Esclarecimentos
Tivemos problemas com o tempo de processamento e a quantidade de memória necessários para a simulação, por isso, não trabalhamos com n = 5000 e respondemos as questões utilizando apenas \(\delta = 0\). O código dos gráficos está no arquivo .Rmd que enviamos junto no e-mail (muito extenso para o relatório).
Gráficos
Com a intenção de replicar as visualizações vistas em sala de aula, desenvolvemos o código abaixo para simular os dados e armazenar as estimativas do efeito do tratamento em um dataset. Depois disso, exportamos os resultados em um arquivo .csv, para diminuir o tempo de processamento do relatório.
# Dados
load("dat.RData")
# Ajuste dos modelos
mean_z1 <- mean(dat$Z1)
mod_Z2 <- lm(Z2 ~ Z1, data = dat)
mod_Z3 <- lm(Z3 ~ Z1 + Z2, data = dat)
mod_Tr <- glm(Tr ~ Z1 + Z2 + Z3, data = dat, family = "binomial")
# Geração dos dados
gerar_dataset <- function(n, b3, delta) {
Z1 <- rbinom(n, size = 1, prob = 0.55)
Z2 <- rnorm(n, mean = 3.698 - 1.191 * Z1, sd = summary(mod_Z2)$sigma)
Z3 <- rnorm(n, mean = 0.611 + 0.754 * Z1 - 0.037 * Z2, sd = summary(mod_Z3)$sigma)
pi <- plogis(0.732 - 2.018 * Z1 - 1.072 * Z2 + 1.798 * Z3)
Tr <- rbinom(n, size = 1, prob = pi)
beta_1 <- 1
beta_2 <- 1
beta_3 <- b3
beta_4 <- -3
sigma <- 1.5
e <- rnorm(n, mean = 0, sd = sigma)
Y_obs <- delta * Tr + beta_1 * sqrt(abs(Z3)) + beta_2 * Z2 + beta_3 * Z1 * Z2 + beta_4 * log10(abs(Z3)) + e
df <- data.frame(Z1, Z2, Z3, Tr, Y_obs)
return(df)
}
# Geração das estimativas
gerar_est <- function(df_sim) {
# Modelo que inclui apenas o tratamento como covariável
lm_unadj <- glm(Y_obs ~ Tr, family = "gaussian", data = df_sim)
# Modelo incluindo as três variáveis confundidoras, mas errando a forma funcional
lm_adj <- glm(Y_obs ~ Tr + Z1 + Z2 + Z3, family = "gaussian", data = df_sim)
# Modelo incluindo as confundidoras e especificando corretamente a forma funcional
lm_adj_real <- glm(Y_obs ~ Tr + I(sqrt(abs(Z3))) + Z2 + Z1 * Z2 + I(log(abs(Z3))),
family = "gaussian", data = df_sim)
# Infos necessárias para o pareamento
Y <- df_sim$Y_obs ; Tr <- df_sim$Tr ; X <- cbind(df_sim$Z1, df_sim$Z2, df_sim$Z3)
mod_PS <- glm(Tr ~ Z1 + Z2 + Z3, data = df_sim, family = "binomial")
XX <- mod_PS$linear.predictors
# Pareamento 1:1, com reposição, incluindo as confundidoras
rr_att_1_1 <- Match(Y = Y, Tr = Tr, X = X, M = 1, estimand = "ATT")
rr_ate_1_1 <- Match(Y = Y, Tr = Tr, X = X, M = 1, estimand = "ATE")
rr_att_3_1 <- Match(Y = Y, Tr = Tr, X = X, M = 3, estimand = "ATT")
# Pareamento 1:1, com reposição, pelo escore de propensão
rrr_att_1_1 <- Match(Y = Y, Tr = Tr, X = XX, M = 1, estimand = "ATT")
rrr_ate_1_1 <- Match(Y = Y, Tr = Tr, X = XX, M = 1, estimand = "ATE")
rrr_att_3_1 <- Match(Y = Y, Tr = Tr, X = XX, M = 3, estimand = "ATT")
return(c(
# Estimativas
lm_unadj = coef(lm_unadj)["Tr"],
lm_adj = coef(lm_adj)["Tr"],
lm_adj_real = coef(lm_adj_real)["Tr"],
rr_att_1_1 = rr_att_1_1$est,
rr_ate_1_1 = rr_ate_1_1$est,
rr_att_3_1 = rr_att_3_1$est,
rrr_att_1_1 = rrr_att_1_1$est,
rrr_ate_1_1 = rrr_ate_1_1$est,
rrr_att_3_1 = rrr_att_3_1$est,
# Erros
lm_unadj_se = summary(lm_unadj)$coefficients["Tr", "Std. Error"],
lm_adj_se = summary(lm_adj)$coefficients["Tr", "Std. Error"],
lm_adj_real_se = summary(lm_adj_real)$coefficients["Tr", "Std. Error"],
rr_att_1_1_se = rr_att_1_1$se.standard,
rr_ate_1_1_se = rr_ate_1_1$se.standard,
rr_att_3_1_se = rr_att_3_1$se.standard,
rrr_att_1_1_se = rrr_att_1_1$se.standard,
rrr_ate_1_1_se = rrr_ate_1_1$se.standard,
rrr_att_3_1_se = rrr_att_3_1$se.standard
))
}
##### Rodamos essa parte apenas fora do relatório:
# b3_vals <- c(1,2,3,4)
# n_vals <- c(100,500,1000,2000)
# delta_vals <- c(0,2)
# resultados_correcao <- data.frame()
# for (n in n_vals) {
# for (b3 in b3_vals) {
# for (delta in delta_vals) {
# ests <- replicate(1000, {
# df_sim <- gerar_dataset(n = n, b3 = b3, delta = delta)
# gerar_est(df_sim)
# }, simplify = "matrix")
# ests_df <- as.data.frame(t(ests))
# ests_df$n <- n
# ests_df$b3 <- b3
# ests_df$delta <- delta
# resultados_correcao <- bind_rows(resultados_correcao, ests_df)
# }
# }
# }
# resultados_correcao <- resultados_correcao %>% rename(lm_unadj = lm_unadj.Tr, lm_adj = lm_adj.Tr, lm_adj_real = lm_adj_real.Tr)
# write.csv(resultados_correcao, "resultados_sim.csv", row.names = F)
resultados_sim <- read.csv("resultados_sim.csv")Gráfico 1:
Conforme discutido em sala de aula, o modelo que inclui apenas o tratamento como covariável (lm_unadj), é o que mais se distancia do verdadeiro valor do efeito do tratamento (\(\delta = 0\)). Além disso, o viés das estimativas geradas por meio de pareamento diminui com o aumento do tamanho amostral.
Resolução das Questões
Questão 1: Alteração do valor de \(\beta_3\)
O aumento do valor de \(\beta_3\) (efeito da interação na geração da resposta), faz com que o viés das estimativas seja cada vez maior, principalmente em modelos onde a interação não é bem capturada.
A performance do pareamento pelo escore de propensão se destaca conforme o valor do parâmetro e o tamanho da amostra aumentam, uma vez que ele tenta equilibrar as covariáveis entre os grupos de tratamento e controle, minimizando o viés de confusão.
\(\beta_3 = 2\):
\(\beta_3 = 3\):
\(\beta_3 = 4\):
Questão 2: Alteração do número de controles
Voltamos para \(\beta_3 = 1\) e adicionamos a extensão dos dois pareamentos na visualização, agora com 3 indivíduos controle para 1 indivíduo tratado.
Com essa alteração, ficamos suscetíveis a indivíduos do grupo controle mais diferentes dos indivíduos tratados, o que pode enfraquecer a qualidade da estimativa. Essa questão pode ser contornada pelo pareamento utilizando o escore de propensão, que garante que os escolhidos são os mais semelhantes ao tratados e performa bem em tamanhos de amostra maiores.
Mesmo assim, a diferença de performance entre os modelos é pequena, e o custo computacional pode fazer com que aumentar o número de controles não seja viável.
Questão 3: Alteração do estimando
Utilizando o ATE, vamos estimar o efeito médio do tratamento em toda a população, e não apenas nos tratados. A medida de efeito é a mesma obtida por regressão, uma vez que ela também estima o ATE se todos têm chance de fazerem parte dos grupos de tratamento ou de controle.
O viés das estimativas continua pequeno, mas a proporção de rejeição de \(H_0\) aumenta muito e a cobertura dos intervalos de confiança cai.
Esses problemas acontecem porque o matching não foi desenhado para estimar o ATE e acaba utilizando indivíduos sem bom pareamento, aumentando a variabilidade e diminuindo a confiança dos resultados.
Questão 4: Balanceamento
Resumo:
No primeiro método (pareamento usual em (Z1, Z2, Z3)), o pareamento é feito através da distância euclideana, e não considera que algumas covariáveis são mais importantes do que outras para estimar o efeito do tratamento. A função GenMatch() (parte do segundo método) trabalha essa questão atribuindo pesos para as covariáveis, buscando otimizar o balanceamento entre os grupos de tratamento e controle. Já no terceiro método, o pareamento é feito usando a probabilidade de cada indivíduo receber o tratamento, o que ajuda a comparar indivíduos semelhantes considerando todas as covariáveis ao mesmo tempo.
Nos nossos dados, entre os três métodos, o segundo (utilização da matriz de pesos da função GenMatch()) foi o que apresentou melhores resultados, mesmo em tamanhos de amostra menores.
Com o aumento do tamanho da amostra, os dois primeiros métodos tiveram uma performance melhor, mas não conseguiram atingir o mesmo nível de balanceamento do segundo.
Código e output (bastante extenso):
set.seed(124)
n_vals <- c(100, 500, 1000, 2000)
for (n in n_vals) {
df_sim <- gerar_dataset(n = n, b3 = 1, delta = 0)
Y <- df_sim$Y_obs ; Tr <- df_sim$Tr ; X <- cbind(df_sim$Z1, df_sim$Z2, df_sim$Z3)
cat("\nPareamento usual em (Z1, Z2, Z3) para n =", n, "\n")
# Pareamento usual em (Z1, Z2, Z3)
match_usual <- Match(Y = Y, Tr = Tr, X = X, M = 1)
MatchBalance(Tr ~ Z1 + Z2 + Z3, data = df_sim, match.out = match_usual, nboots = 500)
cat("\nPareamento em (Z1, Z2, Z3) mas usando a matriz de pesos retornada pela funcao GenMatch() para n =", n, "\n")
# Pareamento em (Z1, Z2, Z3) mas usando a matriz de pesos retornada pela função GenMatch()
genout <- GenMatch(Tr = Tr, X = X, M = 1, pop.size = 100)
match_gen <- Match(Y = Y, Tr = Tr, X = X, M = 1, Weight.matrix = genout)
MatchBalance(Tr ~ Z1 + Z2 + Z3, data = df_sim, match.out = match_gen, nboots = 500)
cat("\nPareamento usual usando o escore de propensao para n =", n, "\n")
# Pareamento usual usando o escore de propensão
mod_PS <- glm(Tr ~ Z1 + Z2 + Z3, data = df_sim, family = "binomial")
pscores <- mod_PS$linear.predictors
match_pscore <- Match(Y = Y, Tr = Tr, X = pscores, M = 1)
MatchBalance(Tr ~ Z1 + Z2 + Z3, data = df_sim, match.out = match_pscore, nboots = 500)
}##
## Pareamento usual em (Z1, Z2, Z3) para n = 100
##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.80952 0.80952
## mean control.......... 0.58228 0.80952
## std mean diff......... 56.476 0
##
## mean raw eQQ diff..... 0.2381 0
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 0
##
## mean eCDF diff........ 0.11362 0
## med eCDF diff........ 0.11362 0
## max eCDF diff........ 0.22725 0
##
## var ratio (Tr/Co)..... 0.65722 1
## T-test p-value........ 0.035241 1
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 1.9473 1.9473
## mean control.......... 3.2193 2.2844
## std mean diff......... -99.908 -26.479
##
## mean raw eQQ diff..... 1.2326 0.34369
## med raw eQQ diff..... 1.1959 0.17198
## max raw eQQ diff..... 1.83 1.6273
##
## mean eCDF diff........ 0.28541 0.085714
## med eCDF diff........ 0.27728 0.047619
## max eCDF diff........ 0.52803 0.28571
##
## var ratio (Tr/Co)..... 1.2849 1.7221
## T-test p-value........ 0.00025596 0.006164
## KS Bootstrap p-value.. < 2.22e-16 0.27
## KS Naive p-value...... 8.523e-05 0.34278
## KS Statistic.......... 0.52803 0.28571
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.5664 1.5664
## mean control.......... 0.79716 1.357
## std mean diff......... 125.81 34.238
##
## mean raw eQQ diff..... 0.80882 0.22649
## med raw eQQ diff..... 0.74416 0.083658
## max raw eQQ diff..... 1.2786 1.127
##
## mean eCDF diff........ 0.31495 0.11837
## med eCDF diff........ 0.3698 0.047619
## max eCDF diff........ 0.52743 0.38095
##
## var ratio (Tr/Co)..... 1.0959 2.5923
## T-test p-value........ 1.3792e-05 0.013164
## KS Bootstrap p-value.. < 2.22e-16 0.054
## KS Naive p-value...... 8.8029e-05 0.082784
## KS Statistic.......... 0.52743 0.38095
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.006164
## Variable Name(s): Z2 Number(s): 2
##
##
## Pareamento em (Z1, Z2, Z3) mas usando a matriz de pesos retornada pela funcao GenMatch() para n = 100##
##
## Sat Apr 26 22:19:30 2025
## Domains:
## 0.000000e+00 <= X1 <= 1.000000e+03
## 0.000000e+00 <= X2 <= 1.000000e+03
## 0.000000e+00 <= X3 <= 1.000000e+03
##
## Data Type: Floating Point
## Operators (code number, name, population)
## (1) Cloning........................... 15
## (2) Uniform Mutation.................. 12
## (3) Boundary Mutation................. 12
## (4) Non-Uniform Mutation.............. 12
## (5) Polytope Crossover................ 12
## (6) Simple Crossover.................. 12
## (7) Whole Non-Uniform Mutation........ 12
## (8) Heuristic Crossover............... 12
## (9) Local-Minimum Crossover........... 0
##
## SOFT Maximum Number of Generations: 100
## Maximum Nonchanging Generations: 4
## Population size : 100
## Convergence Tolerance: 1.000000e-03
##
## Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
## Not Checking Gradients before Stopping.
## Using Out of Bounds Individuals.
##
## Maximization Problem.
## GENERATION: 0 (initializing the population)
## Lexical Fit..... 1.894945e-02 2.603849e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 100, #Total UniqueCount: 100
## var 1:
## best............ 8.474533e+01
## mean............ 4.463824e+02
## variance........ 7.425204e+04
## var 2:
## best............ 8.428378e+02
## mean............ 5.051408e+02
## variance........ 9.631020e+04
## var 3:
## best............ 5.626918e+02
## mean............ 4.744902e+02
## variance........ 8.063290e+04
##
## GENERATION: 1
## Lexical Fit..... 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 66, #Total UniqueCount: 166
## var 1:
## best............ 8.474533e+01
## mean............ 2.384380e+02
## variance........ 5.183044e+04
## var 2:
## best............ 8.428378e+02
## mean............ 7.615031e+02
## variance........ 2.523809e+04
## var 3:
## best............ 3.689695e+02
## mean............ 4.421461e+02
## variance........ 2.732336e+04
##
## GENERATION: 2
## Lexical Fit..... 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 69, #Total UniqueCount: 235
## var 1:
## best............ 8.474533e+01
## mean............ 1.140958e+02
## variance........ 1.716023e+04
## var 2:
## best............ 8.428378e+02
## mean............ 7.858028e+02
## variance........ 1.741487e+04
## var 3:
## best............ 3.689695e+02
## mean............ 3.925051e+02
## variance........ 1.868988e+04
##
## GENERATION: 3
## Lexical Fit..... 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 71, #Total UniqueCount: 306
## var 1:
## best............ 8.474533e+01
## mean............ 1.193168e+02
## variance........ 1.454284e+04
## var 2:
## best............ 8.428378e+02
## mean............ 8.002012e+02
## variance........ 1.013123e+04
## var 3:
## best............ 3.689695e+02
## mean............ 3.680543e+02
## variance........ 7.730222e+03
##
## GENERATION: 4
## Lexical Fit..... 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 61, #Total UniqueCount: 367
## var 1:
## best............ 8.474533e+01
## mean............ 1.146377e+02
## variance........ 1.029097e+04
## var 2:
## best............ 8.428378e+02
## mean............ 8.050867e+02
## variance........ 1.191712e+04
## var 3:
## best............ 3.689695e+02
## mean............ 3.588595e+02
## variance........ 4.022733e+03
##
## GENERATION: 5
## Lexical Fit..... 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 63, #Total UniqueCount: 430
## var 1:
## best............ 8.474533e+01
## mean............ 1.193056e+02
## variance........ 1.180202e+04
## var 2:
## best............ 8.428378e+02
## mean............ 7.883969e+02
## variance........ 2.451133e+04
## var 3:
## best............ 3.689695e+02
## mean............ 3.719135e+02
## variance........ 9.596753e+03
##
## GENERATION: 6
## Lexical Fit..... 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
## #unique......... 63, #Total UniqueCount: 493
## var 1:
## best............ 8.474533e+01
## mean............ 1.092797e+02
## variance........ 7.013449e+03
## var 2:
## best............ 8.428378e+02
## mean............ 8.194338e+02
## variance........ 5.263049e+03
## var 3:
## best............ 3.689695e+02
## mean............ 3.806210e+02
## variance........ 9.533274e+03
##
## 'wait.generations' limit reached.
## No significant improvement in 4 generations.
##
## Solution Lexical Fitness Value:
## 2.218221e-02 2.723026e-02 7.222601e-02 3.177421e-01 3.177421e-01 3.308954e-01
##
## Parameters at the Solution:
##
## X[ 1] : 8.474533e+01
## X[ 2] : 8.428378e+02
## X[ 3] : 3.689695e+02
##
## Solution Found Generation 1
## Number of Generations Run 6
##
## Sat Apr 26 22:19:30 2025
## Total run time : 0 hours 0 minutes and 0 seconds
##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.80952 0.80952
## mean control.......... 0.58228 0.85714
## std mean diff......... 56.476 -11.835
##
## mean raw eQQ diff..... 0.2381 0.047619
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.11362 0.02381
## med eCDF diff........ 0.11362 0.02381
## max eCDF diff........ 0.22725 0.047619
##
## var ratio (Tr/Co)..... 0.65722 1.2593
## T-test p-value........ 0.035241 0.31774
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 1.9473 1.9473
## mean control.......... 3.2193 2.2088
## std mean diff......... -99.908 -20.539
##
## mean raw eQQ diff..... 1.2326 0.30615
## med raw eQQ diff..... 1.1959 0.11392
## max raw eQQ diff..... 1.83 1.6273
##
## mean eCDF diff........ 0.28541 0.066378
## med eCDF diff........ 0.27728 0.047619
## max eCDF diff........ 0.52803 0.28571
##
## var ratio (Tr/Co)..... 1.2849 1.7988
## T-test p-value........ 0.00025596 0.02723
## KS Bootstrap p-value.. < 2.22e-16 0.274
## KS Naive p-value...... 8.523e-05 0.3309
## KS Statistic.......... 0.52803 0.28571
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.5664 1.5664
## mean control.......... 0.79716 1.3703
## std mean diff......... 125.81 32.062
##
## mean raw eQQ diff..... 0.80882 0.22693
## med raw eQQ diff..... 0.74416 0.1525
## max raw eQQ diff..... 1.2786 1.127
##
## mean eCDF diff........ 0.31495 0.11688
## med eCDF diff........ 0.3698 0.047619
## max eCDF diff........ 0.52743 0.38095
##
## var ratio (Tr/Co)..... 1.0959 2.7198
## T-test p-value........ 1.3792e-05 0.022182
## KS Bootstrap p-value.. < 2.22e-16 0.064
## KS Naive p-value...... 8.8029e-05 0.072226
## KS Statistic.......... 0.52743 0.38095
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.022182
## Variable Name(s): Z3 Number(s): 3
##
##
## Pareamento usual usando o escore de propensao para n = 100
##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.80952 0.80952
## mean control.......... 0.58228 0.47619
## std mean diff......... 56.476 82.842
##
## mean raw eQQ diff..... 0.2381 0.31818
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.11362 0.15909
## med eCDF diff........ 0.11362 0.15909
## max eCDF diff........ 0.22725 0.31818
##
## var ratio (Tr/Co)..... 0.65722 0.61818
## T-test p-value........ 0.035241 0.013447
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 1.9473 1.9473
## mean control.......... 3.2193 2.5271
## std mean diff......... -99.908 -45.542
##
## mean raw eQQ diff..... 1.2326 0.73264
## med raw eQQ diff..... 1.1959 0.79439
## max raw eQQ diff..... 1.83 1.7434
##
## mean eCDF diff........ 0.28541 0.19786
## med eCDF diff........ 0.27728 0.22727
## max eCDF diff........ 0.52803 0.40909
##
## var ratio (Tr/Co)..... 1.2849 3.5529
## T-test p-value........ 0.00025596 0.10206
## KS Bootstrap p-value.. < 2.22e-16 0.044
## KS Naive p-value...... 8.523e-05 0.043718
## KS Statistic.......... 0.52803 0.40909
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.5664 1.5664
## mean control.......... 0.79716 1.3819
## std mean diff......... 125.81 30.167
##
## mean raw eQQ diff..... 0.80882 0.21831
## med raw eQQ diff..... 0.74416 0.13687
## max raw eQQ diff..... 1.2786 1.1715
##
## mean eCDF diff........ 0.31495 0.089572
## med eCDF diff........ 0.3698 0.045455
## max eCDF diff........ 0.52743 0.40909
##
## var ratio (Tr/Co)..... 1.0959 2.273
## T-test p-value........ 1.3792e-05 0.078411
## KS Bootstrap p-value.. 0.002 0.032
## KS Naive p-value...... 8.8029e-05 0.040469
## KS Statistic.......... 0.52743 0.40909
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Number(s): 2
##
## After Matching Minimum p.value: 0.013447
## Variable Name(s): Z1 Number(s): 1
##
##
## Pareamento usual em (Z1, Z2, Z3) para n = 500##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.61947 0.61947
## mean control.......... 0.51938 0.61947
## std mean diff......... 20.524 0
##
## mean raw eQQ diff..... 0.097345 0
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 0
##
## mean eCDF diff........ 0.050045 0
## med eCDF diff........ 0.050045 0
## max eCDF diff........ 0.10009 0
##
## var ratio (Tr/Co)..... 0.9503 1
## T-test p-value........ 0.057911 1
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.0052 2.0052
## mean control.......... 3.2153 2.1067
## std mean diff......... -103.44 -8.6801
##
## mean raw eQQ diff..... 1.1991 0.13676
## med raw eQQ diff..... 1.2442 0.094761
## max raw eQQ diff..... 1.4869 0.61363
##
## mean eCDF diff........ 0.26568 0.031189
## med eCDF diff........ 0.29718 0.026549
## max eCDF diff........ 0.43516 0.097345
##
## var ratio (Tr/Co)..... 0.8856 1.1358
## T-test p-value........ < 2.22e-16 0.00044745
## KS Bootstrap p-value.. < 2.22e-16 0.596
## KS Naive p-value...... 8.2278e-15 0.658
## KS Statistic.......... 0.43516 0.097345
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.3651 1.3651
## mean control.......... 0.79857 1.3185
## std mean diff......... 92.004 7.5797
##
## mean raw eQQ diff..... 0.57156 0.067091
## med raw eQQ diff..... 0.57046 0.059879
## max raw eQQ diff..... 1.0388 0.46711
##
## mean eCDF diff........ 0.24137 0.024683
## med eCDF diff........ 0.27086 0.017699
## max eCDF diff........ 0.39318 0.10619
##
## var ratio (Tr/Co)..... 1.0114 1.1458
## T-test p-value........ 3.3307e-15 0.001114
## KS Bootstrap p-value.. < 2.22e-16 0.474
## KS Naive p-value...... 3.6077e-12 0.54703
## KS Statistic.......... 0.39318 0.10619
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.00044745
## Variable Name(s): Z2 Number(s): 2
##
##
## Pareamento em (Z1, Z2, Z3) mas usando a matriz de pesos retornada pela funcao GenMatch() para n = 500##
##
## Sat Apr 26 22:19:30 2025
## Domains:
## 0.000000e+00 <= X1 <= 1.000000e+03
## 0.000000e+00 <= X2 <= 1.000000e+03
## 0.000000e+00 <= X3 <= 1.000000e+03
##
## Data Type: Floating Point
## Operators (code number, name, population)
## (1) Cloning........................... 15
## (2) Uniform Mutation.................. 12
## (3) Boundary Mutation................. 12
## (4) Non-Uniform Mutation.............. 12
## (5) Polytope Crossover................ 12
## (6) Simple Crossover.................. 12
## (7) Whole Non-Uniform Mutation........ 12
## (8) Heuristic Crossover............... 12
## (9) Local-Minimum Crossover........... 0
##
## SOFT Maximum Number of Generations: 100
## Maximum Nonchanging Generations: 4
## Population size : 100
## Convergence Tolerance: 1.000000e-03
##
## Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
## Not Checking Gradients before Stopping.
## Using Out of Bounds Individuals.
##
## Maximization Problem.## GENERATION: 0 (initializing the population)
## Lexical Fit..... 5.254225e-03 1.085796e-02 2.406017e-02 2.406017e-02 7.681216e-01 8.660375e-01
## #unique......... 100, #Total UniqueCount: 100
## var 1:
## best............ 6.421033e+01
## mean............ 5.081529e+02
## variance........ 8.217172e+04
## var 2:
## best............ 5.289203e+02
## mean............ 5.010098e+02
## variance........ 9.570589e+04
## var 3:
## best............ 7.735842e+02
## mean............ 4.862177e+02
## variance........ 9.521279e+04##
## GENERATION: 1
## Lexical Fit..... 6.520124e-03 7.322190e-03 7.322190e-03 3.236402e-02 7.681216e-01 9.395985e-01
## #unique......... 66, #Total UniqueCount: 166
## var 1:
## best............ 4.931111e+01
## mean............ 2.764797e+02
## variance........ 7.604127e+04
## var 2:
## best............ 5.084736e+02
## mean............ 5.095979e+02
## variance........ 5.975188e+04
## var 3:
## best............ 8.163155e+02
## mean............ 4.919546e+02
## variance........ 1.043139e+05##
## GENERATION: 2
## Lexical Fit..... 7.322190e-03 7.322190e-03 7.607637e-03 2.262116e-02 7.681216e-01 9.395985e-01
## #unique......... 68, #Total UniqueCount: 234
## var 1:
## best............ 4.931111e+01
## mean............ 8.343839e+01
## variance........ 1.151787e+04
## var 2:
## best............ 5.268756e+02
## mean............ 4.870453e+02
## variance........ 2.010918e+04
## var 3:
## best............ 7.129389e+02
## mean............ 7.290668e+02
## variance........ 3.298947e+04##
## GENERATION: 3
## Lexical Fit..... 7.322190e-03 7.322190e-03 7.607637e-03 2.262116e-02 7.681216e-01 9.395985e-01
## #unique......... 63, #Total UniqueCount: 297
## var 1:
## best............ 4.931111e+01
## mean............ 7.158513e+01
## variance........ 1.220741e+04
## var 2:
## best............ 5.268756e+02
## mean............ 5.439658e+02
## variance........ 7.448976e+03
## var 3:
## best............ 7.129389e+02
## mean............ 7.410267e+02
## variance........ 1.248603e+04##
## GENERATION: 4
## Lexical Fit..... 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
## #unique......... 58, #Total UniqueCount: 355
## var 1:
## best............ 4.931111e+01
## mean............ 8.269368e+01
## variance........ 1.281110e+04
## var 2:
## best............ 5.268756e+02
## mean............ 5.605082e+02
## variance........ 6.544993e+03
## var 3:
## best............ 6.335561e+02
## mean............ 7.203794e+02
## variance........ 1.026471e+04##
## GENERATION: 5
## Lexical Fit..... 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
## #unique......... 70, #Total UniqueCount: 425
## var 1:
## best............ 4.931111e+01
## mean............ 8.518242e+01
## variance........ 1.123313e+04
## var 2:
## best............ 5.268756e+02
## mean............ 5.200670e+02
## variance........ 7.477628e+03
## var 3:
## best............ 6.335561e+02
## mean............ 6.744778e+02
## variance........ 1.091636e+04##
## GENERATION: 6
## Lexical Fit..... 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
## #unique......... 54, #Total UniqueCount: 479
## var 1:
## best............ 4.931111e+01
## mean............ 7.602007e+01
## variance........ 1.134619e+04
## var 2:
## best............ 5.268756e+02
## mean............ 5.168941e+02
## variance........ 7.677162e+03
## var 3:
## best............ 6.335561e+02
## mean............ 6.377703e+02
## variance........ 1.009803e+04##
## GENERATION: 7
## Lexical Fit..... 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
## #unique......... 51, #Total UniqueCount: 530
## var 1:
## best............ 4.931111e+01
## mean............ 7.038976e+01
## variance........ 9.085109e+03
## var 2:
## best............ 5.268756e+02
## mean............ 5.299783e+02
## variance........ 7.851163e+03
## var 3:
## best............ 6.335561e+02
## mean............ 6.206353e+02
## variance........ 7.614759e+03##
## GENERATION: 8
## Lexical Fit..... 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
## #unique......... 53, #Total UniqueCount: 583
## var 1:
## best............ 4.931111e+01
## mean............ 8.801945e+01
## variance........ 1.374666e+04
## var 2:
## best............ 5.268756e+02
## mean............ 5.252660e+02
## variance........ 6.473520e+03
## var 3:
## best............ 6.335561e+02
## mean............ 6.142421e+02
## variance........ 7.812933e+03##
## GENERATION: 9
## Lexical Fit..... 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
## #unique......... 49, #Total UniqueCount: 632
## var 1:
## best............ 4.931111e+01
## mean............ 7.548888e+01
## variance........ 9.710995e+03
## var 2:
## best............ 5.268756e+02
## mean............ 5.410810e+02
## variance........ 9.278692e+03
## var 3:
## best............ 6.335561e+02
## mean............ 6.208017e+02
## variance........ 3.781446e+03
##
## 'wait.generations' limit reached.
## No significant improvement in 4 generations.
##
## Solution Lexical Fitness Value:
## 8.912331e-03 1.324295e-02 1.324295e-02 1.343818e-02 7.681216e-01 8.660375e-01
##
## Parameters at the Solution:
##
## X[ 1] : 4.931111e+01
## X[ 2] : 5.268756e+02
## X[ 3] : 6.335561e+02
##
## Solution Found Generation 4
## Number of Generations Run 9
##
## Sat Apr 26 22:19:31 2025
## Total run time : 0 hours 0 minutes and 1 seconds##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.61947 0.61947
## mean control.......... 0.51938 0.67257
## std mean diff......... 20.524 -10.888
##
## mean raw eQQ diff..... 0.097345 0.053097
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.050045 0.026549
## med eCDF diff........ 0.050045 0.026549
## max eCDF diff........ 0.10009 0.053097
##
## var ratio (Tr/Co)..... 0.9503 1.0704
## T-test p-value........ 0.057911 0.013243
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.0052 2.0052
## mean control.......... 3.2153 2.0684
## std mean diff......... -103.44 -5.4048
##
## mean raw eQQ diff..... 1.1991 0.10852
## med raw eQQ diff..... 1.2442 0.068104
## max raw eQQ diff..... 1.4869 0.65015
##
## mean eCDF diff........ 0.26568 0.021248
## med eCDF diff........ 0.29718 0.017699
## max eCDF diff........ 0.43516 0.088496
##
## var ratio (Tr/Co)..... 0.8856 1.1216
## T-test p-value........ < 2.22e-16 0.0089123
## KS Bootstrap p-value.. < 2.22e-16 0.754
## KS Naive p-value...... 8.2278e-15 0.76812
## KS Statistic.......... 0.43516 0.088496
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.3651 1.3651
## mean control.......... 0.79857 1.3395
## std mean diff......... 92.004 4.1684
##
## mean raw eQQ diff..... 0.57156 0.049447
## med raw eQQ diff..... 0.57046 0.032155
## max raw eQQ diff..... 1.0388 0.38046
##
## mean eCDF diff........ 0.24137 0.017936
## med eCDF diff........ 0.27086 0.017699
## max eCDF diff........ 0.39318 0.079646
##
## var ratio (Tr/Co)..... 1.0114 1.1186
## T-test p-value........ 3.3307e-15 0.013438
## KS Bootstrap p-value.. < 2.22e-16 0.85
## KS Naive p-value...... 3.6077e-12 0.86604
## KS Statistic.......... 0.39318 0.079646
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.0089123
## Variable Name(s): Z2 Number(s): 2
##
##
## Pareamento usual usando o escore de propensao para n = 500##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.61947 0.61947
## mean control.......... 0.51938 0.64086
## std mean diff......... 20.524 -4.3853
##
## mean raw eQQ diff..... 0.097345 0.014184
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.050045 0.0070922
## med eCDF diff........ 0.050045 0.0070922
## max eCDF diff........ 0.10009 0.014184
##
## var ratio (Tr/Co)..... 0.9503 1.0242
## T-test p-value........ 0.057911 0.72887
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.0052 2.0052
## mean control.......... 3.2153 1.9388
## std mean diff......... -103.44 5.6784
##
## mean raw eQQ diff..... 1.1991 0.1684
## med raw eQQ diff..... 1.2442 0.13276
## max raw eQQ diff..... 1.4869 1.3454
##
## mean eCDF diff........ 0.26568 0.033181
## med eCDF diff........ 0.29718 0.028369
## max eCDF diff........ 0.43516 0.099291
##
## var ratio (Tr/Co)..... 0.8856 0.91061
## T-test p-value........ < 2.22e-16 0.5526
## KS Bootstrap p-value.. < 2.22e-16 0.424
## KS Naive p-value...... 8.2278e-15 0.49043
## KS Statistic.......... 0.43516 0.099291
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.3651 1.3651
## mean control.......... 0.79857 1.3389
## std mean diff......... 92.004 4.2631
##
## mean raw eQQ diff..... 0.57156 0.074107
## med raw eQQ diff..... 0.57046 0.066316
## max raw eQQ diff..... 1.0388 0.41631
##
## mean eCDF diff........ 0.24137 0.030033
## med eCDF diff........ 0.27086 0.021277
## max eCDF diff........ 0.39318 0.10638
##
## var ratio (Tr/Co)..... 1.0114 1.2705
## T-test p-value........ 3.3307e-15 0.6603
## KS Bootstrap p-value.. < 2.22e-16 0.368
## KS Naive p-value...... 3.6077e-12 0.40214
## KS Statistic.......... 0.39318 0.10638
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.368
## Variable Name(s): Z3 Number(s): 3
##
##
## Pareamento usual em (Z1, Z2, Z3) para n = 1000##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.57955 0.57955
## mean control.......... 0.50728 0.57955
## std mean diff......... 14.598 0
##
## mean raw eQQ diff..... 0.073864 0
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 0
##
## mean eCDF diff........ 0.036132 0
## med eCDF diff........ 0.036132 0
## max eCDF diff........ 0.072264 0
##
## var ratio (Tr/Co)..... 0.97928 1
## T-test p-value........ 0.080508 1
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.0891 2.0891
## mean control.......... 3.3253 2.1398
## std mean diff......... -116.36 -4.7766
##
## mean raw eQQ diff..... 1.2358 0.07003
## med raw eQQ diff..... 1.2266 0.042374
## max raw eQQ diff..... 2.5894 0.52974
##
## mean eCDF diff........ 0.26771 0.015152
## med eCDF diff........ 0.29477 0.011364
## max eCDF diff........ 0.40313 0.068182
##
## var ratio (Tr/Co)..... 0.71295 1.0551
## T-test p-value........ < 2.22e-16 0.0030222
## KS Bootstrap p-value.. < 2.22e-16 0.786
## KS Naive p-value...... < 2.22e-16 0.80792
## KS Statistic.......... 0.40313 0.068182
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.2565 1.2565
## mean control.......... 0.7912 1.2049
## std mean diff......... 68.3 7.5805
##
## mean raw eQQ diff..... 0.46911 0.056694
## med raw eQQ diff..... 0.46656 0.040383
## max raw eQQ diff..... 0.68578 0.39523
##
## mean eCDF diff........ 0.18968 0.020737
## med eCDF diff........ 0.22482 0.017045
## max eCDF diff........ 0.27786 0.068182
##
## var ratio (Tr/Co)..... 1.165 1.1237
## T-test p-value........ 5.9952e-15 1.8989e-06
## KS Bootstrap p-value.. < 2.22e-16 0.792
## KS Naive p-value...... 3.7656e-10 0.80792
## KS Statistic.......... 0.27786 0.068182
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 1.8989e-06
## Variable Name(s): Z3 Number(s): 3
##
##
## Pareamento em (Z1, Z2, Z3) mas usando a matriz de pesos retornada pela funcao GenMatch() para n = 1000##
##
## Sat Apr 26 22:19:32 2025
## Domains:
## 0.000000e+00 <= X1 <= 1.000000e+03
## 0.000000e+00 <= X2 <= 1.000000e+03
## 0.000000e+00 <= X3 <= 1.000000e+03
##
## Data Type: Floating Point
## Operators (code number, name, population)
## (1) Cloning........................... 15
## (2) Uniform Mutation.................. 12
## (3) Boundary Mutation................. 12
## (4) Non-Uniform Mutation.............. 12
## (5) Polytope Crossover................ 12
## (6) Simple Crossover.................. 12
## (7) Whole Non-Uniform Mutation........ 12
## (8) Heuristic Crossover............... 12
## (9) Local-Minimum Crossover........... 0
##
## SOFT Maximum Number of Generations: 100
## Maximum Nonchanging Generations: 4
## Population size : 100
## Convergence Tolerance: 1.000000e-03
##
## Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
## Not Checking Gradients before Stopping.
## Using Out of Bounds Individuals.
##
## Maximization Problem.## GENERATION: 0 (initializing the population)
## Lexical Fit..... 2.535507e-04 5.061082e-04 5.449519e-01 9.388519e-01 1.000000e+00 1.000000e+00
## #unique......... 100, #Total UniqueCount: 100
## var 1:
## best............ 5.828004e+02
## mean............ 4.269275e+02
## variance........ 8.086415e+04
## var 2:
## best............ 5.162136e+01
## mean............ 4.603244e+02
## variance........ 9.247828e+04
## var 3:
## best............ 4.227112e+02
## mean............ 5.447330e+02
## variance........ 8.802471e+04##
## GENERATION: 1
## Lexical Fit..... 3.465695e-04 4.148547e-04 1.567139e-01 1.567139e-01 5.449519e-01 9.933560e-01
## #unique......... 71, #Total UniqueCount: 171
## var 1:
## best............ 1.261062e+02
## mean............ 4.431679e+02
## variance........ 4.474901e+04
## var 2:
## best............ 7.638587e+01
## mean............ 1.748338e+02
## variance........ 4.860288e+04
## var 3:
## best............ 6.368547e+02
## mean............ 5.996346e+02
## variance........ 6.368914e+04##
## GENERATION: 2
## Lexical Fit..... 4.618038e-03 5.667391e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
## #unique......... 65, #Total UniqueCount: 236
## var 1:
## best............ 6.577041e+00
## mean............ 3.435153e+02
## variance........ 4.581495e+04
## var 2:
## best............ 8.286741e+01
## mean............ 1.241253e+02
## variance........ 2.077477e+04
## var 3:
## best............ 6.929018e+02
## mean............ 5.780524e+02
## variance........ 3.292219e+04##
## GENERATION: 3
## Lexical Fit..... 5.611552e-03 6.159187e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
## #unique......... 72, #Total UniqueCount: 308
## var 1:
## best............ 6.577041e+00
## mean............ 7.007001e+01
## variance........ 1.316353e+04
## var 2:
## best............ 8.286741e+01
## mean............ 1.278541e+02
## variance........ 1.881292e+04
## var 3:
## best............ 6.676379e+02
## mean............ 6.396328e+02
## variance........ 1.748826e+04##
## GENERATION: 4
## Lexical Fit..... 5.611552e-03 6.159187e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
## #unique......... 73, #Total UniqueCount: 381
## var 1:
## best............ 6.577041e+00
## mean............ 5.100251e+01
## variance........ 1.453608e+04
## var 2:
## best............ 8.286741e+01
## mean............ 1.237228e+02
## variance........ 1.564259e+04
## var 3:
## best............ 6.676379e+02
## mean............ 6.491972e+02
## variance........ 8.735425e+03##
## GENERATION: 5
## Lexical Fit..... 5.611552e-03 6.159187e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
## #unique......... 65, #Total UniqueCount: 446
## var 1:
## best............ 6.577041e+00
## mean............ 6.129252e+01
## variance........ 2.173976e+04
## var 2:
## best............ 8.286741e+01
## mean............ 1.312026e+02
## variance........ 2.309784e+04
## var 3:
## best............ 6.676379e+02
## mean............ 6.637527e+02
## variance........ 5.128636e+03##
## GENERATION: 6
## Lexical Fit..... 5.611552e-03 6.159187e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
## #unique......... 69, #Total UniqueCount: 515
## var 1:
## best............ 6.577041e+00
## mean............ 3.877524e+01
## variance........ 1.444966e+04
## var 2:
## best............ 8.286741e+01
## mean............ 1.192643e+02
## variance........ 1.763940e+04
## var 3:
## best............ 6.676379e+02
## mean............ 6.553172e+02
## variance........ 5.416280e+03##
## GENERATION: 7
## Lexical Fit..... 5.611552e-03 6.159187e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
## #unique......... 62, #Total UniqueCount: 577
## var 1:
## best............ 6.577041e+00
## mean............ 1.831721e+01
## variance........ 5.827632e+03
## var 2:
## best............ 8.286741e+01
## mean............ 1.309244e+02
## variance........ 1.777440e+04
## var 3:
## best............ 6.676379e+02
## mean............ 6.401294e+02
## variance........ 1.357508e+04
##
## 'wait.generations' limit reached.
## No significant improvement in 4 generations.
##
## Solution Lexical Fitness Value:
## 5.611552e-03 6.159187e-03 6.170486e-03 6.170486e-03 5.449519e-01 9.933560e-01
##
## Parameters at the Solution:
##
## X[ 1] : 6.577041e+00
## X[ 2] : 8.286741e+01
## X[ 3] : 6.676379e+02
##
## Solution Found Generation 2
## Number of Generations Run 7
##
## Sat Apr 26 22:19:34 2025
## Total run time : 0 hours 0 minutes and 2 seconds##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.57955 0.57955
## mean control.......... 0.50728 0.63068
## std mean diff......... 14.598 -10.33
##
## mean raw eQQ diff..... 0.073864 0.051136
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.036132 0.025568
## med eCDF diff........ 0.036132 0.025568
## max eCDF diff........ 0.072264 0.051136
##
## var ratio (Tr/Co)..... 0.97928 1.0462
## T-test p-value........ 0.080508 0.0061705
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.0891 2.0891
## mean control.......... 3.3253 2.1556
## std mean diff......... -116.36 -6.2597
##
## mean raw eQQ diff..... 1.2358 0.078981
## med raw eQQ diff..... 1.2266 0.040954
## max raw eQQ diff..... 2.5894 0.81889
##
## mean eCDF diff........ 0.26771 0.015562
## med eCDF diff........ 0.29477 0.011364
## max eCDF diff........ 0.40313 0.085227
##
## var ratio (Tr/Co)..... 0.71295 1.0566
## T-test p-value........ < 2.22e-16 0.0061592
## KS Bootstrap p-value.. < 2.22e-16 0.5
## KS Naive p-value...... < 2.22e-16 0.54495
## KS Statistic.......... 0.40313 0.085227
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.2565 1.2565
## mean control.......... 0.7912 1.2434
## std mean diff......... 68.3 1.9231
##
## mean raw eQQ diff..... 0.46911 0.025556
## med raw eQQ diff..... 0.46656 0.015442
## max raw eQQ diff..... 0.68578 0.39523
##
## mean eCDF diff........ 0.18968 0.0090524
## med eCDF diff........ 0.22482 0.0056818
## max eCDF diff........ 0.27786 0.045455
##
## var ratio (Tr/Co)..... 1.165 1.0449
## T-test p-value........ 5.9952e-15 0.0056116
## KS Bootstrap p-value.. < 2.22e-16 0.988
## KS Naive p-value...... 3.7656e-10 0.99336
## KS Statistic.......... 0.27786 0.045455
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.0056116
## Variable Name(s): Z3 Number(s): 3
##
##
## Pareamento usual usando o escore de propensao para n = 1000##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.57955 0.57955
## mean control.......... 0.50728 0.6285
## std mean diff......... 14.598 -9.8898
##
## mean raw eQQ diff..... 0.073864 0.030405
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.036132 0.015203
## med eCDF diff........ 0.036132 0.015203
## max eCDF diff........ 0.072264 0.030405
##
## var ratio (Tr/Co)..... 0.97928 1.0436
## T-test p-value........ 0.080508 0.32954
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.0891 2.0891
## mean control.......... 3.3253 1.9876
## std mean diff......... -116.36 9.5523
##
## mean raw eQQ diff..... 1.2358 0.12903
## med raw eQQ diff..... 1.2266 0.090002
## max raw eQQ diff..... 2.5894 1.288
##
## mean eCDF diff........ 0.26771 0.02506
## med eCDF diff........ 0.29477 0.023649
## max eCDF diff........ 0.40313 0.070946
##
## var ratio (Tr/Co)..... 0.71295 0.80234
## T-test p-value........ < 2.22e-16 0.24198
## KS Bootstrap p-value.. < 2.22e-16 0.402
## KS Naive p-value...... < 2.22e-16 0.44565
## KS Statistic.......... 0.40313 0.070946
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.2565 1.2565
## mean control.......... 0.7912 1.2402
## std mean diff......... 68.3 2.399
##
## mean raw eQQ diff..... 0.46911 0.083233
## med raw eQQ diff..... 0.46656 0.057274
## max raw eQQ diff..... 0.68578 0.63932
##
## mean eCDF diff........ 0.18968 0.029338
## med eCDF diff........ 0.22482 0.023649
## max eCDF diff........ 0.27786 0.091216
##
## var ratio (Tr/Co)..... 1.165 1.2088
## T-test p-value........ 5.9952e-15 0.79134
## KS Bootstrap p-value.. < 2.22e-16 0.198
## KS Naive p-value...... 3.7656e-10 0.17028
## KS Statistic.......... 0.27786 0.091216
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.198
## Variable Name(s): Z3 Number(s): 3
##
##
## Pareamento usual em (Z1, Z2, Z3) para n = 2000##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.61779 0.61779
## mean control.......... 0.5404 0.61779
## std mean diff......... 15.906 0
##
## mean raw eQQ diff..... 0.076923 0
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 0
##
## mean eCDF diff........ 0.038692 0
## med eCDF diff........ 0.038692 0
## max eCDF diff........ 0.077384 0
##
## var ratio (Tr/Co)..... 0.9524 1
## T-test p-value........ 0.0042059 1
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.1544 2.1544
## mean control.......... 3.234 2.1961
## std mean diff......... -100.24 -3.8756
##
## mean raw eQQ diff..... 1.0778 0.050957
## med raw eQQ diff..... 1.083 0.032351
## max raw eQQ diff..... 1.5216 1.5216
##
## mean eCDF diff........ 0.24931 0.010336
## med eCDF diff........ 0.27455 0.0071942
## max eCDF diff........ 0.38928 0.043165
##
## var ratio (Tr/Co)..... 0.81865 1.08
## T-test p-value........ < 2.22e-16 5.3868e-08
## KS Bootstrap p-value.. < 2.22e-16 0.804
## KS Naive p-value...... < 2.22e-16 0.83203
## KS Statistic.......... 0.38928 0.043165
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.3146 1.3146
## mean control.......... 0.82009 1.2965
## std mean diff......... 83.951 3.0638
##
## mean raw eQQ diff..... 0.49614 0.025909
## med raw eQQ diff..... 0.48446 0.019745
## max raw eQQ diff..... 0.87204 0.2922
##
## mean eCDF diff........ 0.20897 0.0095465
## med eCDF diff........ 0.23499 0.0095923
## max eCDF diff........ 0.30208 0.028777
##
## var ratio (Tr/Co)..... 0.83187 1.0406
## T-test p-value........ < 2.22e-16 3.3793e-06
## KS Bootstrap p-value.. < 2.22e-16 0.998
## KS Naive p-value...... < 2.22e-16 0.99524
## KS Statistic.......... 0.30208 0.028777
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 5.3868e-08
## Variable Name(s): Z2 Number(s): 2
##
##
## Pareamento em (Z1, Z2, Z3) mas usando a matriz de pesos retornada pela funcao GenMatch() para n = 2000##
##
## Sat Apr 26 22:19:35 2025
## Domains:
## 0.000000e+00 <= X1 <= 1.000000e+03
## 0.000000e+00 <= X2 <= 1.000000e+03
## 0.000000e+00 <= X3 <= 1.000000e+03
##
## Data Type: Floating Point
## Operators (code number, name, population)
## (1) Cloning........................... 15
## (2) Uniform Mutation.................. 12
## (3) Boundary Mutation................. 12
## (4) Non-Uniform Mutation.............. 12
## (5) Polytope Crossover................ 12
## (6) Simple Crossover.................. 12
## (7) Whole Non-Uniform Mutation........ 12
## (8) Heuristic Crossover............... 12
## (9) Local-Minimum Crossover........... 0
##
## SOFT Maximum Number of Generations: 100
## Maximum Nonchanging Generations: 4
## Population size : 100
## Convergence Tolerance: 1.000000e-03
##
## Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
## Not Checking Gradients before Stopping.
## Using Out of Bounds Individuals.
##
## Maximization Problem.## GENERATION: 0 (initializing the population)
## Lexical Fit..... 1.294466e-06 1.811379e-05 1.811379e-05 1.265829e-02 8.309462e-01 9.986396e-01
## #unique......... 100, #Total UniqueCount: 100
## var 1:
## best............ 9.106706e+00
## mean............ 4.511397e+02
## variance........ 8.476549e+04
## var 2:
## best............ 3.771460e+02
## mean............ 4.991651e+02
## variance........ 9.759455e+04
## var 3:
## best............ 7.828449e+02
## mean............ 4.610172e+02
## variance........ 7.853307e+04##
## GENERATION: 1
## Lexical Fit..... 1.011019e-05 1.047286e-05 1.047286e-05 6.620686e-03 8.309462e-01 9.997480e-01
## #unique......... 65, #Total UniqueCount: 165
## var 1:
## best............ 7.331535e+00
## mean............ 2.250081e+02
## variance........ 5.935009e+04
## var 2:
## best............ 2.927498e+02
## mean............ 5.002165e+02
## variance........ 5.762704e+04
## var 3:
## best............ 8.726082e+02
## mean............ 5.871691e+02
## variance........ 4.852571e+04##
## GENERATION: 2
## Lexical Fit..... 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
## #unique......... 64, #Total UniqueCount: 229
## var 1:
## best............ 8.054182e+00
## mean............ 5.854034e+01
## variance........ 2.178068e+04
## var 2:
## best............ 3.271063e+02
## mean............ 4.404595e+02
## variance........ 3.278650e+04
## var 3:
## best............ 8.689541e+02
## mean............ 7.102611e+02
## variance........ 3.864836e+04##
## GENERATION: 3
## Lexical Fit..... 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
## #unique......... 71, #Total UniqueCount: 300
## var 1:
## best............ 8.054182e+00
## mean............ 3.905481e+01
## variance........ 1.546238e+04
## var 2:
## best............ 3.271063e+02
## mean............ 3.547473e+02
## variance........ 1.795246e+04
## var 3:
## best............ 8.689541e+02
## mean............ 8.063329e+02
## variance........ 1.628693e+04##
## GENERATION: 4
## Lexical Fit..... 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
## #unique......... 64, #Total UniqueCount: 364
## var 1:
## best............ 8.054182e+00
## mean............ 2.612155e+01
## variance........ 5.928102e+03
## var 2:
## best............ 3.271063e+02
## mean............ 3.342842e+02
## variance........ 9.305397e+03
## var 3:
## best............ 8.689541e+02
## mean............ 8.372630e+02
## variance........ 1.240155e+04##
## GENERATION: 5
## Lexical Fit..... 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
## #unique......... 65, #Total UniqueCount: 429
## var 1:
## best............ 8.054182e+00
## mean............ 3.216653e+01
## variance........ 7.493254e+03
## var 2:
## best............ 3.271063e+02
## mean............ 3.515972e+02
## variance........ 8.236854e+03
## var 3:
## best............ 8.689541e+02
## mean............ 8.451141e+02
## variance........ 1.192220e+04##
## GENERATION: 6
## Lexical Fit..... 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
## #unique......... 59, #Total UniqueCount: 488
## var 1:
## best............ 8.054182e+00
## mean............ 5.004273e+01
## variance........ 1.623131e+04
## var 2:
## best............ 3.271063e+02
## mean............ 3.363621e+02
## variance........ 3.299204e+03
## var 3:
## best............ 8.689541e+02
## mean............ 8.491064e+02
## variance........ 7.129283e+03##
## GENERATION: 7
## Lexical Fit..... 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
## #unique......... 66, #Total UniqueCount: 554
## var 1:
## best............ 8.054182e+00
## mean............ 7.618540e+01
## variance........ 2.986415e+04
## var 2:
## best............ 3.271063e+02
## mean............ 3.462957e+02
## variance........ 1.004209e+04
## var 3:
## best............ 8.689541e+02
## mean............ 8.404292e+02
## variance........ 1.659929e+04
##
## 'wait.generations' limit reached.
## No significant improvement in 4 generations.
##
## Solution Lexical Fitness Value:
## 1.047286e-05 1.047286e-05 1.471558e-05 9.926526e-03 8.309462e-01 9.997480e-01
##
## Parameters at the Solution:
##
## X[ 1] : 8.054182e+00
## X[ 2] : 3.271063e+02
## X[ 3] : 8.689541e+02
##
## Solution Found Generation 2
## Number of Generations Run 7
##
## Sat Apr 26 22:19:41 2025
## Total run time : 0 hours 0 minutes and 6 seconds##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.61779 0.61779
## mean control.......... 0.5404 0.66346
## std mean diff......... 15.906 -9.3878
##
## mean raw eQQ diff..... 0.076923 0.045673
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.038692 0.022837
## med eCDF diff........ 0.038692 0.022837
## max eCDF diff........ 0.077384 0.045673
##
## var ratio (Tr/Co)..... 0.9524 1.0575
## T-test p-value........ 0.0042059 1.0473e-05
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.1544 2.1544
## mean control.......... 3.234 2.1886
## std mean diff......... -100.24 -3.174
##
## mean raw eQQ diff..... 1.0778 0.046266
## med raw eQQ diff..... 1.083 0.027096
## max raw eQQ diff..... 1.5216 1.5216
##
## mean eCDF diff........ 0.24931 0.0092529
## med eCDF diff........ 0.27455 0.0072115
## max eCDF diff........ 0.38928 0.043269
##
## var ratio (Tr/Co)..... 0.81865 1.0961
## T-test p-value........ < 2.22e-16 1.4716e-05
## KS Bootstrap p-value.. < 2.22e-16 0.82
## KS Naive p-value...... < 2.22e-16 0.83095
## KS Statistic.......... 0.38928 0.043269
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.3146 1.3146
## mean control.......... 0.82009 1.3075
## std mean diff......... 83.951 1.21
##
## mean raw eQQ diff..... 0.49614 0.019009
## med raw eQQ diff..... 0.48446 0.012796
## max raw eQQ diff..... 0.87204 0.2922
##
## mean eCDF diff........ 0.20897 0.0069441
## med eCDF diff........ 0.23499 0.0048077
## max eCDF diff........ 0.30208 0.024038
##
## var ratio (Tr/Co)..... 0.83187 1.04
## T-test p-value........ < 2.22e-16 0.0099265
## KS Bootstrap p-value.. < 2.22e-16 1
## KS Naive p-value...... < 2.22e-16 0.99975
## KS Statistic.......... 0.30208 0.024038
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 1.0473e-05
## Variable Name(s): Z1 Number(s): 1
##
##
## Pareamento usual usando o escore de propensao para n = 2000##
## ***** (V1) Z1 *****
## Before Matching After Matching
## mean treatment........ 0.61779 0.61779
## mean control.......... 0.5404 0.62438
## std mean diff......... 15.906 -1.3554
##
## mean raw eQQ diff..... 0.076923 0.00097276
## med raw eQQ diff..... 0 0
## max raw eQQ diff..... 1 1
##
## mean eCDF diff........ 0.038692 0.00048638
## med eCDF diff........ 0.038692 0.00048638
## max eCDF diff........ 0.077384 0.00097276
##
## var ratio (Tr/Co)..... 0.9524 1.0068
## T-test p-value........ 0.0042059 0.84503
##
##
## ***** (V2) Z2 *****
## Before Matching After Matching
## mean treatment........ 2.1544 2.1544
## mean control.......... 3.234 2.1386
## std mean diff......... -100.24 1.4692
##
## mean raw eQQ diff..... 1.0778 0.091212
## med raw eQQ diff..... 1.083 0.09052
## max raw eQQ diff..... 1.5216 1.5216
##
## mean eCDF diff........ 0.24931 0.021411
## med eCDF diff........ 0.27455 0.021401
## max eCDF diff........ 0.38928 0.051556
##
## var ratio (Tr/Co)..... 0.81865 0.95104
## T-test p-value........ < 2.22e-16 0.77721
## KS Bootstrap p-value.. < 2.22e-16 0.138
## KS Naive p-value...... < 2.22e-16 0.13008
## KS Statistic.......... 0.38928 0.051556
##
##
## ***** (V3) Z3 *****
## Before Matching After Matching
## mean treatment........ 1.3146 1.3146
## mean control.......... 0.82009 1.3103
## std mean diff......... 83.951 0.71864
##
## mean raw eQQ diff..... 0.49614 0.047805
## med raw eQQ diff..... 0.48446 0.036181
## max raw eQQ diff..... 0.87204 0.37497
##
## mean eCDF diff........ 0.20897 0.019347
## med eCDF diff........ 0.23499 0.016537
## max eCDF diff........ 0.30208 0.058366
##
## var ratio (Tr/Co)..... 0.83187 0.96164
## T-test p-value........ < 2.22e-16 0.90239
## KS Bootstrap p-value.. < 2.22e-16 0.066
## KS Naive p-value...... < 2.22e-16 0.060276
## KS Statistic.......... 0.30208 0.058366
##
##
## Before Matching Minimum p.value: < 2.22e-16
## Variable Name(s): Z2 Z3 Number(s): 2 3
##
## After Matching Minimum p.value: 0.066
## Variable Name(s): Z3 Number(s): 3