This code generates population level data to test the estimation function. This data set incorporates splines in the MTRs.
gendistSplines()a list of two data.frame objects. One is the distribution of the simulated data, the other is the full simulated data set.
The distribution of the data is as follows
| Z X/Z | 0 1 _______|___________ -1 | 0.1 0.1 | X 0 | 0.2 0.2 | 1 | 0.1 0.2
The data presented below will have already integrated over the unobservable terms U, and U | X, Z ~ Unif[0, 1].
The propensity scores are generated according to the model
p(x, z) = 0.5 - 0.1 * x + 0.2 * z
| Z p(X,Z) | 0 1 _______|___________ -1 | 0.6 0.8 | X 0 | 0.5 0.7 | 1 | 0.4 0.6
The lowest common multiple of the first table is 12. The lowest common multiple of the second table is 84. It turns out that 840 * 5 = 4200 observations is enough to generate the population data set, such that each group has a whole-number of observations.
The MTRs are defined as follows:
y1 ~ beta0 + beta1 * x + uSpline(degree = 2, knots = c(0.3, 0.6), intercept = FALSE)
The coefficients (beta1, beta2), and the coefficients on the splines, will be defined below.
y0 = x : uSpline(degree = 0, knots = c(0.2, 0.5, 0.8), intercept = TRUE) + uSpline(degree = 1, knots = c(0.4), intercept = TRUE) + beta3 * I(u ^ 2)
The coefficient beta3, and the coefficients on the splines, will be defined below.