear initial data. In the process of such marketing research, the questionnaires contain similar questions, and the answers received will correspond to the principles of multicollinearity.

The method of the main components is expedientconsider in the aggregate of indicators, which should be for the researcher a reference point with a preliminary choice of the number of components or factors. The most important of these are the eigenvalues, expressing the variance of the variables, explained by this factor. There is also one important empirical rule, which is very useful for estimating the number of factors (there must be as many factors as there are eigenvalues ​​over one). It is possible to explain this rule in a somewhat simpler way - the eigenvalues ​​express the fraction of the normalized variances of variables that are explained by the factor, and in the case of exceeding one they must express these variances contained in more than one variable.

It is necessary to clarify once again that rule"Individual eigenvalues" is an empirical one, and the question of the necessity of its application can be solved only by the researcher himself. For example, an eigenvalue has a value less than one, but it explains the spread that is distributed between the variables. For a specialist in marketing, it is very important that when segmenting the identified factors have a meaningful meaning. And those factors containing their own numbers above unity, but not having a meaningful interpretation, will not be taken into account. And the situation can arise quite the opposite.

Another important issue related to the practicalthe application of methods of factor analysis - the question of rotation. Such variants of rotation can be considered. The most popular of these is the varimax method. It is based on the achievement of the maximum level of variance of variables for each individual factor. This method helps to find a rotation in which some variables take high values, while others - are sufficiently low for each individual factor.

Another method of rotation is quartax, it helps to find a certain turn in which factors for each individual variable have both low and high loads.

The method of rotation of equimax is some compromise between the two methods discussed above.

All these methods relate to orthogonal with mutually perpendicular axes; when used, there is a lack of correlation between individual factors.

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