Question

Personality traits and job performance. Refer to the Journal of Applied Psychology (January 2011) study of the determinants of task performance, Exercise 12.94 (p. 766). In addition to x₁ = conscientiousness score and x₂ = {1 if highly complex job, 0 if not}, the researchers also used x₃ = emotional stability score, x₄ = organizational citizenship behavior score, and x₅ = counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. Below is a matrix of correlations for all possible pairs of independent variables. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations?

Short answer

Multicollinearity is checked by checking the correlation amongst the independent variables. If there is high correlation amongst any two independent variables, it is said that the problem of multicollinearity exists in the model.

Step-by-step solution

Multicollinearity check

Multicollinearity is checked by checking the correlation amongst the independent variables. If there is high correlation amongst any two independent variables, it is said that the problem of multicollinearity exists in the model.

Application of multicollinearity check 

Based on the table provided in the question, there is a moderate level of multicollinearity between emotional stability (x₃) and conscientiousness score (x₁) since the correlation coefficient value of 0.62 and between organizational citizenship (x₄) and counterproductive work (x₅) since the correlation coefficient value is -0.62. For all the other variables the correlation coefficient value is less than 0.25 indicating very low level of multicollinearity.

Recommendations to avoid multicollinearity

Recommendations to avoid multicollinearity are

Drop one or more correlated variables from the model

Do not make inferences about E(y) or future y-values to values of x’s that fall outside the range of the sample data.