When you apply the MEM to non-linear models, the slopes are no longer linear and will change based on varying levels of the continuous predictor x. Therefore, an incremental increase in predictor variable x will have the same incremental marginal increase in outcome variable y. Why are these the same? The linear regression is predictable in terms of the slope coefficients.
5251667*(.025702) = 24.42243 kg/m^2, which is the same as the value presented in the adjusted prediction output. We will use the Second National Health and Nutrition Examination Survey (NHANES) data from the 1980s, which can be found in Stata’s library using the following command:īMI for a 25-year old subject at the mean = intercept + 25*(beta1) + (mean of Black)*(beta2) + (mean of Other)*(beta3) + (mean of Female)*(beta4) = 24.42243 kg/m^2.īMI for a 25-year old subject at the mean = 23.0528 + 25*(0.0493881) +. (We will focus on the first two, since the third one is an extension of the AME.) The objective of this tutorial is to review these marginal effects and understand their interpretations through examples using Stata.
Marginal effect at representative values (MER)Įach of these marginal effects have unique interpretations that will impact how you examine the regression results. There are three types of marginal effects of interest:ģ. For example, Stata’s margins command can tell us the marginal effect of body mass index (BMI) between a 50-year old versus a 25-year old subject. The marginal effect allows us to examine the impact of variable x on outcome y for representative or prototypical cases. This finding may explain predictor variable x’s impact on outcome variable y, but it doesn’t not tell us the impact of a representative or prototypical case. Where y_i denotes the outcome (dependent) variable for subject i, beta0 denotes the intercept, beta1 is the model coefficient that denotes the change in y due to a 1-unit change in x, and epsilon_i is the error term for subject i.Ī 1-unit increase in x is associated with some change in the outcome y.
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