I'm attempting to run a regression analysis on a continuous outcome variable
y, using a primary predictor variable that represents a treatment (
x1, dummy coded with the control group=0, treatment group=1), as well as some other categorical and continuous variables that, for various reasons, I am including in the model as control variables. What I want to do is to be able to take the coefficient result for
x1/the treatment group and and interpret it as the mean difference in
y between the treatment group and the control group, holding all of the confounding variables constant, using the intercept to represent the mean for the control group.
I understand that the intercept is the mean of
y when all X = 0, and thus it represents the mean of
y at the reference category for all categorical variables. I want to be able to take the difference for the treatment effect and calculate that difference as a percentage from Y. Here is my code and output:
> model <- lm(y ~ x1 + x2 + x3 + x4 + x6 + x7, data=df) > summary(model) Call: lm(formula = y ~ x1 + x2 + x3 + x4 + x6 + x7, data = df) Residuals: Min 1Q Median 3Q Max -111.58 -33.77 -8.21 19.02 447.32 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 90.2631 10.8291 8.335 1.50e-14 *** x1Group 2 -31.0268 10.0981 -3.073 0.002433 ** x2Graduate -16.3094 13.3664 -1.220 0.223901 x2HS 11.6441 10.7229 1.086 0.278887 x3yes -2.1632 9.8294 -0.220 0.826047 x4 -1.3587 0.4511 -3.012 0.002944 ** x6yes 43.9864 11.2346 3.915 0.000126 *** x7 14.8018 2.8292 5.232 4.39e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 60.73 on 191 degrees of freedom (1 observation deleted due to missingness) Multiple R-squared: 0.3439, Adjusted R-squared: 0.3199 F-statistic: 14.3 on 7 and 191 DF, p-value: 6.751e-15
In this case, I would want to be able to say that, given the mean of
y = 90.26 and the mean difference for
x1 = -31.03 (resulting in an estimated mean of
58.23) the treatment is associated with a
36% difference in y between the treatment and control groups (58.23/90.26=0.64; 1-0.64=36).
My concern is that the intercept coefficient changes based on which reference category I have chosen for the confounding categorical variables. Assuming that the reference category is college for
x2/education category, would my 36% reduction only apply to patients with a college education and "no" responses for
x6? For my purposes, the categories are arbitrary. I just need to include them in the model because they're associated with
y, and are imbalanced between the treatment and control groups due to some issues with randomization.
Any advice would be greatly appreciated. Thanks in advance.