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August 22, 2024 15:05
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SCM factor structure (WIP)
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| # panel data factor model simulation | |
| # See hollingsworth & wing (2022) tactics for design.. | |
| # paragraph 2.3, assumption 2 | |
| n_timepoints <- 100 | |
| n_unobserved <- 1 | |
| n_units <- 200 | |
| n_covar <- 5 | |
| ru <- 0.6 | |
| mean_ly <- 1 | |
| sd_ly <- 0.1 | |
| sd_ey <- 0.4 | |
| mean_lx <- 1 | |
| sd_lx <- 0.1 | |
| sd_ex <- 0.4 | |
| rarnorm <- function(n, mean = 0, sd = 1, phi = 0) { | |
| # argument checks | |
| stopifnot(abs(phi) < 1) | |
| if (phi == 0) return(rnorm(n, mean, sd)) | |
| # create vector, pick first value, and fill remaining ones | |
| x <- numeric(n) | |
| x[1] <- rnorm(1, mean, sd) | |
| for (i in 2:n) | |
| x[i] <- rnorm(1, mean + phi*(x[i-1]-mean), sqrt(sd^2 - sd^2 * phi^2)) | |
| return(x) | |
| } | |
| # Unobserved common time trend | |
| U <- sapply(1:n_unobserved, \(x) rarnorm(n_timepoints, sd = 1, phi = ru)) | |
| # outcome is a function of common time trend | |
| # the loadings | |
| LY <- matrix(rnorm(n_units*n_unobserved, mean = mean_ly, sd = sd_ly), n_unobserved) | |
| # the residuals, vary over time and units | |
| # transitory shock | |
| EY <- matrix(rnorm(n_timepoints*n_units, sd = sd_ey), n_timepoints) | |
| Y <- U%*%LY + EY | |
| # covariates are also a function of common time trend plus error | |
| LX <- array(rnorm(n_unobserved * n_units * n_covar, mean = mean_lx, sd = sd_lx), dim = c(n_unobserved, n_units, n_covar)) | |
| EX <- array(rnorm(n_timepoints * n_units * n_covar, sd = sd_ex), dim = c(n_timepoints, n_units, n_covar)) | |
| X <- array(dim = c(n_timepoints, n_units, n_covar)) | |
| for (j in 1:n_covar) { | |
| X[,,j] <- U %*% LX[,,j] | |
| } | |
| X <- X + EX | |
| plot(X[,1,1],type = "l") | |
| lines(Y[,1],type = "l", lty = 2) | |
| cor(X[,1,1], Y[,1]) | |
| # the loadings, vary over units but not over time | |
| L <- matrix(rnorm(n_units*n_factors, sd = 1), n_factors) | |
| scores <- array(dim = c(n_timepoints, n_units, n_factors)) | |
| for (t in 1:n_timepoints) { | |
| for (i in 1:n_units) { | |
| scores[t,i,] <- A[t,] * L[,i] | |
| } | |
| } | |
| Y <- A%*%L + E | |
| Y1 <- Y[13:18, 1, drop = FALSE] + 1.5 | |
| Y0 <- Y[13:18, -1] | |
| Z1 <- Y[1:12, 1, drop = FALSE] | |
| Z0 <- Y[1:12, -1] | |
| fit <- pensynth::pensynth(X1 = Y[1:12,1,drop=FALSE], X0 = Y[1:12,-1], lambda = 1e-2) | |
| Y0 <- predict(fit, Y[13:18, -1]) | |
| Ys <- scale(Y[1:12,], scale = FALSE) | |
| Yst <- t(scale(t(Ys), scale = FALSE)) | |
| # fit <- glmnet::cv.glmnet(x = Y[1:12,-1], y = Y[1:12,1]) | |
| # Y0 <- predict(fit, newx = Y[13:18, -1]) | |
| hist(ATT, breaks = "FD") | |
| mean(ATT) | |
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