Question

Question: Study of supervisor-targeted aggression. “Moonlighters” are workers who hold two jobs at the same time. What are the factors that impact the likelihood of a moonlighting worker becoming aggressive toward his/her supervisor? This was the research question of interest in the Journal of Applied Psychology (July 2005). Completed questionnaires were obtained from n = 105 moonlighters, and the data were used to fit several multiple regression models for supervisor-directed aggression score 1y2. Two of the models (with R²-values in parentheses) are given below:

a. Interpret the R²-values for the models.

b. Give the null and alternative hypotheses for comparing the fits of models 1 and 2.

c. Are the two models nested? Explain.

d. The nested F-test for comparing the two models resulted in F = 42.13 and p-value < .001. What can you conclude from these results?

e. A third model was fit, one that hypothesizes all possible pairs of interactions between self-esteem, history of aggression, interactional injustice at primary job, and abusive supervisor at primary job. Give the equation of this model (model 3).

f. A nested F-test to compare models 2 and 3 resulted in a p-value > .10. What can you conclude from this result?

Short answer

Answer

a. The R² values for the two models are 0.101 and 0.555 respectively. Higher value of R²denotes that the model is a good fit for the data and that approximately what percentage of the variation in the variables is explained by the model. This number is very less for model 1 (only 10%) indicating that the model is not a good fit while for model 2 the value of R² is 55.5% which is still able to explain around 55% variation in the model.

b. The null and alternate hypothesis to test whether the complete model contributes more information for the prediction of y than the reduced model can be written as

H₀: β₅ = β₆ = β₇ = β₈ = 0 whileH_a: At least one of β parameters are nonzero.

c. Two models are nested if one model contains all the terms of the second model and at least one additional term. IN the question model 1 contains 4 terms while model 2 contains 9 terms where 4 are additional terms (β₅, β₆, β₇, and β₈). Hence the two models are nested models where model 1 is reduced model and model 2 is complete model.

d. The nested F-test for comparing the two models resulted in F = 42.13 and p-value < .001. H₀ is rejected if p-value < α. For α = 0.10 or 0.05, p-value <0.001 is very less. Hence, H₀ is rejected.

e. The equation for model 3 with all possible pairs of interaction can be written as ${\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_4{x}_4+{\beta }_5{x}_5+{\beta }_6{x}_6+{\beta }_7{x}_7+{\beta }_8{x}_8+{\beta }_9{x}_5{x}_6+{\beta }_{1}0x_7{x}_8+{\beta }_{1}1x_5{x}_7+{\beta }_{1}2x_5{x}_8+{\beta }_{1}3x_6{x}_7+{\beta }_{1}4x_6{x}_8.$.

f. The nested F-test for comparing model 2 and 3 resulted in p-value > .10. H₀ is rejected if p-value < α. For α = 0.10 or 0.05, p-value > 0.10. Hence, H₀ is not rejected.

Step-by-step solution

Interpretation of R2

The R² values for the two models are 0.101 and 0.555 respectively. Higher value of R²denotes that the model is a good fit for the data and that approximately what percentage of the variation in the variables is explained by the model. This number is very less for model 1 (only 10%) indicating that the model is not a good fit while for model 2 the value of R² is 55.5% which is still able to explain around 55% variation in the model.

Hypotheses

The null and alternate hypothesis to test whether the complete model contributes more information for the prediction of y than the reduced model can be written as

H₀: β₅ = β₆ = β₇ = β₈ = 0 whileH_a: At least one of β parameters are nonzero.

Nested models

Two models are nested if one model contains all the terms of the second model and at least one additional term. IN the question model 1 contains 4 terms while model 2 contains 9 terms where 4 are additional terms (β₅, β₆, β₇, and β₈). Hence the two models are nested models where model 1 is reduced model and model 2 is complete model.

Hypothesis testing

The nested F-test for comparing the two models resulted in F = 42.13 andp-value < .001.

H₀ is rejected if p-value < α. For α = 0.10 or 0.05, p-value <0.001 is very less

Hence, H₀ is rejected.

Model 3 equation

The equation for model 3 with all possible pairs of interaction can be written as${\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_4{x}_4+{\beta }_5{x}_5+{\beta }_6{x}_6+{\beta }_7{x}_7+{\beta }_8{x}_8+{\beta }_9{x}_5{x}_6+{\beta }_{1}0x_7{x}_8+{\beta }_{1}1x_5{x}_7+{\beta }_{1}2x_5{x}_8+{\beta }_{1}3x_6{x}_7+{\beta }_{1}4x_6{x}_8.$.

Hypothesis testing

The nested F-test for comparing model 2 and 3 resulted in p-value > .10.

H₀ is rejected if p-value < α. For α = 0.10 or 0.05, p-value > 0.10.

Thus, H₀ is not rejected.