Multicollinearity

Multicollinearity is a state of very high intercorrelations or inter-associations among the independent variables. It is therefore a type of disturbance in the data, and if present in the data the statistical inferences made about the data may not be reliable.

There are certain reasons why multicollinearity occurs:

• It is caused by an inaccurate use of dummy variables.
• It is caused by the inclusion of a variable which is computed from other variables in the data set.
• Multicollinearity can also result from the repetition of the same kind of variable.
• Generally occurs when the variables are highly correlated to each other.

Multicollinearity can result in several problems. These problems are as follows:

• The partial regression coefficient due to multicollinearity may not be estimated precisely. 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.

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.

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 10 and above, then the multicollinearity is problematic.