Interaction between numerical variables in regression model, and its graphical interpretation

Abstract

Background and aim: One of the most important steps in the models to be established in order to define the relationships between the measured characteristics in health field research is to define the effects in the model correctly. One of these effects is the interaction effect, which is rarely used in practice, but on the contrary, should be required frequently used. The aim of this study, the concept of interaction between numerical independent variables, which is rarely used because it is little known in regression-like models, is to be presented with an easily interpretable graphical result.

Materials and methods: The data used to emphasize the interpretation and importance of the interaction in the regression model were produced by simulation based on the descriptive statistics and distribution patterns of the data in a real study. The data set includes the systolic blood pressures (SBP) of 167 people aged between 40 and 76 and a body mass index between 21 and 52. Age and body mass index were defined as independent variables and SBP as dependent variables.

Results: In the model without interaction, it was observed that an increase in body mass index increased SBP when age was kept constant, and an increase in age increased SBP when body mass index was kept constant. Although this result is sufficient, appropriate, and meaningful for the practitioner, it will not make sense without knowing the importance and meaning of the interaction between body mass index and age. When the interaction term was added to the model, it was seen that the above described result could lead to an invalid and erroneous interpretation. It was seen that the effect of a 1-unit change observed in body mass index on SBP differs at various ages and the effect of a 1-year increase in age on SBP differs according to body mass index values. In this case, it has emerged that a physician who will make a clinical decision should also consider age when deciding on SBP according to body mass index (or vice versa). In addition, the contour graphic method, which will facilitate the work of the practitioners in the interpretation of the interaction, will make a significant contribution to the evaluation of this term in models.

Conclusion: Using an incorrect or incomplete model in data analysis results in, erroneous or incomplete results. The modeling process in healthcare research involving complex relationships requires substantial knowledge, domain knowledge, modeling knowledge, and accurate interpretation of results. Examining the interaction terms is of great importance in the modeling process. If this effect is significant, the actual effects of the interacting effects are meaningless and their interpretation will yield erroneous results.

Bangladesh Journal of Medical Science Vol. 22 No. 01 January’23 Page : 189-194