Interaction variable

In statistics, an interaction variable is one of variables often used in regression analysis. It is formed by the multiplication of two independent variables.

Usage of interaction variables, while offering some useful data, also raises the issues of multicollinearity.

Example

There is a group of participants. Their postural control is being analysed and scored. Each participant performs 6 trials. These trials are based on two manipulated factors.

The two factors are stance (feet apart [S1], feet together [S2]) and vision (normal vision [V1], dim lighting [V2], blindfold [V3]). So the six trials each participant completes are S1+V1, S1+V2, S1+V3, S2+V1, S2+V2, S2+V3.

Now with a repeated measures analysis of variance (ANOVA-RM), the data will be based on two within-subject factors (ie factors which the same subject can perform, as opposed to between subject factors such as gender, age group, intervention protocol, et cetera).

The ANOVA-RM will produce the significance of the difference for each factor (ie main effects) as well as the significance of factor interrelationships (ie interaction effects). So an example of a main effect might be the ANOVA-RM returns a significance level of p=0.001 for the factor 'stance'. This means that there was a significant difference in performance, assuming p=0.001 (or a 0.1% probability that the result is due to chance and not an actual difference) is an acceptable level of significance. What this means is that 99.9% of the time, the difference between the feet apart and feet together conditions will be a result of there being an actual difference in performance (0.1% of the time it is due to coincidence).

With an interaction effect, a significant p-value is returned when multiple factors are considered. For example if stance*vision returns p=0.03. Whilst the significance of the interaction effect is less than that of the main effect, if the p=0.03 meets the pre-determined acceptable significance levels, interaction effects will take precedence over the main effects.

This means a main effect for stance or main effect for vision cannot be considered without acknowledging that an interaction effect was present.

What the interaction effect actually means in this example is that an interrelationship between the factors was found. So in this case, stance influences vision and/or vision influences stance. Assuming the vision influencing stance is true, the postural control system will be more dependent upon vision when the stance condition is more difficult.

That is, in the feet together stance, there is a reduced base of support (so it is a more difficult stance to maintain). In this condition of a reduced base of support, the body might have to compensate by increasing the influence that visual feedback has on the balance control system.

Subsequently, even though the feet together trial might produce a reduced level of postural control compared to the feet apart trial (stance condition - main effect), the stance*vision interaction effect indicates that differences in performance associated with stance are influenced by visual feedback.

Where an interaction effect is present, it is necessary to run a post-hoc test (for example Scheffe, Tukey, Bonferroni) to determine where abouts the interaction effect occurs. In the 2x3 (2 stance conditions x 3 vision conditions) example it may be found that there is only an interaction effect present between one or a few of the variables. So the post-hoc test may indicate that the significance is identified between the following pairs S2V1 and S2V2, S2V2 and S2V3, S2V1 and S2V3, S1V1 and S1V3; whilst the pairs of S1V1 and S1V2 and S1V2 and S1V3 did not produce a significant interaction. Where a significant interaction effect is noted, it is important to remember that this significance may only apply to one of the pairs of conditions.

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Interaction variable

Example

References

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See also