Multicollinearity and Lack of Specification in Econometric Models

The coincidence in time between the advertising campaigns that the advertiser carry out in different media (TV, Radio, Internet,…) can lead to high correlations between the investments in these media.

The same can happen when sales promotions are conducted in different ways (sales brochure, display, …) simultaneously.

Highly correlated variables can cause problems when we want to build an Econometric Model, the most common problems are: Multicollinearity and the Expulsion of Interesting Variables from the Model. Multicollinearity occurs when there are strong relationships among two or more variables of the model, making it difficult or impossible to isolate their individual effect on the dependent variable. The Expulsion of Interesting Variables from the Model can deprive us of an empirical basis to support specific recommendations related to these variables.

MULTICOLLINEARITY

Originally Multicollinearity meant the existence of a perfect linear relationship among some or all the independent variables in an Econometric Model but today this term means the existence of an approximate linear relationship between them. The absence of Multicollinearity is one of the assumptions of Classical Linear Regression Model because under Multicollinearity several problems related to the precision of the estimates can arise (high variance and covariance, wider Confidence Intervals, higher sensitivity of the estimates to slight variations in the data, … ).

In literature we can find several solutions to this problem: from doing nothing (due to a poor availability of data) to complex statistical methods, including other techniques as: variable transformations, using prior information on the model parameters and many others.

For many years, in Conento we have combined two of the most used methods in Multivariate Statistics: Factor Analysis and Principal Components Analysis. However we have found that these methods are not suitable in certain situations and they pose some limitations: interpretation and scaling problems, they do not take into account the relationship between the explanatory variables and the dependent variable…

These limitations have led us to open new research lines to improve the treatment of Multicollinearity by incorporating new techniques into our method (e.g. factor rotation) and innovative methods such as PLS (Partial Least Squares) Regression.

The wide variety of issues posed by our clients drives us to have a comprehensive set of tools for Statistical Analysis, so that we can offer our clients more precise and accurate solutions.

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