Interaction
- One predictor’s effect on the outcome changes depending on the level or value of another predictor.
- When interaction is present, the relationship between the response and a given explanatory variable differs across values of a second explanatory variable.
- Detecting and interpreting interactions typically requires statistical methods that include interaction terms and assess their significance.
Definition
Section titled “Definition”Interaction in explanatory variables occurs when the effect of one explanatory variable on the response variable depends on the value of another explanatory variable. In other words, the relationship between the response variable and one of the explanatory variables is different for different values of the other explanatory variable.
Explanation
Section titled “Explanation”If two explanatory variables interact, the influence of one explanatory variable on the response cannot be fully described without specifying the value of the other explanatory variable. This means that the marginal relationship between the response and a single explanatory variable varies across subgroups defined by the other explanatory variable.
Examples
Section titled “Examples”Student study time (variable A) and home environment (variable B)
Section titled “Student study time (variable A) and home environment (variable B)”We expect that more time spent studying leads to better academic performance. However, the relationship between study time and academic performance might differ by home environment. For students with a high-quality home environment, the relationship between study time and academic performance might be relatively strong, while for students with a low-quality home environment, the relationship between the two variables might be weaker. This constitutes an interaction between the two explanatory variables.
Medical treatment (variable A), medical condition, and patient age (variable B)
Section titled “Medical treatment (variable A), medical condition, and patient age (variable B)”A study on the effectiveness of a medical treatment might include the type of medical condition (variable A) and the patient’s age (variable B). The treatment could be more effective for some medical conditions than others, and its effectiveness might also depend on the patient’s age. For example, the treatment might be more effective for younger patients with certain medical conditions and less effective for older patients with the same conditions. This is an example of interaction between explanatory variables.
Use cases
Section titled “Use cases”- Properly analyzing and interpreting data when the effect of one explanatory variable depends on another.
- Using statistical techniques that account for interaction effects to determine whether an observed interaction is statistically significant and to provide insight into the nature of the relationships between variables.
Related terms
Section titled “Related terms”- Explanatory variables
- Response variable
- Interaction effects