Question

Workplace bullying and intention to leave. Refer to the Human Resource Management Journal (October 2008) study of workplace bullying, Exercise 12.91 (p. 765). Recall that multiple regression was used to model an employee’s intention to leave (y) as a function of bullying (x₁, measured on a quantitative scale) and perceived organizational support (measured qualitatively as “low POS,” “neutral POS,” or “high POS”). In Exercise 12.91b, you wrote a model for E(y) as a function of bullying and POS that hypothesizes three parallel straight lines, one for each level of POS. In Exercise 12.91c, you wrote a model for E(y) as a function of bullying and POS that hypothesizes three nonparallel straight lines, one for each level of POS.

a) Explain why the two models are nested. Which is the complete model? Which is the reduced model?

b) Give the null hypothesis for comparing the two models.

c) If you reject H₀ in part b, which model do you prefer? Why?

d) If you fail to reject H₀ in part b, which model do you prefer? Why?

Short answer

a) The two models are nested models because the first model is a reduced model because this model represents three parallel lines indicating no interaction. While the other model is a complete model representing three nonparallel lines denoting model with interaction hence added variables representing interaction amongst the variables.

b) The null and alternate hypothesis for comparing the two models can be written as H₀: β₄ = β₅ = 0 while H_a: At least one of β parameters are nonzero.

c) If H₀ is rejected in part b, then model with interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is statistically useful for predicting E(y).

d) If H₀ is not rejected in part b, then model without any interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is not statistically useful for predicting E(y).

Step-by-step solution

Nested and complete model

The two models are nested models because the first model is a reduced model because this model ($E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3$)represents three parallel lines indicating no interaction. While the other model ($E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_4{x}_1{x}_3+{\beta }_5{x}_2{x}_3$

)is a complete model representing three nonparallel lines denoting model with interaction hence added variables representing interaction amongst the variables.

Hypotheses

The null and alternate hypothesis for comparing the two models can be written as

H₀: β₄ = β₅ = 0while H_a: At least one of β parameters are nonzero.

Interpretation of thesis testing

If H₀ is rejected in part b, then model with interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is statistically useful for predicting E(y).

Clarification of theorem testing

If H₀ is not rejected in part b, then model without any interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is not statistically useful for predicting E(y).