Question

Question: Workplace bullying and intention to leave. Workplace bullying has been shown to have a negative psychological effect on victims, often leading the victim to quit or resign. In Human Resource Management Journal (October 2008), researchers employed multiple regression to examine whether perceived organizational support (POS) would moderate the relationship between workplace bullying and victims’ intention to leave the firm. The dependent variable in the analysis, intention to leave (y), was measured on a quantitative scale. The two key independent variables in the study were bullying (, measured on a quantitative scale) and perceived organizational support (measured qualitatively as “low,” “neutral,” or “high”).

1. Set up the dummy variables required to represent POS in the regression model.
2. Write a model for E(y) as a function of bullying and POS that hypothesizes three parallel straight lines, one for each level of POS.
3. Write a model for E(y) as a function of bullying and POS that hypothesizes three non-parallel straight lines, one for each level of POS.
4. The researchers discovered that the effect of bullying on intention to leave was greater at the low level of POS than at the high level of POS. Which of the two models, parts b and c, support these findings?

Short answer

Answer

1. To represent k levels, (k-1) no of variables will be introduced in the model. Let’s say represents low level of POS while x₂ represents neutral level of POS.
2. A model without interaction can be written as$\mathit{E}\mathbf{\left(}\mathit{Y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathit{x}}_{\mathbf{3}}$
3. A model with interaction can be written as$\mathit{E}\mathbf{\left(}\mathit{Y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathit{x}}_{\mathbf{3}}\mathbf{+}{\mathit{\beta }}_{\mathbf{4}}{\mathit{x}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{5}}{\mathit{x}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{3}}$
4. Model written in part c will be a better fit for the data since the researchers have concluded that there is some interaction between the two variables.

Step-by-step solution

Dummy variables for qualitative variable

The qualitative variable here is perceived organizational support (POS) which has 3 levels of low, neutral and high. To represent k levels, (k-1) no of variables will be introduced in the model. Let’s say x₁represents low level of POS while x₂ represents neutral level of POS.

Model for E(y)

A model for E(y) as a function of bullying and POS that hypothesizes three parallel straight lines, one for each level of POS will be represented by a model without any interaction amongst the variables.

$\mathit{E}\mathbf{\left(}\mathit{Y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathit{x}}_{\mathbf{3}}$

Therefore, a model without interaction can be written as

Where,x₁= low level of POS

x₂ = neutral level of POS.

x₃= bullying

Reproduction for E(y)

A model for E(y) as a function of bullying and POS that hypothesizes three nonparallel straight lines, one for each level of POS will be represented by a model with interaction amongst the variables.

Therefore, a model with interaction can be written as

$\mathit{E}\mathbf{\left(}\mathit{Y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathit{x}}_{\mathbf{3}}\mathbf{+}{\mathit{\beta }}_{\mathbf{4}}{\mathit{x}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{2}}\mathbf{+}{\mathit{\beta }}_{\mathbf{5}}{\mathit{x}}_{\mathbf{2}}{\mathit{x}}_{\mathbf{3}}$

Where, x₁= low level of POS

x₂ = neutral level of POS.

x₃= bullying

Imitation fit for the data

The researchers have concluded that the effect of bullying on intention to leave (y) was greater at low level of POS than at high level of POS indicating that there is some interaction amongst the two variables; bullying and level of POS.

Hence, model written in part c will be a better fit for the data.