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Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to x1 = conscientiousness score and

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asked 2021-06-24

Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to \(x_{1} =\) conscientiousness score and \(x_{2} = \{1 \text{if highly complex job, 0 if not}\}\), the researchers also used \(x_{3} =\) emotional stability score, \(x_{4} =\) organizational citizenship behavior score, and \(x_{5} =\) counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations?

\(x_{1}\ x_{2}\ x_{3}\ x_{4}\)

Conscientiousness \((x_{1})\)

Job Complexity \((x_{2}).\ 13\)

Emotional Stability \((x_{3}).\ 62.\ 14\)

Organizational Citizenship \((x_{4}).\ 24.\ 03.\ 24\)

Counterproductive Work \((x_{5})-\ .23-\ .23-\ .02-\ .62\)

Answers (1)

2021-06-25

There is a high level of multicollinearity if there is a correlation between a pair of independent variables that is higher than 0.8 or is below —0.8. We note that all values in the matrix are hetween —0.8 and 0.8, thus there is no high level of multicollinearity.
There is a, moderate level of multicollinearity if there is a correlation between a pair of independent variables that is between 0.2 and 0.8 in absolute value. We note that the correlation between emotional stability \(x_{3}\) and conscientiousness 7 is 0.62, which is between 0.2 and 0.8. We then detect a moderate level of multicollinearity.
Since there exists multicollinearity between somepairs of independent variables, we would recommend removing 1 or more independent variables that are moderately correlated.

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