Studies that aim to determine the relationship between two variables, the regression equation is typically applied. However, sometimes the strength or the direction of this relationship could be controlled by other variables. This influencing or control variables are said to be a moderating variable and the effect of these interactions is represented as an interaction effect.
For example, in a causal relationship between salary and health-related expenses, age has an interaction effect. Young people spend comparatively less on their health as compared to older people. Age is thus the moderating variable in the determination of the amount of money spent on health from their salary.
Process of examining the moderating effect presence in regression
As the moderating variable is considered as an independent variable, thus multiple regression analysis is performed for examining the impact of moderating variable and its interaction effect. Following steps are followed to assess the presence of moderating variable in a linkage between variables.
Step 1: Import the data into SPSS
Step 2: Compute the standardized value of independent variables by clicking on Analyze > Descriptive Statistics > Descriptive as shown below.
Select all the independent variables including the moderation variable for computation of standardized values. Click on ‘Save standardized values as variables’ and then select ‘ok’.
Computed standardized values will appear in the datasheet of SPSS as shown below.
Step 3: Determine the interaction effect by clicking on Transform > Compute variables
The new variable needs to be created to store the value of the interaction effect. Name the variable by entering its name in ‘Target Variable’.
Multiply the standardized value of moderator with the standardized value of the independent variable individually and select click on ‘OK’.
A new variable will be created in SPSS Datasheet consisting of interaction effect as shown below.
Note: Repeat the step 3 until interaction effect for each independent variable is computed i.e. in case of three independent variables i.e. A, B, and C and one moderator i.e. M. Step 3 will be repeated thrice i.e. for computing ZA*ZM, ZB*ZM, and ZC*ZM.
Step 4: Regress the dependent variable on the independent variable, moderator, and interaction effect in two blocks wherein 1 block consist of the only independent variable and 2nd block include interaction effect along with independent variable and moderator.
Does age work as a moderating variable factor between salary and health expenses?
In order to validate whether age act as an interacting variable in linking the salary and health expenses, the regression analysis is necessary. Below stated hypothesis is tested to verify this linkage:
H0: There is no moderating effect of age on the linkage between salary and health expenses.
HA: There is a moderating effect of age on the linkage between salary and health expenses.
Results are shown in the below table.
|Health Expense||Coefficient||T-statistic||p-value||R2||Adjusted R2||F Ratio|
|Model without moderation effect|
Above table shows that with the inclusion of the interaction effect of age in the relationship between salary and health expenses, the value of R2 is same i.e. 0.731 but the Adjusted R2 has decreased i.e. from 0.719 to 0.714. Adjusted R2 value shows that about 71.4% of the variation in health expenses is represented by salary wherein age work as a moderator. Furthermore, though still more accurate prediction about health expenses could be done (F-ratio > 1) with the inclusion of interaction effect, this accuracy has decreased i.e. F-ratio decreased from 63.756 to 41.772. Finally, Model 2 has the p-value of 0.710 for interaction effect which shows that the null hypothesis of having no moderating effect of age on the linkage between salary and health expenses is not rejected because the value is greater than the significance level of the study i.e. 0.05. However, the p-value of age shown in model 1 is less than the significance level of the study i.e. 0.005 < 0.05. Thus, age works as an independent variable in influencing the health expenses of a person instead of a moderator.
- Conditional CAPM analysis for stock-based investing - February 20, 2021
- Short term momentum analysis of growth, income and value stocks - February 9, 2021
- Inferential analysis to compare the performance of stocks listed in the BSE (2011-2020) - January 30, 2021