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--- re-building ‘v00_geex_intro.Rmd’ using rmarkdown

Attaching package: 'geex'

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label: SB1_estfun (with options) 
List of 2
 $ echo   : logi TRUE
 $ results: chr "hide"

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   SB1_estfun <- function(data){
     Y1 <- data$Y1
     function(theta){
         c(Y1 - theta[1],
          (Y1 - theta[1])^2 - theta[2])
     }
   } 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:13 2022 ------##

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label: SB1_run (with options) 
List of 3
 $ echo   : logi TRUE
 $ eval   : logi TRUE
 $ message: logi FALSE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   library(geex)
   results <- m_estimate(
       estFUN = SB1_estfun, 
       data   = geexex,
       root_control = setup_root_control(start = c(1,1))) 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:13 2022 ------##

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label: SB1_clsform (with options) 
List of 2
 $ echo: logi TRUE
 $ eval: logi TRUE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   n <- nrow(geexex)
   A <- diag(1, nrow = 2)
   
   B <- with(geexex, {
     Ybar <- mean(Y1)
     B11 <- mean( (Y1 - Ybar)^2 )
     B12 <- mean( (Y1 - Ybar) * ((Y1 - Ybar)^2 - B11) )
     B22 <- mean( ((Y1 - Ybar)^2 - B11)^2 )
     matrix(
       c(B11, B12,
         B12, B22), nrow = 2
     )
   })
   
   # closed form roots
   theta_cls <- c(mean(geexex$Y1),
                  # since var() divides by n - 1, not n
                  var(geexex$Y1) * (n - 1)/ n ) 
   
   # closed form sigma
   Sigma_cls <- (solve(A) %*% B %*% t(solve(A))) / n
   
   comparison <- list(geex = list(estimates = coef(results), vcov = vcov(results)), 
                      cls  = list(estimates = theta_cls, vcov = Sigma_cls)) 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

   ---------------------- inline R code fragments ----------------------- 
    757:891 format(max(abs(comparison$geex$estimates - comparison$cls$estimates), abs(comparison$geex$vcov - comparison$cls$vcov)), digits = 1)
   ---------------------------------------------------------------------- 

label: SB1_results (with options) 
List of 1
 $ echo: logi FALSE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   comparison 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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label: SB2_eefun (with options) 
List of 1
 $ echo: logi TRUE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   SB2_estfun <- function(data){
     Y1 <- data$Y1; Y2 <- data$Y2
     function(theta){
         c(Y1 - theta[1],
           Y2 - theta[2],
           theta[1] - (theta[3] * theta[2]) 
       )
     }
   } 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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label: SB2_run (with options) 
List of 2
 $ echo   : logi TRUE
 $ message: logi FALSE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   results <- m_estimate(
       estFUN = SB2_estfun, 
       data  = geexex, 
       root_control = setup_root_control(start = c(1, 1, 1))) 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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label: SB2_clsform (with options) 
List of 1
 $ echo: logi TRUE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   # Comparison to an analytically derived sanwich estimator
   A <- with(geexex, {
    matrix(
     c(1 , 0, 0,
       0 , 1, 0,
       -1, mean(Y1)/mean(Y2), mean(Y2)),
     byrow = TRUE, nrow = 3)
   })
   
   B <- with(geexex, {
     matrix(
       c(var(Y1)   , cov(Y1, Y2), 0,
         cov(Y1, Y2), var(Y2)   , 0,
         0, 0, 0),
       byrow = TRUE, nrow = 3)
   })
   
   ## closed form roots
   theta_cls <- c(mean(geexex$Y1), mean(geexex$Y2))
   theta_cls[3] <- theta_cls[1]/theta_cls[2]
   ## closed form covariance
   Sigma_cls <- (solve(A) %*% B %*% t(solve(A))) / nrow(geexex)
   comparison <- list(geex = list(estimates = coef(results), vcov = vcov(results)), 
                      cls  = list(estimates = theta_cls, vcov = Sigma_cls)) 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

   ---------------------- inline R code fragments ----------------------- 
    261:346 format(max(abs(comparison$geex$estimates - comparison$cls$estimates)), digits = 2)
    438:532 format(max(abs(comparison$geex$vcov - comparison$cls$vcov)), scientific = TRUE, digits = 2)
   ---------------------------------------------------------------------- 

label: SB2_results (with options) 
List of 1
 $ echo: logi TRUE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   comparison 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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label: SB3_eefun (with options) 
List of 3
 $ echo   : logi TRUE
 $ warning: logi FALSE
 $ message: logi FALSE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   SB3_estfun <- function(data){
     Y1 <- data$Y1
     function(theta){
         c(Y1 - theta[1],
          (Y1 - theta[1])^2 - theta[2],
          sqrt(theta[2]) - theta[3],
          log(theta[2]) - theta[4])
     }
   } 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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label: SB3_run (with options) 
List of 2
 $ echo   : logi FALSE
 $ message: logi FALSE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   results <- m_estimate(
      estFUN= SB3_estfun, 
      data  = geexex,
      root_control = setup_root_control(start = rep(2, 4, 4, 4))) 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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label: SB3_clsform (with options) 
List of 1
 $ echo: logi TRUE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   ## closed form roots
   theta_cls <- numeric(4)
   theta_cls[1] <- mean(geexex$Y1)
   theta_cls[2] <- sum((geexex$Y1 - theta_cls[1])^2)/nrow(geexex)
   theta_cls[3] <- sqrt(theta_cls[2])
   theta_cls[4] <- log(theta_cls[2])
   
   ## Compare to closed form ##
   theta2 <- theta_cls[2]
   mu3 <- moments::moment(geexex$Y1, order = 3, central = TRUE)
   mu4 <- moments::moment(geexex$Y1, order = 4, central = TRUE)
   ## closed form covariance
   Sigma_cls <- matrix(
     c(theta2, mu3, mu3/(2*sqrt(theta2)), mu3/theta2,
       mu3, mu4 - theta2^2, (mu4 - theta2^2)/(2*sqrt(theta2)), (mu4 - theta2^2)/theta2,
       mu3/(2 * sqrt(theta2)), (mu4 - theta2^2)/(2*sqrt(theta2)), (mu4 - theta2^2)/(4*theta2), (mu4 - theta2^2)/(2*theta2^(3/2)),
       mu3/theta2, (mu4 - theta2^2)/theta2, (mu4 - theta2^2)/(2*theta2^(3/2)), (mu4/theta2^2) - 1) ,
     nrow = 4, byrow = TRUE) / nrow(geexex)
   ## closed form covariance
   # Sigma_cls <- (solve(A) %*% B %*% t(solve(A))) / n
   comparison <- list(geex = list(estimates = coef(results), vcov = vcov(results)), 
                      cls  = list(estimates = theta_cls, vcov = Sigma_cls)) 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

   ---------------------- inline R code fragments ----------------------- 
    234:368 format(max(abs(comparison$geex$estimates - comparison$cls$estimates), abs(comparison$geex$vcov - comparison$cls$vcov)), digits = 2)
   ---------------------------------------------------------------------- 

label: SB3_results (with options) 
List of 1
 $ echo: logi FALSE

   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R code chunk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
   comparison 
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
##------ Sat Jun 25 20:30:14 2022 ------##

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Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
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SUMMARY: processing the following file failed:
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Error: Vignette re-building failed.
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