Multicollinearity is a state of very high intercorrelations or inter-associations among the independent variables. Multicollinearity is therefore a type of disturbance in the data. If multicollinearity is present in the data, then the statistical inferences made about the data may not be reliable.
Multicollinearity can result in several problems. These problems are as follows:
- The partial regression coefficient due to multicollinearity may not be estimated precisely. Due to multicollinearity, the standard errors are likely to be high.
- Multicollinearity results in a change in the signs as well as in the magnitudes of the partial regression coefficients from one sample to another sample.
- Multicollinearity makes it tedious to assess the relative importance of the independent variables in explaining the variation caused by the dependent variable.
There are certain reasons why multicollinearity occurs:
- Multicollinearity is caused by an inaccurate use of dummy variables.
- Multicollinearity is caused by the inclusion of a variable which is computed from other variables in the equation.
- Multicollinearity can also result from the repetition of the same kind of variable. Practical examples of this include a Nokia N Series user and Nokia 1101 user; the height of the person in feet and the height of the person in inches, etc. In other words, multicollinearity is caused by the inclusion of an almost identical variable twice.
- Multicollinearity generally occurs when the variables are highly and truly correlated to each other.
In the presence of high multicollinearity, the confidence intervals of the coefficients tend to become very wide and the statistics tend to be very small. It becomes difficult to reject the null hypothesis of any study when multicollinearity is present in the data under study.
- Multicollinearity is not something that can be counted.
- Multicollinearity is not discrete in nature; rather, it is continuous.
- Multicollinearity is nothing but a matter of degree.
There are certain signals which help the researcher to detect the degree of multicollinearity.
One such signal is if the individual outcome of a statistic is not significant but the overall outcome of the statistic is significant. In this instance, the researcher might get a mix of significant and insignificant results that show the presence of multicollinearity.
Suppose the researcher, after dividing the sample into two parts, finds that the coefficients of the sample differ drastically. This indicates the presence of multicollinearity. This means that the coefficients are unstable due to the presence of multicollinearity.
Suppose the researcher observes drastic change in the model by simply adding or dropping some variable. This also indicates that multicollinearity is present in the data.
Multicollinearity can also be detected with the help of tolerance and its reciprocal, called variance inflation factor (VIF). If the value of tolerance is less than 0.2 or 0.1 and, simultaneously, the value of VIF is 5 or 10 and above, then the multicollinearity is very severe.
Multicollinearity can also be examined with the help of a condition number. It is a conditional index having the largest value. Mathematically, it can be defined as the square root of the largest eigenvalue being divided by the square root of the smallest eigenvalue. If there is no multicollinearity, then the condition number will give the value of one. If the multicollinearity increases, then the eigenvalues will be greater and smaller than one. If the eigenvalue becomes close to zero, then there is a serious multicollinearity problem. Basically, if the condition number is 15, then multicollinearity is a concern. If it is greater than 30, then multicollinearity is a very serious concern for the researcher performing the study.
Contact Statistics Solutions today for a free consultation on multicollinearity.
