tests/integration/test_integration__case_2_square_noncartesian.R
In LukeCe/spflow: Spatial Econometric Interaction Models
# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
# Project: spflow - integration test case 2
# Author: Lukas Dargel
# = = = = = = = = = = = = = = = = = = =
# Description:
#
# The script tests the integration of the package functions based on the
# simulated flows within the stylized states of the USA.
# The test case covers:
# - "model_1" and "model_2" and "model_9"
# - "non-Cartesian" flows: only a subset of all possible OD pairs are used
# - "Square" flows: within the same network
# - estimators: "ols" and "twosls" (exact tests)
# - estimators: "mle" and "mcmc" (approximate tests)
# = = = = = = = = = = = = = = = = = = =
# Date: Aug 2022
opts <- options(warn = 1)
# cran packages
library("Matrix")
library("spflow")
library("tinytest")
# data
data("multi_net_usa_ge")
data("simulation_params")
test_dir <- ""
# test_dir <- "tests/integration/" # uncomment for interactive check
usa_usa_vec_data <-
readRDS(paste0(test_dir,"vec_data_usa_ge.Rds"))[["usa_usa"]]
usa_usa_pairnb <-
readRDS(paste0(test_dir,"pair_neighborhoods_usa_ge.Rds"))[["usa_usa"]]
# ---- define target objects --------------------------------------------------
# ---- ... model matrices -----------------------------------------------------
OW <- W <- neighborhood(multi_net_usa_ge, "usa")
OX <- dat(multi_net_usa_ge, "usa")[,"X", drop = FALSE]
OX[["X_lag.1"]] <- as.vector(W %*% OX$X)
n <- nrow(W)
OX[["X_lag.1"]] <- as.vector(OW %*% OX$X)
OX_inst <- data.frame(
"X_lag.2" = as.vector(OW %*% OX$X_lag.1),
"X_lag.3" = as.vector(OW %*% OW %*% OX$X_lag.1))
DX <- OX
DX_inst <- OX_inst
od_dat <- dat(multi_net_usa_ge, "usa_usa")
o_index <- as.integer(od_dat[["ID_ORIG"]])
d_index <- as.integer(od_dat[["ID_DEST"]])
sparse_matrix_form <- function(vec) {
sparseMatrix(i = d_index,
j = o_index,
x = vec,
dims = c(n,n))
}
dense_matrix_form <- function(vec) {
mat <- matrix(0, n,n)
mat[cbind(d_index, o_index)] <- vec
return(mat)
}
flow_indicator <- sparse_matrix_form(1L)
target_matrices <- list(
"D_" = as.matrix(OX),
"O_" = as.matrix(OX),
"I_" = as.matrix(OX[,1]),
"OW" = W,
"P_" = list(
"DISTANCE" = sparse_matrix_form(usa_usa_vec_data[,"P_DISTANCE"])),
"Y1_" = list(
"y1" = sparse_matrix_form(usa_usa_vec_data[,"y1"])),
"Y2_" = list(
"y2" = sparse_matrix_form(usa_usa_vec_data[,"y2"]),
"y2.d" = flow_indicator * (W %*% sparse_matrix_form(usa_usa_vec_data[,"y2"]))),
"Y9_" = list(
"y9" = sparse_matrix_form(usa_usa_vec_data[,"y9"]),
"y9.d" = flow_indicator * (W %*% sparse_matrix_form(usa_usa_vec_data[,"y9"])),
"y9.o" = flow_indicator * tcrossprod(sparse_matrix_form(usa_usa_vec_data[,"y9"]),W),
"y9.w" = flow_indicator * tcrossprod(W %*% sparse_matrix_form(usa_usa_vec_data[,"y9"]),W)),
"flow_indicator" = flow_indicator
)
# ---- ... moments ------------------------------------------------------------
dep_vars <- paste0("y", c(9,2,1))
Z <- usa_usa_vec_data[,!colnames(usa_usa_vec_data) %in% dep_vars]
## derive lags
od_indicator <- as.logical(as.vector(flow_indicator))
W_o <- W %x% diag(n)
W_o <- W_o[od_indicator,od_indicator]
W_d <- diag(n) %x% W
W_d <- W_d[od_indicator,od_indicator]
W_w <- W %x% W
W_w <- W_w[od_indicator,od_indicator]
# lags of flows
Y_t2 <- usa_usa_vec_data[,"y2", drop = FALSE]
Y_t2 <- cbind(
Y_t2,
"y2.d"= as.vector(W_d %*% Y_t2))
Y_t9 <- usa_usa_vec_data[,"y9", drop = FALSE]
Y_t9 <- cbind(
Y_t9,
"y9.d" = as.vector(W_d %*% Y_t9),
"y9.o" = as.vector(W_o %*% Y_t9),
"y9.w" = as.vector(W_w %*% Y_t9))
# lags as instruments
U_alpha <- usa_usa_vec_data[,"(Intercept)", drop = FALSE]
iota_I <- usa_usa_vec_data[,"(Intra)"]
U_alpha_I <- cbind(
"wI" = as.vector(W_d %*% iota_I),
"Iw" = as.vector(W_o %*% iota_I),
"wIw" = as.vector(W_w %*% iota_I),
"wwI" = as.vector(W_d %*% W_d %*% iota_I),
"Iww" = as.vector(W_o %*% W_o %*% iota_I),
"wwIw" = as.vector(W_d %*% W_w %*% iota_I),
"wIww" = as.vector(W_w %*% W_o %*% iota_I),
"wwIww" = as.vector(W_w %*% W_w %*% iota_I))
colnames(U_alpha_I) <- paste0("(Intra).", colnames(U_alpha_I))
U_alpha_I <- cbind("(Intra)" = iota_I, U_alpha_I)
lag_names <- c("", paste0(".lag",1:3))
U_beta_d <- usa_usa_vec_data[,c("D_X","D_X.lag1")]
U_beta_d <- cbind(U_beta_d,as.matrix(DX_inst[d_index,]))
colnames(U_beta_d) <- paste0("D_X", lag_names)
U_beta_o <- usa_usa_vec_data[,c("O_X","O_X.lag1")]
U_beta_o <- cbind(U_beta_o,as.matrix(DX_inst[o_index,]))
colnames(U_beta_o) <- paste0("O_X", lag_names)
lag_names <- c("", paste0(".lag",1:2))
U_beta_I <- U_beta_o[,1:3] * iota_I
colnames(U_beta_I) <- paste0("I_X", lag_names)
U_gamma <- usa_usa_vec_data[,"P_DISTANCE"]
U_gamma <- cbind(U_gamma, W_w %*% U_gamma, W_w %*% W_w %*% U_gamma)
colnames(U_gamma) <- paste0("P_DISTANCE", c("", ".wGw", ".wwGww"))
U <- cbind(U_alpha,U_alpha_I,U_beta_d,U_beta_o,U_beta_I,U_gamma)
target_moments <- list(
# all models
"ZZ" = as.matrix(crossprod(Z)),
"UU" = as.matrix(crossprod(U)),
# model 1
"ZY1" = as.matrix(crossprod(Z,usa_usa_vec_data[,"y1", drop = FALSE])),
"TSS1" = as.matrix(crossprod(usa_usa_vec_data[,"y1", drop = FALSE])),
# model 2
"ZY2" = as.matrix(crossprod(Z,Y_t2)),
"UY2" = as.matrix(crossprod(U,Y_t2)),
"TSS2" = as.matrix(crossprod(Y_t2)),
# model 9
"ZY9" = as.matrix(crossprod(Z,Y_t9)),
"UY9" = as.matrix(crossprod(U,Y_t9)),
"TSS9" = as.matrix(crossprod(Y_t9)))
# ---- ... results ------------------------------------------------------------
# ols_results
N_s <- nrow(usa_usa_vec_data)
delta1_ols <- solve(
as.matrix(target_moments[["ZZ"]]),
as.vector(target_moments[["ZY1"]]))
e1 <- usa_usa_vec_data[,"y1"] - (Z %*% delta1_ols)
sigma1_ols <- as.vector(sqrt(crossprod(e1)/N_s))
# s2sls results for model 2
L2_hat <- U %*% solve(
target_moments[["UU"]],
target_moments[["UY2"]][, -1])
colnames(L2_hat) <- "rho_d"
Z2_hat <- cbind(L2_hat,Z)
ZZ2 <- crossprod(Z2_hat)
ZY2_hat <- as.vector(crossprod(Z2_hat,usa_usa_vec_data[,"y2",drop = FALSE]))
mu2_s2sls <- solve(as.matrix(ZZ2),ZY2_hat)
ZY2_tilde <- cbind(Y_t2[,-1], Z)
e2 <- usa_usa_vec_data[,"y2"] - ZY2_tilde %*% mu2_s2sls
sigma2_s2sls <- as.vector(sqrt(crossprod(e2)/N_s))
# s2sls results for model 9
L9_hat <- U %*% solve(
target_moments[["UU"]],
target_moments[["UY9"]][, -1])
colnames(L9_hat) <- paste0("rho_",c("d","o","w"))
Z9_hat <- cbind(L9_hat,Z)
ZZ9 <- crossprod(Z9_hat)
ZY9_hat <- as.vector(crossprod(Z9_hat,usa_usa_vec_data[,"y9",drop = FALSE]))
mu9_s2sls <- solve(as.matrix(ZZ9),ZY9_hat)
ZY9_tilde <- cbind(Y_t9[,-1], Z)
e9 <- usa_usa_vec_data[,"y9"] - ZY9_tilde %*% mu9_s2sls
sigma9_s2sls <- as.vector(sqrt(crossprod(e9)/N_s))
# all results
target_results <- list(
# ols
"delta1_ols" = delta1_ols,
"sigma1_ols" = sigma1_ols,
# s2sls
"mu2_s2sls" = mu2_s2sls,
"sigma2_s2sls" = sigma2_s2sls,
"mu9_s2sls" = mu9_s2sls,
"sigma9_s2sls" = sigma9_s2sls,
# ground truth
"mu2_input" = c(simulation_params$rho["rho_d"], simulation_params$delta),
"mu9_input" = c(simulation_params$rho, simulation_params$delta),
"sigma_input" = simulation_params$sd_error
)
# ---- run tests --------------------------------------------------------------
expect_zero_diff <- function(y,x) expect_equal(max(abs(x - y)), 0)
# ---- ... ols - model 1 ------------------------------------------------------
res_model_1_ols <- spflow(
y1 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "ols", model = "model_1"))
# test results
expect_inherits(res_model_1_ols, "spflow_model_ols")
expect_true(res_model_1_ols@estimation_diagnostics[["R2_corr"]] > 0)
expect_equal(target_results$delta1_ols, coef(res_model_1_ols))
expect_equal(target_results$sigma1_ols, sd_error(res_model_1_ols))
# test moments
actual_moments <- res_model_1_ols@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY1"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS1"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_1_ols@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y1_"]][[1]], actual_matrices[["Y_"]][[1]])
# test residuals and goodness of fit
expectied_signal <- as.vector(Z %*% target_results$delta1_ols)
expect_zero_diff(expectied_signal, fitted(res_model_1_ols))
expect_zero_diff(expectied_signal, predict(res_model_1_ols, return_type = "V"))
rm(res_model_1_ols)
# ---- ... s2sls - model 2 ----------------------------------------------------
res_model_2_s2sls <- spflow(
y2 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_2"))
# test results
expect_inherits(res_model_2_s2sls, "spflow_model_s2sls")
expect_equal(target_results$mu2_s2sls, coef(res_model_2_s2sls))
expect_equal(target_results$sigma2_s2sls, sd_error(res_model_2_s2sls))
# test moments
actual_moments <- res_model_2_s2sls@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["UU"]], actual_moments[["UU"]])
expect_zero_diff(target_moments[["ZY2"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["UY2"]], actual_moments[["UY"]])
expect_zero_diff(target_moments[["TSS2"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_2_s2sls@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[2]], actual_matrices[["Y_"]][[2]])
# test predictors
expected_signal <- as.vector(Z %*% target_results$mu2_s2sls[-1])
expect_zero_diff(expected_signal, res_model_2_s2sls@spflow_indicators$SIGNAL)
rd <- target_results$mu2_s2sls[1]
expected_trend <- W_d %*% usa_usa_vec_data[,"y2"] * rd
expect_zero_diff(expected_signal + expected_trend, predict(res_model_2_s2sls,method = "TS", return_type = "V"))
A2 <- diag(length(expected_trend)) - W_d * rd
dg_AA2 <- diag(crossprod(A2))
y2 <- usa_usa_vec_data[,"y2"]
bpi_corr <- crossprod(A2, y2 - expected_trend - expected_signal)
expected_bpi <- y2 - bpi_corr/dg_AA2
expect_zero_diff(expected_bpi, predict(res_model_2_s2sls,method = "BPI", return_type = "V"))
expected_tc <- solve(A2, expected_signal)
expected_tca <- expected_signal + (W_d * rd + W_d %*% W_d * rd^2 + W_d %*% W_d %*% W_d * rd^3) %*% expected_signal
expect_zero_diff(expected_tca, predict(res_model_2_s2sls,method = "TC", return_type = "V",expectation_approx_order = 3))
expect_zero_diff(expected_tc, predict(res_model_2_s2sls,method = "TC", return_type = "V",approx_expectation = FALSE))
bpa_corr <- A2 %*% crossprod(A2, y2 - expected_tc)
expected_bpa <- expected_tc - bpa_corr/dg_AA2
expect_zero_diff(expected_bpa, predict(res_model_2_s2sls,method = "BPA", return_type = "V",approx_expectation = FALSE))
bp_corr <- A2 %*% crossprod(A2, y2 - expected_tc)
expected_bp <- expected_tc - solve(crossprod(A2), bp_corr)
expect_zero_diff(expected_bp, predict(res_model_2_s2sls,method = "BP", return_type = "V",approx_expectation = FALSE))
rm(res_model_2_s2sls, rd)
# ---- ... s2sls - model 9 ----------------------------------------------------
res_model_9_s2sls <- spflow(
y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_9"))
# test results
expect_inherits(res_model_9_s2sls, "spflow_model_s2sls")
expect_equal(target_results$mu9_s2sls, coef(res_model_9_s2sls))
expect_equal(target_results$sigma9_s2sls, sd_error(res_model_9_s2sls))
# test moments
actual_moments <- res_model_9_s2sls@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["UU"]], actual_moments[["UU"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["UY9"]], actual_moments[["UY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_s2sls@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[2]], actual_matrices[["Y_"]][[2]])
expect_zero_diff(target_matrices[["Y9_"]][[3]], actual_matrices[["Y_"]][[3]])
expect_zero_diff(target_matrices[["Y9_"]][[4]], actual_matrices[["Y_"]][[4]])
# test predictors
expected_signal <- as.vector(Z %*% target_results$mu9_s2sls[-(1:3)])
expect_zero_diff(expected_signal, res_model_9_s2sls@spflow_indicators$SIGNAL)
r9 <- target_results$mu9_s2sls[1:3]
WF9 <- W_d * r9[1] + W_o * r9[2] + W_w * r9[3]
expected_trend <- expected_trend <- WF9 %*% usa_usa_vec_data[,"y9"]
expect_zero_diff(expected_signal + expected_trend, predict(res_model_9_s2sls, method = "TS", return_type = "V"))
A9 <- diag(length(expected_trend)) - WF9
dg_AA9 <- diag(crossprod(A9))
y9 <- usa_usa_vec_data[,"y9"]
bpi_corr <- crossprod(A9, y9 - expected_trend - expected_signal)
expected_bpi <- y9 - bpi_corr/dg_AA9
expect_zero_diff(expected_bpi, predict(res_model_9_s2sls,method = "BPI", return_type = "V"))
expected_tc <- solve(A9, expected_signal)
expected_tca <- expected_signal + (WF9 + WF9 %*% WF9 + WF9 %*% WF9 %*% WF9) %*% expected_signal
expect_zero_diff(expected_tca, predict(res_model_9_s2sls,method = "TC", return_type = "V",expectation_approx_order = 3))
expect_zero_diff(expected_tc, predict(res_model_9_s2sls,method = "TC", return_type = "V",approx_expectation = FALSE))
bpa_corr <- A9 %*% crossprod(A9, y9 - expected_tc)
expected_bpa <- expected_tc - bpa_corr/dg_AA9
expect_zero_diff(expected_bpa, predict(res_model_9_s2sls,method = "BPA", return_type = "V",approx_expectation = FALSE))
bp_corr <- A9 %*% crossprod(A9, y9 - expected_tc)
expected_bp <- expected_tc - solve(crossprod(A9), bp_corr)
expect_zero_diff(expected_bp, predict(res_model_9_s2sls,method = "BP", return_type = "V",approx_expectation = FALSE))
rm(res_model_9_s2sls)
# ---- ... mle - model 2 ------------------------------------------------------
res_model_2_mle <- spflow(
y2 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "mle", model = "model_2"))
# test results
expect_inherits(res_model_2_mle, "spflow_model_mle")
expect_equal(names(target_results$mu2_input),
names(coef(res_model_2_mle)))
expect_equal(target_results$mu2_input / coef(res_model_2_mle),
rep(1,9), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_2_mle),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_2_mle@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY2"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS2"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_2_mle@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[2]], actual_matrices[["Y_"]][[2]])
rm(res_model_2_mle)
# ---- ... mle - model 9 ------------------------------------------------------
res_model_9_mle <- spflow(
y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "mle", model = "model_9"))
# test results
expect_inherits(res_model_9_mle, "spflow_model_mle")
expect_equal(names(target_results$mu9_input), names(coef(res_model_9_mle)))
expect_equal(target_results$mu9_input / coef(res_model_9_mle),
rep(1,11), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_9_mle),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_9_mle@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_mle@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[2]], actual_matrices[["Y_"]][[2]])
expect_zero_diff(target_matrices[["Y9_"]][[3]], actual_matrices[["Y_"]][[3]])
expect_zero_diff(target_matrices[["Y9_"]][[4]], actual_matrices[["Y_"]][[4]])
rm(res_model_9_mle)
# ---- ... mcmc - model 2 -----------------------------------------------------
res_model_2_mcmc <- spflow(
spflow_formula = y2 ~ . + P_(DISTANCE),
spflow_networks = multi_net_usa_ge,
id_net_pair = "usa_usa",
estimation_control = spflow_control(estimation_method = "mcmc", model = "model_2"))
# test results
expect_inherits(res_model_2_mcmc, "spflow_model_mcmc")
expect_equal(names(target_results$mu2_input), names(coef(res_model_2_mcmc)))
expect_equal(target_results$mu2_input / coef(res_model_2_mcmc),
rep(1,9), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_2_mcmc),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_2_mcmc@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY2"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS2"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_2_mcmc@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[2]], actual_matrices[["Y_"]][[2]])
rm(res_model_2_mcmc)
# ---- ... mcmc - model 9 -----------------------------------------------------
res_model_9_mcmc <- spflow(
y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "mcmc", model = "model_9"))
# test results
expect_inherits(res_model_9_mcmc, "spflow_model_mcmc")
expect_equal(names(target_results$mu9_input), names(coef(res_model_9_mcmc)))
expect_equal(target_results$mu9_input / coef(res_model_9_mcmc),
rep(1,11), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_9_mcmc),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_9_mcmc@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_mcmc@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[2]], actual_matrices[["Y_"]][[2]])
expect_zero_diff(target_matrices[["Y9_"]][[3]], actual_matrices[["Y_"]][[3]])
expect_zero_diff(target_matrices[["Y9_"]][[4]], actual_matrices[["Y_"]][[4]])
rm(res_model_9_mcmc)
options(opts)
# ---- test NA's handling and prediction --------------------------------------
multi_net_usa_ge2 <- complete_pairs(
multi_net_usa_ge,
ids_spflow_pairs = "usa_usa")
coords <- dat(multi_net_usa_ge, "usa")[,c("COORD_X","COORD_Y")]
distm <- as.matrix(dist(coords))
#diag(distm) <- .5
dat(multi_net_usa_ge2, "usa_usa")[["DISTANCE2"]] <- as.vector((distm))
dist_usa_usa <- pair_merge(multi_net_usa_ge,"usa_usa",orig_cols = TRUE)
expect_equal(npairs(multi_net_usa_ge2, "usa_usa"), 51^2)
expect_error(spflow(
y9 ~ . + P_(DISTANCE2), multi_net_usa_ge2, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_9")),
pattern = "NA's")
expect_error(spflow(
y9 ~ . + P_(DISTANCE2), multi_net_usa_ge2, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_9", na_rm = TRUE),
pattern = "too few complete observations"))
# to deal with NA's give them zero values and weight them by zero in the estimation
na_y9 <- is.na(dat(multi_net_usa_ge2, "usa_usa")[["y9"]])
dat(multi_net_usa_ge2, "usa_usa")[["wt_9"]] <- 1 - na_y9
dat(multi_net_usa_ge2, "usa_usa")[["y9i"]] <- spflow:::na2zero(dat(multi_net_usa_ge2, "usa_usa")[["y9"]])
dat(multi_net_usa_ge2, "usa_usa")[["DISTANCEi"]] <- spflow:::na2zero(dat(multi_net_usa_ge2, "usa_usa")[["DISTANCE"]])
res_model_9_s2sls_narm <- spflow(
spflow_formula = y9i ~ . + P_(DISTANCEi), multi_net_usa_ge2,
id_net_pair = "usa_usa",
estimation_control = spflow_control(
estimation_method = "s2sls",
model = "model_9",
na_rm = TRUE,
weight_functions = list(pair = function(x) x[["wt_9"]])))
# test results
new_input <- target_results$mu9_input
names(new_input)[length(new_input)] <- "P_DISTANCEi"
expect_inherits(res_model_9_s2sls_narm, "spflow_model")
expect_equal(names(new_input), names(coef(res_model_9_s2sls_narm)))
# Results are different because higher order lags can reflect back on the sample
expect_equal(target_results$mu9_s2sls, coef(res_model_9_s2sls_narm), check.attributes = FALSE, tolerance = .1)
expect_equal(target_results$sigma9_s2sls, sd_error(res_model_9_s2sls_narm), tolerance = .1)
# test moments (moments that contain only zero and first order lags should be identical)
actual_moments <- res_model_9_s2sls_narm@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_s2sls_narm@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(0, target_matrices[["P_"]][[1]] * (target_matrices[["P_"]][[1]] - actual_matrices[["P_"]][[1]]))
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
# predictions
expect_equal(fitted(res_model_9_s2sls_narm),
predict(res_model_9_s2sls_narm, return_type = "V", method = "TS"))
expect_equal(npairs(multi_net_usa_ge2, "usa_usa"),
length(predict(res_model_9_s2sls_narm, return_type = "V", method = "TC")))
rm(res_model_9_s2sls_narm)
# ---- test logdet approx -----------------------------------------------------
expect_spflow_model <- function(ap_order = 10) expect_inherits(
spflow(y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
estimation_control = list(logdet_approx_order = ap_order)), "spflow_model")
suppressWarnings({
expect_spflow_model(20)
expect_spflow_model(10)
expect_spflow_model(4)
expect_spflow_model(2)
})
LukeCe/spflow documentation built on Nov. 11, 2023, 8:20 p.m.
R Package Documentation
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# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
# Project: spflow - integration test case 2
# Author: Lukas Dargel
# = = = = = = = = = = = = = = = = = = =
# Description:
#
# The script tests the integration of the package functions based on the
# simulated flows within the stylized states of the USA.
# The test case covers:
# - "model_1" and "model_2" and "model_9"
# - "non-Cartesian" flows: only a subset of all possible OD pairs are used
# - "Square" flows: within the same network
# - estimators: "ols" and "twosls" (exact tests)
# - estimators: "mle" and "mcmc" (approximate tests)
# = = = = = = = = = = = = = = = = = = =
# Date: Aug 2022
opts <- options(warn = 1)
# cran packages
library("Matrix")
library("spflow")
library("tinytest")
# data
data("multi_net_usa_ge")
data("simulation_params")
test_dir <- ""
# test_dir <- "tests/integration/" # uncomment for interactive check
usa_usa_vec_data <-
readRDS(paste0(test_dir,"vec_data_usa_ge.Rds"))[["usa_usa"]]
usa_usa_pairnb <-
readRDS(paste0(test_dir,"pair_neighborhoods_usa_ge.Rds"))[["usa_usa"]]
# ---- define target objects --------------------------------------------------
# ---- ... model matrices -----------------------------------------------------
OW <- W <- neighborhood(multi_net_usa_ge, "usa")
OX <- dat(multi_net_usa_ge, "usa")[,"X", drop = FALSE]
OX[["X_lag.1"]] <- as.vector(W %*% OX$X)
n <- nrow(W)
OX[["X_lag.1"]] <- as.vector(OW %*% OX$X)
OX_inst <- data.frame(
"X_lag.2" = as.vector(OW %*% OX$X_lag.1),
"X_lag.3" = as.vector(OW %*% OW %*% OX$X_lag.1))
DX <- OX
DX_inst <- OX_inst
od_dat <- dat(multi_net_usa_ge, "usa_usa")
o_index <- as.integer(od_dat[["ID_ORIG"]])
d_index <- as.integer(od_dat[["ID_DEST"]])
sparse_matrix_form <- function(vec) {
sparseMatrix(i = d_index,
j = o_index,
x = vec,
dims = c(n,n))
}
dense_matrix_form <- function(vec) {
mat <- matrix(0, n,n)
mat[cbind(d_index, o_index)] <- vec
return(mat)
}
flow_indicator <- sparse_matrix_form(1L)
target_matrices <- list(
"D_" = as.matrix(OX),
"O_" = as.matrix(OX),
"I_" = as.matrix(OX[,1]),
"OW" = W,
"P_" = list(
"DISTANCE" = sparse_matrix_form(usa_usa_vec_data[,"P_DISTANCE"])),
"Y1_" = list(
"y1" = sparse_matrix_form(usa_usa_vec_data[,"y1"])),
"Y2_" = list(
"y2" = sparse_matrix_form(usa_usa_vec_data[,"y2"]),
"y2.d" = flow_indicator * (W %*% sparse_matrix_form(usa_usa_vec_data[,"y2"]))),
"Y9_" = list(
"y9" = sparse_matrix_form(usa_usa_vec_data[,"y9"]),
"y9.d" = flow_indicator * (W %*% sparse_matrix_form(usa_usa_vec_data[,"y9"])),
"y9.o" = flow_indicator * tcrossprod(sparse_matrix_form(usa_usa_vec_data[,"y9"]),W),
"y9.w" = flow_indicator * tcrossprod(W %*% sparse_matrix_form(usa_usa_vec_data[,"y9"]),W)),
"flow_indicator" = flow_indicator
)
# ---- ... moments ------------------------------------------------------------
dep_vars <- paste0("y", c(9,2,1))
Z <- usa_usa_vec_data[,!colnames(usa_usa_vec_data) %in% dep_vars]
## derive lags
od_indicator <- as.logical(as.vector(flow_indicator))
W_o <- W %x% diag(n)
W_o <- W_o[od_indicator,od_indicator]
W_d <- diag(n) %x% W
W_d <- W_d[od_indicator,od_indicator]
W_w <- W %x% W
W_w <- W_w[od_indicator,od_indicator]
# lags of flows
Y_t2 <- usa_usa_vec_data[,"y2", drop = FALSE]
Y_t2 <- cbind(
Y_t2,
"y2.d"= as.vector(W_d %*% Y_t2))
Y_t9 <- usa_usa_vec_data[,"y9", drop = FALSE]
Y_t9 <- cbind(
Y_t9,
"y9.d" = as.vector(W_d %*% Y_t9),
"y9.o" = as.vector(W_o %*% Y_t9),
"y9.w" = as.vector(W_w %*% Y_t9))
# lags as instruments
U_alpha <- usa_usa_vec_data[,"(Intercept)", drop = FALSE]
iota_I <- usa_usa_vec_data[,"(Intra)"]
U_alpha_I <- cbind(
"wI" = as.vector(W_d %*% iota_I),
"Iw" = as.vector(W_o %*% iota_I),
"wIw" = as.vector(W_w %*% iota_I),
"wwI" = as.vector(W_d %*% W_d %*% iota_I),
"Iww" = as.vector(W_o %*% W_o %*% iota_I),
"wwIw" = as.vector(W_d %*% W_w %*% iota_I),
"wIww" = as.vector(W_w %*% W_o %*% iota_I),
"wwIww" = as.vector(W_w %*% W_w %*% iota_I))
colnames(U_alpha_I) <- paste0("(Intra).", colnames(U_alpha_I))
U_alpha_I <- cbind("(Intra)" = iota_I, U_alpha_I)
lag_names <- c("", paste0(".lag",1:3))
U_beta_d <- usa_usa_vec_data[,c("D_X","D_X.lag1")]
U_beta_d <- cbind(U_beta_d,as.matrix(DX_inst[d_index,]))
colnames(U_beta_d) <- paste0("D_X", lag_names)
U_beta_o <- usa_usa_vec_data[,c("O_X","O_X.lag1")]
U_beta_o <- cbind(U_beta_o,as.matrix(DX_inst[o_index,]))
colnames(U_beta_o) <- paste0("O_X", lag_names)
lag_names <- c("", paste0(".lag",1:2))
U_beta_I <- U_beta_o[,1:3] * iota_I
colnames(U_beta_I) <- paste0("I_X", lag_names)
U_gamma <- usa_usa_vec_data[,"P_DISTANCE"]
U_gamma <- cbind(U_gamma, W_w %*% U_gamma, W_w %*% W_w %*% U_gamma)
colnames(U_gamma) <- paste0("P_DISTANCE", c("", ".wGw", ".wwGww"))
U <- cbind(U_alpha,U_alpha_I,U_beta_d,U_beta_o,U_beta_I,U_gamma)
target_moments <- list(
# all models
"ZZ" = as.matrix(crossprod(Z)),
"UU" = as.matrix(crossprod(U)),
# model 1
"ZY1" = as.matrix(crossprod(Z,usa_usa_vec_data[,"y1", drop = FALSE])),
"TSS1" = as.matrix(crossprod(usa_usa_vec_data[,"y1", drop = FALSE])),
# model 2
"ZY2" = as.matrix(crossprod(Z,Y_t2)),
"UY2" = as.matrix(crossprod(U,Y_t2)),
"TSS2" = as.matrix(crossprod(Y_t2)),
# model 9
"ZY9" = as.matrix(crossprod(Z,Y_t9)),
"UY9" = as.matrix(crossprod(U,Y_t9)),
"TSS9" = as.matrix(crossprod(Y_t9)))
# ---- ... results ------------------------------------------------------------
# ols_results
N_s <- nrow(usa_usa_vec_data)
delta1_ols <- solve(
as.matrix(target_moments[["ZZ"]]),
as.vector(target_moments[["ZY1"]]))
e1 <- usa_usa_vec_data[,"y1"] - (Z %*% delta1_ols)
sigma1_ols <- as.vector(sqrt(crossprod(e1)/N_s))
# s2sls results for model 2
L2_hat <- U %*% solve(
target_moments[["UU"]],
target_moments[["UY2"]][, -1])
colnames(L2_hat) <- "rho_d"
Z2_hat <- cbind(L2_hat,Z)
ZZ2 <- crossprod(Z2_hat)
ZY2_hat <- as.vector(crossprod(Z2_hat,usa_usa_vec_data[,"y2",drop = FALSE]))
mu2_s2sls <- solve(as.matrix(ZZ2),ZY2_hat)
ZY2_tilde <- cbind(Y_t2[,-1], Z)
e2 <- usa_usa_vec_data[,"y2"] - ZY2_tilde %*% mu2_s2sls
sigma2_s2sls <- as.vector(sqrt(crossprod(e2)/N_s))
# s2sls results for model 9
L9_hat <- U %*% solve(
target_moments[["UU"]],
target_moments[["UY9"]][, -1])
colnames(L9_hat) <- paste0("rho_",c("d","o","w"))
Z9_hat <- cbind(L9_hat,Z)
ZZ9 <- crossprod(Z9_hat)
ZY9_hat <- as.vector(crossprod(Z9_hat,usa_usa_vec_data[,"y9",drop = FALSE]))
mu9_s2sls <- solve(as.matrix(ZZ9),ZY9_hat)
ZY9_tilde <- cbind(Y_t9[,-1], Z)
e9 <- usa_usa_vec_data[,"y9"] - ZY9_tilde %*% mu9_s2sls
sigma9_s2sls <- as.vector(sqrt(crossprod(e9)/N_s))
# all results
target_results <- list(
# ols
"delta1_ols" = delta1_ols,
"sigma1_ols" = sigma1_ols,
# s2sls
"mu2_s2sls" = mu2_s2sls,
"sigma2_s2sls" = sigma2_s2sls,
"mu9_s2sls" = mu9_s2sls,
"sigma9_s2sls" = sigma9_s2sls,
# ground truth
"mu2_input" = c(simulation_params$rho["rho_d"], simulation_params$delta),
"mu9_input" = c(simulation_params$rho, simulation_params$delta),
"sigma_input" = simulation_params$sd_error
)
# ---- run tests --------------------------------------------------------------
expect_zero_diff <- function(y,x) expect_equal(max(abs(x - y)), 0)
# ---- ... ols - model 1 ------------------------------------------------------
res_model_1_ols <- spflow(
y1 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "ols", model = "model_1"))
# test results
expect_inherits(res_model_1_ols, "spflow_model_ols")
expect_true(res_model_1_ols@estimation_diagnostics[["R2_corr"]] > 0)
expect_equal(target_results$delta1_ols, coef(res_model_1_ols))
expect_equal(target_results$sigma1_ols, sd_error(res_model_1_ols))
# test moments
actual_moments <- res_model_1_ols@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY1"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS1"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_1_ols@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y1_"]][[1]], actual_matrices[["Y_"]][[1]])
# test residuals and goodness of fit
expectied_signal <- as.vector(Z %*% target_results$delta1_ols)
expect_zero_diff(expectied_signal, fitted(res_model_1_ols))
expect_zero_diff(expectied_signal, predict(res_model_1_ols, return_type = "V"))
rm(res_model_1_ols)
# ---- ... s2sls - model 2 ----------------------------------------------------
res_model_2_s2sls <- spflow(
y2 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_2"))
# test results
expect_inherits(res_model_2_s2sls, "spflow_model_s2sls")
expect_equal(target_results$mu2_s2sls, coef(res_model_2_s2sls))
expect_equal(target_results$sigma2_s2sls, sd_error(res_model_2_s2sls))
# test moments
actual_moments <- res_model_2_s2sls@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["UU"]], actual_moments[["UU"]])
expect_zero_diff(target_moments[["ZY2"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["UY2"]], actual_moments[["UY"]])
expect_zero_diff(target_moments[["TSS2"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_2_s2sls@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[2]], actual_matrices[["Y_"]][[2]])
# test predictors
expected_signal <- as.vector(Z %*% target_results$mu2_s2sls[-1])
expect_zero_diff(expected_signal, res_model_2_s2sls@spflow_indicators$SIGNAL)
rd <- target_results$mu2_s2sls[1]
expected_trend <- W_d %*% usa_usa_vec_data[,"y2"] * rd
expect_zero_diff(expected_signal + expected_trend, predict(res_model_2_s2sls,method = "TS", return_type = "V"))
A2 <- diag(length(expected_trend)) - W_d * rd
dg_AA2 <- diag(crossprod(A2))
y2 <- usa_usa_vec_data[,"y2"]
bpi_corr <- crossprod(A2, y2 - expected_trend - expected_signal)
expected_bpi <- y2 - bpi_corr/dg_AA2
expect_zero_diff(expected_bpi, predict(res_model_2_s2sls,method = "BPI", return_type = "V"))
expected_tc <- solve(A2, expected_signal)
expected_tca <- expected_signal + (W_d * rd + W_d %*% W_d * rd^2 + W_d %*% W_d %*% W_d * rd^3) %*% expected_signal
expect_zero_diff(expected_tca, predict(res_model_2_s2sls,method = "TC", return_type = "V",expectation_approx_order = 3))
expect_zero_diff(expected_tc, predict(res_model_2_s2sls,method = "TC", return_type = "V",approx_expectation = FALSE))
bpa_corr <- A2 %*% crossprod(A2, y2 - expected_tc)
expected_bpa <- expected_tc - bpa_corr/dg_AA2
expect_zero_diff(expected_bpa, predict(res_model_2_s2sls,method = "BPA", return_type = "V",approx_expectation = FALSE))
bp_corr <- A2 %*% crossprod(A2, y2 - expected_tc)
expected_bp <- expected_tc - solve(crossprod(A2), bp_corr)
expect_zero_diff(expected_bp, predict(res_model_2_s2sls,method = "BP", return_type = "V",approx_expectation = FALSE))
rm(res_model_2_s2sls, rd)
# ---- ... s2sls - model 9 ----------------------------------------------------
res_model_9_s2sls <- spflow(
y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_9"))
# test results
expect_inherits(res_model_9_s2sls, "spflow_model_s2sls")
expect_equal(target_results$mu9_s2sls, coef(res_model_9_s2sls))
expect_equal(target_results$sigma9_s2sls, sd_error(res_model_9_s2sls))
# test moments
actual_moments <- res_model_9_s2sls@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["UU"]], actual_moments[["UU"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["UY9"]], actual_moments[["UY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_s2sls@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[2]], actual_matrices[["Y_"]][[2]])
expect_zero_diff(target_matrices[["Y9_"]][[3]], actual_matrices[["Y_"]][[3]])
expect_zero_diff(target_matrices[["Y9_"]][[4]], actual_matrices[["Y_"]][[4]])
# test predictors
expected_signal <- as.vector(Z %*% target_results$mu9_s2sls[-(1:3)])
expect_zero_diff(expected_signal, res_model_9_s2sls@spflow_indicators$SIGNAL)
r9 <- target_results$mu9_s2sls[1:3]
WF9 <- W_d * r9[1] + W_o * r9[2] + W_w * r9[3]
expected_trend <- expected_trend <- WF9 %*% usa_usa_vec_data[,"y9"]
expect_zero_diff(expected_signal + expected_trend, predict(res_model_9_s2sls, method = "TS", return_type = "V"))
A9 <- diag(length(expected_trend)) - WF9
dg_AA9 <- diag(crossprod(A9))
y9 <- usa_usa_vec_data[,"y9"]
bpi_corr <- crossprod(A9, y9 - expected_trend - expected_signal)
expected_bpi <- y9 - bpi_corr/dg_AA9
expect_zero_diff(expected_bpi, predict(res_model_9_s2sls,method = "BPI", return_type = "V"))
expected_tc <- solve(A9, expected_signal)
expected_tca <- expected_signal + (WF9 + WF9 %*% WF9 + WF9 %*% WF9 %*% WF9) %*% expected_signal
expect_zero_diff(expected_tca, predict(res_model_9_s2sls,method = "TC", return_type = "V",expectation_approx_order = 3))
expect_zero_diff(expected_tc, predict(res_model_9_s2sls,method = "TC", return_type = "V",approx_expectation = FALSE))
bpa_corr <- A9 %*% crossprod(A9, y9 - expected_tc)
expected_bpa <- expected_tc - bpa_corr/dg_AA9
expect_zero_diff(expected_bpa, predict(res_model_9_s2sls,method = "BPA", return_type = "V",approx_expectation = FALSE))
bp_corr <- A9 %*% crossprod(A9, y9 - expected_tc)
expected_bp <- expected_tc - solve(crossprod(A9), bp_corr)
expect_zero_diff(expected_bp, predict(res_model_9_s2sls,method = "BP", return_type = "V",approx_expectation = FALSE))
rm(res_model_9_s2sls)
# ---- ... mle - model 2 ------------------------------------------------------
res_model_2_mle <- spflow(
y2 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "mle", model = "model_2"))
# test results
expect_inherits(res_model_2_mle, "spflow_model_mle")
expect_equal(names(target_results$mu2_input),
names(coef(res_model_2_mle)))
expect_equal(target_results$mu2_input / coef(res_model_2_mle),
rep(1,9), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_2_mle),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_2_mle@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY2"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS2"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_2_mle@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[2]], actual_matrices[["Y_"]][[2]])
rm(res_model_2_mle)
# ---- ... mle - model 9 ------------------------------------------------------
res_model_9_mle <- spflow(
y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "mle", model = "model_9"))
# test results
expect_inherits(res_model_9_mle, "spflow_model_mle")
expect_equal(names(target_results$mu9_input), names(coef(res_model_9_mle)))
expect_equal(target_results$mu9_input / coef(res_model_9_mle),
rep(1,11), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_9_mle),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_9_mle@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_mle@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[2]], actual_matrices[["Y_"]][[2]])
expect_zero_diff(target_matrices[["Y9_"]][[3]], actual_matrices[["Y_"]][[3]])
expect_zero_diff(target_matrices[["Y9_"]][[4]], actual_matrices[["Y_"]][[4]])
rm(res_model_9_mle)
# ---- ... mcmc - model 2 -----------------------------------------------------
res_model_2_mcmc <- spflow(
spflow_formula = y2 ~ . + P_(DISTANCE),
spflow_networks = multi_net_usa_ge,
id_net_pair = "usa_usa",
estimation_control = spflow_control(estimation_method = "mcmc", model = "model_2"))
# test results
expect_inherits(res_model_2_mcmc, "spflow_model_mcmc")
expect_equal(names(target_results$mu2_input), names(coef(res_model_2_mcmc)))
expect_equal(target_results$mu2_input / coef(res_model_2_mcmc),
rep(1,9), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_2_mcmc),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_2_mcmc@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY2"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS2"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_2_mcmc@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y2_"]][[2]], actual_matrices[["Y_"]][[2]])
rm(res_model_2_mcmc)
# ---- ... mcmc - model 9 -----------------------------------------------------
res_model_9_mcmc <- spflow(
y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
spflow_control(estimation_method = "mcmc", model = "model_9"))
# test results
expect_inherits(res_model_9_mcmc, "spflow_model_mcmc")
expect_equal(names(target_results$mu9_input), names(coef(res_model_9_mcmc)))
expect_equal(target_results$mu9_input / coef(res_model_9_mcmc),
rep(1,11), tolerance = 0.3, check.names = FALSE)
expect_equal(target_results$sigma_input / sd_error(res_model_9_mcmc),
rep(1,1), tolerance = 0.1, check.names = FALSE)
# test moments
actual_moments <- res_model_9_mcmc@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_mcmc@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(target_matrices[["P_"]][[1]], actual_matrices[["P_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
expect_zero_diff(target_matrices[["Y9_"]][[2]], actual_matrices[["Y_"]][[2]])
expect_zero_diff(target_matrices[["Y9_"]][[3]], actual_matrices[["Y_"]][[3]])
expect_zero_diff(target_matrices[["Y9_"]][[4]], actual_matrices[["Y_"]][[4]])
rm(res_model_9_mcmc)
options(opts)
# ---- test NA's handling and prediction --------------------------------------
multi_net_usa_ge2 <- complete_pairs(
multi_net_usa_ge,
ids_spflow_pairs = "usa_usa")
coords <- dat(multi_net_usa_ge, "usa")[,c("COORD_X","COORD_Y")]
distm <- as.matrix(dist(coords))
#diag(distm) <- .5
dat(multi_net_usa_ge2, "usa_usa")[["DISTANCE2"]] <- as.vector((distm))
dist_usa_usa <- pair_merge(multi_net_usa_ge,"usa_usa",orig_cols = TRUE)
expect_equal(npairs(multi_net_usa_ge2, "usa_usa"), 51^2)
expect_error(spflow(
y9 ~ . + P_(DISTANCE2), multi_net_usa_ge2, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_9")),
pattern = "NA's")
expect_error(spflow(
y9 ~ . + P_(DISTANCE2), multi_net_usa_ge2, "usa_usa",
spflow_control(estimation_method = "s2sls", model = "model_9", na_rm = TRUE),
pattern = "too few complete observations"))
# to deal with NA's give them zero values and weight them by zero in the estimation
na_y9 <- is.na(dat(multi_net_usa_ge2, "usa_usa")[["y9"]])
dat(multi_net_usa_ge2, "usa_usa")[["wt_9"]] <- 1 - na_y9
dat(multi_net_usa_ge2, "usa_usa")[["y9i"]] <- spflow:::na2zero(dat(multi_net_usa_ge2, "usa_usa")[["y9"]])
dat(multi_net_usa_ge2, "usa_usa")[["DISTANCEi"]] <- spflow:::na2zero(dat(multi_net_usa_ge2, "usa_usa")[["DISTANCE"]])
res_model_9_s2sls_narm <- spflow(
spflow_formula = y9i ~ . + P_(DISTANCEi), multi_net_usa_ge2,
id_net_pair = "usa_usa",
estimation_control = spflow_control(
estimation_method = "s2sls",
model = "model_9",
na_rm = TRUE,
weight_functions = list(pair = function(x) x[["wt_9"]])))
# test results
new_input <- target_results$mu9_input
names(new_input)[length(new_input)] <- "P_DISTANCEi"
expect_inherits(res_model_9_s2sls_narm, "spflow_model")
expect_equal(names(new_input), names(coef(res_model_9_s2sls_narm)))
# Results are different because higher order lags can reflect back on the sample
expect_equal(target_results$mu9_s2sls, coef(res_model_9_s2sls_narm), check.attributes = FALSE, tolerance = .1)
expect_equal(target_results$sigma9_s2sls, sd_error(res_model_9_s2sls_narm), tolerance = .1)
# test moments (moments that contain only zero and first order lags should be identical)
actual_moments <- res_model_9_s2sls_narm@spflow_moments
expect_zero_diff(target_moments[["ZZ"]], actual_moments[["ZZ"]])
expect_zero_diff(target_moments[["ZY9"]], actual_moments[["ZY"]])
expect_zero_diff(target_moments[["TSS9"]], actual_moments[["TSS"]])
# test model matrices
actual_matrices <- res_model_9_s2sls_narm@spflow_matrices
expect_zero_diff(target_matrices[["D_"]], actual_matrices[["D_"]])
expect_zero_diff(target_matrices[["O_"]], actual_matrices[["O_"]])
expect_zero_diff(target_matrices[["I_"]], actual_matrices[["I_"]])
expect_zero_diff(0, target_matrices[["P_"]][[1]] * (target_matrices[["P_"]][[1]] - actual_matrices[["P_"]][[1]]))
expect_zero_diff(target_matrices[["Y9_"]][[1]], actual_matrices[["Y_"]][[1]])
# predictions
expect_equal(fitted(res_model_9_s2sls_narm),
predict(res_model_9_s2sls_narm, return_type = "V", method = "TS"))
expect_equal(npairs(multi_net_usa_ge2, "usa_usa"),
length(predict(res_model_9_s2sls_narm, return_type = "V", method = "TC")))
rm(res_model_9_s2sls_narm)
# ---- test logdet approx -----------------------------------------------------
expect_spflow_model <- function(ap_order = 10) expect_inherits(
spflow(y9 ~ . + P_(DISTANCE), multi_net_usa_ge, "usa_usa",
estimation_control = list(logdet_approx_order = ap_order)), "spflow_model")
suppressWarnings({
expect_spflow_model(20)
expect_spflow_model(10)
expect_spflow_model(4)
expect_spflow_model(2)
})
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