diff --git a/DESCRIPTION b/DESCRIPTION
index 4430c35..7820357 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Package: WebPower
 Title: Basic and Advanced Statistical Power Analysis
-Version: 0.9.0
-Date: 2023-04-16
+Version: 0.9.2
+Date: 2023-05-09
 Authors@R: c(person("Zhiyong", "Zhang", role = c("aut", "cre"),
                      email = "johnnyzhz@gmail.com"),
               person("Yujiao", "Mai", role = "aut"),
@@ -25,6 +25,6 @@ Encoding: UTF-8
 LazyLoad: yes
 LazyData: yes
 NeedsCompilation: no
-Packaged: 2023-04-20 17:05:43 UTC; zzhang4
+Packaged: 2023-05-10 01:01:20 UTC; zzhang4
 Repository: CRAN
-Date/Publication: 2023-04-20 18:02:37 UTC
+Date/Publication: 2023-05-10 02:30:02 UTC
diff --git a/MD5 b/MD5
index b09b306..85c953c 100644
--- a/MD5
+++ b/MD5
@@ -1,10 +1,10 @@
-c789f5404bdf5b6774c5fde70fe240b2 *DESCRIPTION
+268d8f29a27a853530f1423bdad590fd *DESCRIPTION
 7d64335ba38d220709a921137814ee14 *NAMESPACE
-a0bcec493c022a6e90c045aff311c3a6 *R/model14.R
-e27c5aff1b059e0363768f2d08fa7e1e *R/model15.R
-5208bbf4ba29a6d91130aa89f2a4060c *R/model58.R
-bf344a714d712897d11ca09860ab631a *R/model7.R
-df3ac23988eb7f24ce567e8c9f2ea0c6 *R/model8.R
+950a9b89b49627f0f4d37baf4b901a1b *R/model14.R
+11d33652db6615837b9b682f2ab7a2da *R/model15.R
+ee4d00e15593b6ec2b9f583171095aef *R/model58.R
+cf095a79c2a8266843b3d147df174096 *R/model7.R
+19cd026ef07667091f1bd61ffc17b15a *R/model8.R
 7e04ca484da8d6ceb462867d83b1ada8 *R/webpower.R
 83b0027813eefbbbb56cdfae00a9adcf *data/webpower.RData
 f4c53917e7a6ce6720539abe8c6f18a1 *inst/CRT2.txt
@@ -44,11 +44,11 @@ f93dcccad006d428281f7e0a359bacb0 *man/wp.mc.sem.power.curve.Rd
 e3aa54355131249a67530e681459f10a *man/wp.mc.t.Rd
 60375052e10b52d9268e0edb729742e2 *man/wp.mediation.Rd
 b82ac428a511dcf6b45e9af35422e00b *man/wp.mmrm.Rd
-dda9ad6387dcd7282f099fc61ff2e8f9 *man/wp.modmed.m14.Rd
-997b1223aa006f8f095ca550cef30a6d *man/wp.modmed.m15.Rd
-7bb3072286b579188a32716c571c1617 *man/wp.modmed.m58.Rd
-0a91119994e601cb5b8dde2c92595d4f *man/wp.modmed.m7.Rd
-71cb09b42c462ecb0c5ddde411530cc1 *man/wp.modmed.m8.Rd
+c97d1a521efad8bfe8b5a2f8a4c9b598 *man/wp.modmed.m14.Rd
+6a70dca0f9a5479a08ea3053943961cc *man/wp.modmed.m15.Rd
+6014bbfc4c4a41fcc2f617a0681cb093 *man/wp.modmed.m58.Rd
+241b0ad20c9c7ba24f9ad71e8ca0880a *man/wp.modmed.m7.Rd
+cb4817b654955c55b6c5aba5a4c72886 *man/wp.modmed.m8.Rd
 25eb6c557b4a4accd999ef15bc8cac40 *man/wp.mrt2arm.Rd
 9015883be37879a88e9585d072e03de6 *man/wp.mrt3arm.Rd
 cf30c06a5737b7fa17b8f3f65fd7a6f0 *man/wp.poisson.Rd
diff --git a/R/model14.R b/R/model14.R
index 6bd7342..45a3735 100644
--- a/R/model14.R
+++ b/R/model14.R
@@ -5,10 +5,10 @@
 #' power analysis of model 14 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 #'
 #' @param a1 regression coefficient of mediator (m) on predictor (x)
-#' @param cc regression coefficient of outcome (y) on predictor (x)
+#' @param cp regression coefficient of outcome (y) on predictor (x)
 #' @param b1 regression coefficient of outcome (y) on mediator (m)
-#' @param c1 regression coefficient of outcome (y) on moderator (w)
-#' @param c2 regression coefficient of outcome (y) on the product (mw)
+#' @param d1 regression coefficient of outcome (y) on moderator (w)
+#' @param b2 regression coefficient of outcome (y) on the product (mw)
 #' @param sigx2 variance of predictor (x)
 #' @param sigw2 variance of moderator (w)
 #' @param sige12 variance of error in the first regression equation
@@ -28,13 +28,13 @@
 #' @return power of indirect effect, direct effect, and moderation
 #' @export
 #' @examples
-#' test = wp.modmed.m14(a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2, sigx2 = 1,
+#' test = wp.modmed.m14(a1 = 0.2, cp = 0.2, b1 = 0.5, d1 = 0.5, b2 = 0.2, sigx2 = 1,
 #'                     sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5, n = 50,
 #'                     nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 #' print(test)
-wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
+wp.modmed.m14 <- function (a1 = 0.2, cp = 0.2, b1 = 0.5, d1 = 0.5, b2 = 0.2,
                            sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1,
-                           sigx_w = 0.5, n = 100, nrep = 1000, alpha = 0.05,
+                           sigx_w = 0.5, n = 100, nrep = 100, alpha = 0.05,
                            b = 1000, nb = n, w_value = 0, method = "value",
                            ncore = 1, pop.cov = NULL, mu = NULL,
                            varnames =  c('y', 'x', 'w', 'm', 'mw'))
@@ -43,15 +43,15 @@ wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
   if (is.null(pop.cov) || is.null(mu)) {
     sigm2 = a1^2*sigx2 + sige12
     sigxw2 = sigx2*sigw2 + sigx_w^2
-    sigy2 = (cc + a1*b1)^2*sigx2 + c1^2*sigw2 + c2^2*sige12 *
-      sigw2 + (a1*c2)^2*sigxw2 + b1^2*sige12 + sige22 + 2*(cc + a1*b1)*c1*sigx_w
+    sigy2 = (cp + a1*b1)^2*sigx2 + d1^2*sigw2 + b2^2*sige12 *
+      sigw2 + (a1*b2)^2*sigxw2 + b1^2*sige12 + sige22 + 2*(cp + a1*b1)*d1*sigx_w
     sigmw2 = a1^2*sigxw2 + sige12*sigw2
     sigx_m = a1*sigx2
-    sigx_y = (cc + a1*b1)*sigx2 + c1*sigx_w
-    sigm_y = a1*(cc + a1*b1)*sigx2 + a1*c1*sigx_w + b1*sige12
+    sigx_y = (cp + a1*b1)*sigx2 + d1*sigx_w
+    sigm_y = a1*(cp + a1*b1)*sigx2 + a1*d1*sigx_w + b1*sige12
     sigm_w = a1*sigx_w
-    sigy_w = (cc + a1*b1)*sigx_w + c1*sigw2
-    sigy_mw = a1^2*c2*sigxw2 + c2*sige12*sigw2
+    sigy_w = (cp + a1*b1)*sigx_w + d1*sigw2
+    sigy_mw = a1^2*b2*sigxw2 + b2*sige12*sigw2
 
     # y, x, w, m, mw
     pop.cov = array(
@@ -64,7 +64,7 @@ wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
     )
 
     u_mw = a1*sigx_w
-    u_y = a1*c2*sigx_w
+    u_y = a1*b2*sigx_w
     colnames(pop.cov) = rownames(pop.cov) = c('y', 'x', 'w', 'm', 'mw')
     mu = c(u_y, 0, 0, 0, u_mw)
   }else{
@@ -86,21 +86,21 @@ wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
       test_boot2 = lm(y ~ x + m + w + mw, data = boot_data)
       boot_CI = test_boot1$coefficients[2]*(test_boot2$coefficients[3] + test_boot2$coefficients[5]*w_value)
       boot_CD = test_boot2$coefficients[2]
-      boot_c2 = as.numeric(test_boot2$coefficients[5])
+      boot_b2 = as.numeric(test_boot2$coefficients[5])
       boot_CI1 = test_boot1$coefficients[2]
       boot_CI2 = (test_boot2$coefficients[3] + test_boot2$coefficients[5]*w_value)
-      return(list(boot_CI, boot_CD, boot_c2, boot_CI1, boot_CI2))
+      return(list(boot_CI, boot_CD, boot_b2, boot_CI1, boot_CI2))
     }
     boot_effect = lapply(1:b, bootstrap)
     boot_CI = matrix(0, ncol = 1, nrow = b)
     boot_CD = matrix(0, ncol = 1, nrow = b)
-    boot_c2 = matrix(0, ncol = 1, nrow = b)
+    boot_b2 = matrix(0, ncol = 1, nrow = b)
     boot_CI1 = matrix(0, ncol = 1, nrow = b)
     boot_CI2 = matrix(0, ncol = 1, nrow = b)
 
     boot_CI = t(sapply(1:b, function(i) unlist(boot_effect[[i]][1])))
     boot_CD = t(sapply(1:b, function(i) unlist(boot_effect[[i]][2])))
-    boot_c2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][3])))
+    boot_b2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][3])))
     boot_CI1 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][4])))
     boot_CI2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][5])))
 
@@ -109,7 +109,7 @@ wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
     interval_CI1 = matrix(0, ncol = 1, nrow = 2)
     interval_CI2 = matrix(0, ncol = 1, nrow = 2)
     interval_CD = matrix(0, ncol = 1, nrow = 2)
-    interval_c2 = matrix(0, ncol = 1, nrow = 2)
+    interval_b2 = matrix(0, ncol = 1, nrow = 2)
 
     interval_CI[, 1] = quantile(boot_CI,
                                 probs = c(alpha / 2, 1 - alpha / 2),
@@ -123,18 +123,18 @@ wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
     interval_CD[, 1] = quantile(boot_CD,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
-    interval_c2[, 1] = quantile(boot_c2,
+    interval_b2[, 1] = quantile(boot_b2,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
 
 
     r_CI = as.numeric(!sapply(1, function(i) dplyr::between(0, interval_CI[1, i], interval_CI[2, i])))
     r_CD = as.numeric(!sapply(1, function(i) dplyr::between(0, interval_CD[1, i], interval_CD[2, i])))
-    r_c2 = as.numeric(!sapply(1, function(i) dplyr::between(0, interval_c2[1, i], interval_c2[2, i])))
+    r_b2 = as.numeric(!sapply(1, function(i) dplyr::between(0, interval_b2[1, i], interval_b2[2, i])))
     if (method == "joint") {
       r_CI = as.numeric(!dplyr::between(0, interval_CI1[1, 1], interval_CI1[2, 1]))*as.numeric(!dplyr::between(0, interval_CI2[1, 1], interval_CI2[2, 1]))
     }
-    power = c(r_CI, r_CD, r_c2)
+    power = c(r_CI, r_CD, r_b2)
     return(power)
   }
 
@@ -143,7 +143,7 @@ wp.modmed.m14 <- function (a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2,
     
     parallel::clusterExport(
       CL1,
-      c('a1', 'cc', 'b1', 'c1', 'c2', 'sigx2', 'sigw2',
+      c('a1', 'cp', 'b1', 'd1', 'b2', 'sigx2', 'sigw2',
         'sige12', 'sige22', 'sigx_w', 'n', 'nrep',
         'alpha', 'b','nb', 'pop.cov', 'mu', 'method'
       ),
@@ -182,4 +182,3 @@ power3 is the power of moderation on the path m to y."
 }
 
 
-
diff --git a/R/model15.R b/R/model15.R
index 62db577..09c0765 100644
--- a/R/model15.R
+++ b/R/model15.R
@@ -4,11 +4,11 @@
 #' power analysis of model 15 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 #'
 #' @param a1 regression coefficient of mediator (m) on predictor (x)
-#' @param c regression coefficient of outcome (y) on predictor (x)
+#' @param cp regression coefficient of outcome (y) on predictor (x)
 #' @param b1 regression coefficient of outcome (y) on mediator (m)
 #' @param b2 regression coefficient of outcome (y) on the product (mw)
-#' @param c1 regression coefficient of outcome (y) on moderator (w)
-#' @param c2 regression coefficient of outcome (y) on the product (xw)
+#' @param d1 regression coefficient of outcome (y) on moderator (w)
+#' @param d2 regression coefficient of outcome (y) on the product (xw)
 #' @param sigx2 variance of predictor (x)
 #' @param sigw2 variance of moderator (w)
 #' @param sige12 variance of error in the first regression equation
@@ -28,13 +28,13 @@
 #' @return power of indirect effect, direct effect, and moderation
 #' @export
 #' @examples
-#' test = wp.modmed.m15(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.2, c1 = 0.2, c2 = 0.1,
+#' test = wp.modmed.m15(a1 = 0.6, cp = 0.2, b1 = 0.3, b2 = 0.2, d1 = 0.2, d2 = 0.1,
 #'                      sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.4,
 #'                      n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 #'print(test)
-wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 = 0.1,
+wp.modmed.m15 <- function(a1 = 0.6, cp = 0.2, b1 = 0.3, b2 = 0.5, d1 = 0.2, d2 = 0.1,
                    sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.4,
-                   n = 500, nrep = 1000, alpha = 0.05, b = 1000, nb = n,
+                   n = 100, nrep = 100, alpha = 0.05, b = 1000, nb = n,
                    w_value = 0, method = "value", ncore = 1,
                    pop.cov = NULL, mu = NULL,
                    varnames = c('y','x','w','m','xw','mw'))
@@ -42,18 +42,18 @@ wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 =
   if (is.null(pop.cov) || is.null(mu)){
     sigxw2 = sigx2*sigw2 + sigx_w^2
     sigm_xw = 0
-    sigy_xw = (c2 + a1*b2)*sigxw2
+    sigy_xw = (d2 + a1*b2)*sigxw2
     sigm_x = a1*sigx2
     sigm_w = a1*sigx_w
-    sigy_x = c1*sigx_w + (c + a1*b1)*sigx2
-    sigy_w = c1*sigw2 + (c + a1*b1)*sigx_w
+    sigy_x = d1*sigx_w + (cp + a1*b1)*sigx2
+    sigy_w = d1*sigw2 + (cp + a1*b1)*sigx_w
     sige1w2 = sige12*sigw2
-    sigy2 = (c + a1*b1)^2*sigx2 + (c2 + a1*b2)^2*sigxw2 + b2 ^
-      2*sige1w2 + c1^2*sigw2 + 2*c1*(c + a1*b1)*sigx_w + b1^2 *
+    sigy2 = (cp + a1*b1)^2*sigx2 + (d2 + a1*b2)^2*sigxw2 + b2 ^
+      2*sige1w2 + d1^2*sigw2 + 2*d1*(cp + a1*b1)*sigx_w + b1^2 *
       sige12 + sige22
     sigm2 = a1^2*sigx2 + sige12
-    sigy_m = a1*(c + a1*b1)*sigx2 + a1*c1*sigx_w + b1*sige12
-    sigy_mw = a1*(c2 + a1*b2)*sigxw2 + b2*sige1w2
+    sigy_m = a1*(cp + a1*b1)*sigx2 + a1*d1*sigx_w + b1*sige12
+    sigy_mw = a1*(d2 + a1*b2)*sigxw2 + b2*sige1w2
     sigxw_mw = a1*sigxw2
     sigmw2 = a1^2*sigxw2 + sige1w2
 
@@ -71,7 +71,7 @@ wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 =
     rownames(pop.cov) = colnames(pop.cov) = c('y', 'x', 'w', 'm', 'xw', 'mw')
     u_xw = sigx_w
     u_mw = sigm_w
-    u_y = c2*u_xw + b2*u_mw
+    u_y = d2*u_xw + b2*u_mw
     mu = c(u_y, 0, 0, 0, u_xw, u_mw)
   }else{
     pop.cov = pop.cov
@@ -93,23 +93,23 @@ wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 =
       test_boot2 = lm(y ~ x + m + w + xw + mw, data = boot_data)
       boot_CI = (test_boot2$coefficients[3] + test_boot2$coefficients[6]*w_value)*test_boot1$coefficients[2]
       boot_CD = test_boot2$coefficients[2] + test_boot2$coefficients[5]*w_value
-      boot_c2 = test_boot2$coefficients[5]
+      boot_d2 = test_boot2$coefficients[5]
       boot_b2 = test_boot2$coefficients[6]
       boot_CI1 = test_boot1$coefficients[2]
       boot_CI2 = (test_boot2$coefficients[3] + test_boot2$coefficients[6]*w_value)
-      return(list(boot_CI, boot_CD, boot_c2, boot_b2, boot_CI1, boot_CI2))
+      return(list(boot_CI, boot_CD, boot_d2, boot_b2, boot_CI1, boot_CI2))
     }
     boot_effect = lapply(1:b, bootstrap)
     boot_CI = matrix(0, ncol = 1, nrow = b)
     boot_CI1 = matrix(0, ncol = 1, nrow = b)
     boot_CI2 = matrix(0, ncol = 1, nrow = b)
     boot_CD = matrix(0, ncol = 1, nrow = b)
-    boot_c2 = matrix(0, ncol = 1, nrow = b)
+    boot_d2 = matrix(0, ncol = 1, nrow = b)
     boot_b2 = matrix(0, ncol = 1, nrow = b)
 
     boot_CI=t(sapply(1:b,function(i) unlist(boot_effect[[i]][1])))
     boot_CD=t(sapply(1:b,function(i) unlist(boot_effect[[i]][2])))
-    boot_c2=t(sapply(1:b,function(i) unlist(boot_effect[[i]][3])))
+    boot_d2=t(sapply(1:b,function(i) unlist(boot_effect[[i]][3])))
     boot_b2=t(sapply(1:b,function(i) unlist(boot_effect[[i]][4])))
     boot_CI1=t(sapply(1:b,function(i) unlist(boot_effect[[i]][5])))
     boot_CI2=t(sapply(1:b,function(i) unlist(boot_effect[[i]][6])))
@@ -118,7 +118,7 @@ wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 =
     interval_CI1=matrix(0,ncol=1,nrow=2)
     interval_CI2=matrix(0,ncol=1,nrow=2)
     interval_CD=matrix(0,ncol=1,nrow=2)
-    interval_c2=matrix(0,ncol=1,nrow=2)
+    interval_d2=matrix(0,ncol=1,nrow=2)
     interval_b2=matrix(0,ncol=1,nrow=2)
 
     interval_CI[, 1] = quantile(boot_CI,
@@ -133,7 +133,7 @@ wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 =
     interval_CD[, 1] = quantile(boot_CD,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
-    interval_c2[, 1] = quantile(boot_c2,
+    interval_d2[, 1] = quantile(boot_d2,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
     interval_b2[, 1] = quantile(boot_b2,
@@ -143,17 +143,17 @@ wp.modmed.m15 <- function(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.5, c1 = 0.2, c2 =
 
     r_CI=as.numeric(!sapply(1,function(i) dplyr::between(0,interval_CI[1,i],interval_CI[2,i])))
     r_DI=as.numeric(!sapply(1,function(i) dplyr::between(0,interval_CD[1,i],interval_CD[2,i])))
-    r_c2=as.numeric(!sapply(1:1,function(i) dplyr::between(0,interval_c2[1,i],interval_c2[2,i])))
+    r_d2=as.numeric(!sapply(1:1,function(i) dplyr::between(0,interval_d2[1,i],interval_d2[2,i])))
     r_b2=as.numeric(!sapply(1:1,function(i) dplyr::between(0,interval_b2[1,i],interval_b2[2,i])))
     if (method =="joint"){
       r_CI=as.numeric(!dplyr::between(0,interval_CI1[1,1],interval_CI1[2,1]))*as.numeric(!dplyr::between(0,interval_CI2[1,1],interval_CI2[2,1]))
     }
-    power=c(r_CI,r_DI, r_c2, r_b2)
+    power=c(r_CI,r_DI, r_d2, r_b2)
     return(power)
   }
   if (ncore > 1){
     CL1=parallel::makeCluster(ncore)
-    parallel::clusterExport(CL1,c('a1','c','b1','b2','c1','c2',
+    parallel::clusterExport(CL1,c('a1','c','b1','b2','d1','d2',
                                   'sigx2','sigw2','sige12','sige22','sigx_w',
                                   'n','nrep','alpha','b','nb','pop.cov','u_y','u_xw',
                                   'u_mw', 'mu', 'method', 'w_value'),envir = environment())
@@ -187,3 +187,4 @@ power4 is the power of moderation on the path m to y."), class = "webpower")
 }
 
 
+
diff --git a/R/model58.R b/R/model58.R
index c7907e8..0397c38 100644
--- a/R/model58.R
+++ b/R/model58.R
@@ -3,13 +3,13 @@
 #'
 #' power analysis of model 58 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 #'
-#' @param a1 regression coefficient of outcome (m) on moderator (w)
-#' @param b1 regression coefficient of mediator (m) on predictor (x)
-#' @param c1 regression coefficient of outcome (m) on the product (xw)
-#' @param a2 regression coefficient of outcome (y) on moderator (w)
-#' @param b2 regression coefficient of outcome (y) on mediator (m)
-#' @param c2 regression coefficient of outcome (y) on the product (mw)
-#' @param b3 regression coefficient of outcome (y) on predictor (x)
+#' @param c1 regression coefficient of outcome (m) on moderator (w)
+#' @param a1 regression coefficient of mediator (m) on predictor (x)
+#' @param c2 regression coefficient of outcome (m) on the product (xw)
+#' @param d1 regression coefficient of outcome (y) on moderator (w)
+#' @param b1 regression coefficient of outcome (y) on mediator (m)
+#' @param b2 regression coefficient of outcome (y) on the product (mw)
+#' @param cp regression coefficient of outcome (y) on predictor (x)
 #' @param sigx2 variance of predictor (x)
 #' @param sigw2 variance of moderator (w)
 #' @param sige12 variance of error in the first regression equation
@@ -29,47 +29,47 @@
 #' @return power of indirect effect, direct effect, and moderation
 #' @export
 #' @examples
-#' test = wp.modmed.m58(a1 = 0.2, b1 = 0.2, c1 = 0.1, c2 = 0.1,
-#'      b2 = 0.2, b3 = 0.2, a2 = 0.2,
+#' test = wp.modmed.m58(c1 = 0.2, a1 = 0.2, c2 = 0.1, b2 = 0.1,
+#'      b1 = 0.2, cp = 0.2, d1 = 0.2,
 #'      sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
 #'      n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 #' print(test)
-wp.modmed.m58 <- function(a1 = 0.5, b1 = 0.75, c1 = 0.1, a2 = 0.4, b2 = 0.6, c2 = 0.1,
-                   b3 = 0.5, sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.4,
-                   n = 500, nrep = 1000, alpha = 0.05, b=1000, nb = n,
+wp.modmed.m58 <- function(c1 = 0.5, a1 = 0.75, c2 = 0.1, d1 = 0.4, b1 = 0.6, b2 = 0.1,
+                   cp = 0.5, sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.4,
+                   n = 100, nrep = 100, alpha = 0.05, b = 1000, nb = n,
                    w_value = 0, method = "value", ncore = 1,
                    pop.cov = NULL, mu = NULL, varnames =  c('x', 'w', 'm', 'xw', 'mw', 'y'))
 {
   if (is.null(pop.cov) || is.null(mu)){
-    sigx_m = b1*sigx2 + a1*sigx_w
-    sigx_mw = c1*(1 + 2*sigx_w^2 / sigx2 / sigw2)*sigx2*sigw2
-    sigx_y = a2*sigx_w + b3*sigx2 + b2*sigx_m + c2*sigx_mw
+    sigx_m = a1*sigx2 + c1*sigx_w
+    sigx_mw = c2*(1 + 2*sigx_w^2 / sigx2 / sigw2)*sigx2*sigw2
+    sigx_y = d1*sigx_w + cp*sigx2 + b1*sigx_m + b2*sigx_mw
     sigx_xw = sigw_xw = 0
 
     sigw2 = sigw2
-    sigw_m = b1*sigx_w + a1*sigw2
-    sigw_mw = 3*c1*sigx_w / sqrt(sigx2) / sqrt(sigw2)*sqrt(sigx2)*(sqrt(sigw2))^3
-    sigw_y = a2*sigw2 + b3*sigx_w + b2*sigw_m + c2*sigw_mw
+    sigw_m = a1*sigx_w + c1*sigw2
+    sigw_mw = 3*c2*sigx_w / sqrt(sigx2) / sqrt(sigw2)*sqrt(sigx2)*(sqrt(sigw2))^3
+    sigw_y = d1*sigw2 + cp*sigx_w + b1*sigw_m + b2*sigw_mw
 
     sigxw2 = sigx2*sigw2 + sigx_w^2
     sigxw_w2 = 3*sigx_w*sigw2 - sigx_w*sigw2
 
-    sigm2 = b1^2*sigx2 + a1^2*sigw2 + c1^2*sigxw2 + sige12 +
-      2*b1*a1*sigx_w
-    sigm_xw = c1*sigxw2
-    sigm_mw = b1*c1*(sigx2*sigw2 + 2*sigx_w^2) + 3*a1*c1*sigx_w*sigw2 + c1*b1*sigxw2 + c1*a1*sigxw_w2
-    sigm_y = (a2 + a1*b2)*sigw_m + (b3 + b1*b2)*sigx_m + b2*c1*sigm_xw + c2*sigm_mw + b2*sige12
+    sigm2 = a1^2*sigx2 + c1^2*sigw2 + c2^2*sigxw2 + sige12 +
+      2*a1*c1*sigx_w
+    sigm_xw = c2*sigxw2
+    sigm_mw = a1*c2*(sigx2*sigw2 + 2*sigx_w^2) + 3*c1*c2*sigx_w*sigw2 + c2*a1*sigxw2 + c2*c1*sigxw_w2
+    sigm_y = (d1 + c1*b1)*sigw_m + (cp + a1*b1)*sigx_m + b1*c2*sigm_xw + b2*sigm_mw + b1*sige12
 
-    sigxw_mw = b1*sigxw2 + a1*(3*sigx_w*sigw2 - sigx_w*sigw2)
-    sigxw_y = (a2 + a1*b2)*sigw_xw + (b3 + b1*b2)*sigx_xw + b2*c1*sigxw2 + c2*sigxw_mw
+    sigxw_mw = a1*sigxw2 + c1*(3*sigx_w*sigw2 - sigx_w*sigw2)
+    sigxw_y = (d1 + c1*b1)*sigw_xw + (cp + a1*b1)*sigx_xw + b1*c2*sigxw2 + b2*sigxw_mw
 
     sigxw22 = 3*sigx2*sigw2^2 - 3*sigx_w^2*sigw2 + 15*sigx_w^2*sigw2
     sige1w2 = sige12*sigw2
 
-    sigmw2 = b1^2*sigxw2 + 2*a1^2*sigw2^2 + c1^2*sigxw22 + sige1w2 + 2*b1*a1*sigxw_w2
-    sigmw_y = (a2 + a1*b2)*sigw_mw + (b3 + b1*b2)*sigx_mw + b2*c1*sigxw_mw + c2*sigmw2
+    sigmw2 = a1^2*sigxw2 + 2*c1^2*sigw2^2 + c2^2*sigxw22 + sige1w2 + 2*a1*c1*sigxw_w2
+    sigmw_y = (d1 + c1*b1)*sigw_mw + (cp + a1*b1)*sigx_mw + b1*c2*sigxw_mw + b2*sigmw2
 
-    sigy2 = (a2 + a1*b2)^2*sigw2 + (b3 + b1*b2)^2*sigx2 + (b2*c1)^2*sigxw2 + c2^2*sigmw2 + b2^2*sige12 + sige22 + 2*(a2 + a1*b2)*(b3 + b1*b2)*sigx_w + 2*(a2 + a1*b2)*b2*c1*sigw_xw + 2*(a2 + a1*b2)*c2*sigw_mw + 2*(b3 + b1*b2)*c2*sigx_mw + 2*b2*c1*c2*sigxw_mw
+    sigy2 = (d1 + c1*b1)^2*sigw2 + (cp + a1*b1)^2*sigx2 + (b1*c2)^2*sigxw2 + b2^2*sigmw2 + b1^2*sige12 + sige22 + 2*(d1 + c1*b1)*(cp + a1*b1)*sigx_w + 2*(d1 + c1*b1)*b1*c2*sigw_xw + 2*(d1 + c1*b1)*b2*sigw_mw + 2*(cp + a1*b1)*b2*sigx_mw + 2*b1*c2*b2*sigxw_mw
 
 
     pop.cov=array(c(sigx2, sigx_w, sigx_m, sigx_xw, sigx_mw, sigx_y, 0, 0,
@@ -77,15 +77,15 @@ wp.modmed.m58 <- function(a1 = 0.5, b1 = 0.75, c1 = 0.1, a2 = 0.4, b2 = 0.6, c2
                     sigx_m, sigw_m, sigm2, sigm_xw, sigm_mw, sigm_y, sige12, 0,
                     sigx_xw, sigw_xw, sigm_xw, sigxw2, sigxw_mw, sigxw_y, 0, 0,
                     sigx_mw, sigw_mw, sigm_mw, sigxw_mw, sigmw2, sigmw_y, 0, 0,
-                    sigx_y, sigw_y, sigm_y, sigxw_y, sigmw_y, sigy2, b2*sige12, sige22,
-                    0, 0, sige12, 0, 0, b2*sige12, sige12, 0,
+                    sigx_y, sigw_y, sigm_y, sigxw_y, sigmw_y, sigy2, b1*sige12, sige22,
+                    0, 0, sige12, 0, 0, b1*sige12, sige12, 0,
                     0, 0, 0, 0, 0, sige22, 0, sige22), dim=c(8, 8))
 
     pop.cov = pop.cov[1:6, 1:6]
     u_xw = sigx_w
-    u_m = c1*u_xw
-    u_mw = b1*u_xw + a1*sigw2
-    u_y = b2*u_m + c2*u_mw
+    u_m = c2*u_xw
+    u_mw = a1*u_xw + c1*sigw2
+    u_y = b1*u_m + b2*u_mw
     mu = c(0, 0, u_m, u_xw, u_mw, u_y)
     rownames(pop.cov) = colnames(pop.cov) = c('x', 'w', 'm', 'xw', 'mw', 'y')
   }else{
@@ -112,29 +112,29 @@ wp.modmed.m58 <- function(a1 = 0.5, b1 = 0.75, c1 = 0.1, a2 = 0.4, b2 = 0.6, c2
       boot_CI1 = (test_boot1$coefficients[2] + test_boot1$coefficients[4]*w_value)
       boot_CI2 = (test_boot2$coefficients[3] + test_boot2$coefficients[5]*w_value)
       boot_DI = test_boot2$coefficients[2]
-      boot_c1 = test_boot1$coefficients[4]
-      boot_c2 = test_boot2$coefficients[5]
-      return(list(boot_CI, boot_DI, boot_c1, boot_c2, boot_CI1, boot_CI2))
+      boot_c2 = test_boot1$coefficients[4]
+      boot_b2 = test_boot2$coefficients[5]
+      return(list(boot_CI, boot_DI, boot_c2, boot_b2, boot_CI1, boot_CI2))
     }
     boot_effect = lapply(1:b, bootstrap)
     boot_CI = matrix(0, ncol = 1, nrow = b)
     boot_CI1 = matrix(0, ncol = 1, nrow = b)
     boot_CI2 = matrix(0, ncol = 1, nrow = b)
     boot_DI = matrix(0, ncol = 1, nrow = b)
-    boot_c1 = matrix(0, ncol = 1, nrow = b)
     boot_c2 = matrix(0, ncol = 1, nrow = b)
+    boot_b2 = matrix(0, ncol = 1, nrow = b)
 
     boot_CI = t(sapply(1:b,function(i) unlist(boot_effect[[i]][1])))
     boot_DI = as.matrix(sapply(1:b,function(i) unlist(boot_effect[[i]][2])))
-    boot_c1 = as.matrix(sapply(1:b,function(i) unlist(boot_effect[[i]][3])))
-    boot_c2 = as.matrix(sapply(1:b,function(i) unlist(boot_effect[[i]][4])))
+    boot_c2 = as.matrix(sapply(1:b,function(i) unlist(boot_effect[[i]][3])))
+    boot_b2 = as.matrix(sapply(1:b,function(i) unlist(boot_effect[[i]][4])))
     boot_CI1 = t(sapply(1:b,function(i) unlist(boot_effect[[i]][5])))
     boot_CI2 = t(sapply(1:b,function(i) unlist(boot_effect[[i]][6])))
 
     interval_CI = matrix(0, ncol = 1, nrow = 2)
     interval_DI = matrix(0, ncol = 1, nrow = 2)
-    interval_c1 = matrix(0, ncol = 1, nrow = 2)
     interval_c2 = matrix(0, ncol = 1, nrow = 2)
+    interval_b2 = matrix(0, ncol = 1, nrow = 2)
     interval_CI1 = matrix(0, ncol = 1, nrow = 2)
     interval_CI2 = matrix(0, ncol = 1, nrow = 2)
 
@@ -150,18 +150,18 @@ wp.modmed.m58 <- function(a1 = 0.5, b1 = 0.75, c1 = 0.1, a2 = 0.4, b2 = 0.6, c2
     interval_DI[, 1] = quantile(boot_DI[, 1],
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
-    interval_c1[, 1] = quantile(boot_c1[, 1],
+    interval_c2[, 1] = quantile(boot_c2[, 1],
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
-    interval_c2[, 1] = quantile(boot_c2[, 1],
+    interval_b2[, 1] = quantile(boot_b2[, 1],
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
 
     r_CI = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_CI[1,i],interval_CI[2,i])))
     r_DI = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_DI[1,i],interval_DI[2,i])))
-    r_c1 = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_c1[1,i],interval_c1[2,i])))
     r_c2 = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_c2[1,i],interval_c2[2,i])))
-    power = c(r_CI, r_DI, r_c1, r_c2)
+    r_b2 = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_b2[1,i],interval_b2[2,i])))
+    power = c(r_CI, r_DI, r_c2, r_b2)
     if (method == "joint"){
       r_CI = as.numeric(!dplyr::between(0,interval_CI1[1,1], interval_CI1[2,1]))*as.numeric(!dplyr::between(0, interval_CI2[1,1], interval_CI2[2,1]))
     }
@@ -169,7 +169,7 @@ wp.modmed.m58 <- function(a1 = 0.5, b1 = 0.75, c1 = 0.1, a2 = 0.4, b2 = 0.6, c2
   }
   if (ncore > 1){
     CL1 = parallel::makeCluster(ncore)
-    parallel::clusterExport(CL1,c('a1', 'b1', 'c1', 'c2', 'b2', 'b3', 'a2',
+    parallel::clusterExport(CL1,c('c1', 'a1', 'c2', 'b2', 'b1', 'cp', 'd1',
                                   'sigx2', 'sigw2', 'sige12', 'sige22', 'sigx_w',
                                   'n', 'nrep', 'alpha','b','nb','pop.cov',
                                   'mu', 'method', 'w_value'),envir = environment())
@@ -198,9 +198,7 @@ wp.modmed.m58 <- function(a1 = 0.5, b1 = 0.75, c1 = 0.1, a2 = 0.4, b2 = 0.6, c2
                  note="power1 is the power of the conditional indirect effect of x on y through m.
 power2 is  the power of the direct effect of x on y.
 power3 is the power of moderation on the path x to m.
-power4 is the powe of moderation on the path m to y."), class = "webpower")
+power4 is the power of moderation on the path m to y."), class = "webpower")
   return(power.structure)
 
 }
-
-
diff --git a/R/model7.R b/R/model7.R
index 9504625..6d787c9 100644
--- a/R/model7.R
+++ b/R/model7.R
@@ -4,11 +4,11 @@
 #'
 #' power analysis of model 7 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 #'
-#' @param beta1 regression coefficient of mediator (m) on predictor (x)
-#' @param beta2 regression coefficient of outcome (y) on predictor (x)
-#' @param beta3 regression coefficient of outcome (y) on mediator (m)
-#' @param a1 regression coefficient of mediator (m) on moderator (w)
-#' @param c1 regression coefficient of mediator (m) on the product (xw)
+#' @param a1 regression coefficient of mediator (m) on predictor (x)
+#' @param cp regression coefficient of outcome (y) on predictor (x)
+#' @param b1 regression coefficient of outcome (y) on mediator (m)
+#' @param c1 regression coefficient of mediator (m) on moderator (w)
+#' @param c2 regression coefficient of mediator (m) on the product (xw)
 #' @param sigx2 variance of predictor (x)
 #' @param sigw2 variance of moderator (w)
 #' @param sige12 variance of error in the first regression equation
@@ -29,14 +29,14 @@
 #' @export
 #' @examples
 #' # usage of wp.modmed.m7
-#' test = wp.modmed.m7(beta1 = 0.39, beta2 = 0.2, beta3 = 0.3, a1 = 0.39,
-#'           c1 = 0.2, sigx2 = 1, sigw2 = 1, sige12 = 1,
+#' test = wp.modmed.m7(a1 = 0.39, cp = 0.2, b1 = 0.3, c1 = 0.39,
+#'           c2 = 0.2, sigx2 = 1, sigw2 = 1, sige12 = 1,
 #'          sige22 = 1, sigx_w = 0.5, n = 50, nrep = 100,
 #'          alpha = 0.05, b = 1000, ncore = 1)
 #' print(test)
-wp.modmed.m7 <- function (beta1 = 0.39, beta2 = 0.2, beta3 = 0.3, a1 = 0.39,
-                  c1 = 0.2, sigx2 = 1, sigw2 = 1, sige12 = 1,
-                  sige22 = 1, sigx_w = 0.5, n = 500, nrep = 1000,
+wp.modmed.m7 <- function (a1 = 0.39, cp = 0.2, b1 = 0.3, c1 = 0.39,
+                  c2 = 0.2, sigx2 = 1, sigw2 = 1, sige12 = 1,
+                  sige22 = 1, sigx_w = 0.5, n = 100, nrep = 100,
                   alpha = 0.05, b = 1000, nb = n, w_value = 0, method="value",
                   ncore = 1, pop.cov = NULL, mu = NULL,
                   varnames = c('y', 'x', 'w', 'm', 'xw'))
@@ -44,30 +44,30 @@ wp.modmed.m7 <- function (beta1 = 0.39, beta2 = 0.2, beta3 = 0.3, a1 = 0.39,
 
   if (is.null(pop.cov) || is.null(mu)){
     sigxw2 = sigx2*sigw2 + sigx_w^2
-    sigm_x = beta1*sigx2 + a1*sigx_w
-    sigm_w = beta1*sigx_w + a1*sigw2
-    sigm_xw = c1*sigxw2
-    sigm2 = beta1^2*sigx2 + a1^2*sigw2 + c1^2*sigxw2 + sige12 + 2*beta1*a1*sigx_w
-    sigy_x = (beta2 + beta3*beta1)*sigx2 + beta3*a1*sigx_w
-    sigy_w = (beta2 + beta3*beta1)*sigx_w + beta3*a1*sigw2
-    sigy_xw = beta3*c1*sigxw2
-    sigy_m = beta2*sigm_x + beta3*sigm2
-    sigy2 = (beta2 + beta3*beta1)^2*sigx2 + beta3^2*a1^2*sigw2 + beta3^2*c1^2*sigxw2 + beta3^2*sige12 + sige22 + 2*beta3*a1*(beta2 + beta3*beta1)*sigx_w
-
-    pop.cov = array(c(sigy2, sigy_x, sigy_w, sigy_m, sigy_xw, beta3*sige12,sige22,
+    sigm_x = a1*sigx2 + c1*sigx_w
+    sigm_w = a1*sigx_w + c1*sigw2
+    sigm_xw = c2*sigxw2
+    sigm2 = a1^2*sigx2 + c1^2*sigw2 + c2^2*sigxw2 + sige12 + 2*a1*c1*sigx_w
+    sigy_x = (cp + b1*a1)*sigx2 + b1*c1*sigx_w
+    sigy_w = (cp + b1*a1)*sigx_w + b1*c1*sigw2
+    sigy_xw = b1*c2*sigxw2
+    sigy_m = cp*sigm_x + b1*sigm2
+    sigy2 = (cp + b1*a1)^2*sigx2 + b1^2*c1^2*sigw2 + b1^2*c2^2*sigxw2 + b1^2*sige12 + sige22 + 2*b1*c1*(cp + b1*a1)*sigx_w
+
+    pop.cov = array(c(sigy2, sigy_x, sigy_w, sigy_m, sigy_xw, b1*sige12,sige22,
                     sigy_x, sigx2, sigx_w, sigm_x, 0, 0, 0,
                     sigy_w, sigx_w, sigw2, sigm_w, 0, 0, 0,
                     sigy_m, sigm_x, sigm_w, sigm2, sigm_xw, sige12, 0,
                     sigy_xw, 0, 0, sigm_xw, sigxw2, 0, 0,
-                    beta3*sige12, 0, 0, sige12, 0, sige12, 0,
+                    b1*sige12, 0, 0, sige12, 0, sige12, 0,
                     sige22, 0, 0, 0, 0, 0, sige22),
                     dim = c(7, 7))
     pop.cov = pop.cov[1:5, 1:5]
     colnames(pop.cov) = rownames(pop.cov)=c('y','x','w','m','xw')
     # means
     u_xw = sigx_w
-    u_m = c1*u_xw
-    u_y = beta3*u_m
+    u_m = c2*u_xw
+    u_y = b1*u_m
     mu = c(u_y, 0, 0, u_m, u_xw)
   }else{
     pop.cov = pop.cov
@@ -141,7 +141,7 @@ wp.modmed.m7 <- function (beta1 = 0.39, beta2 = 0.2, beta3 = 0.3, a1 = 0.39,
   }
   if (ncore > 1){
     CL1 = parallel::makeCluster(ncore)
-    parallel::clusterExport(CL1, c('beta1', 'beta2', 'beta3', 'a1', 'c1',
+    parallel::clusterExport(CL1, c('a1', 'cp', 'b1', 'c1', 'c2',
                                    'sigx2', 'sigw2', 'sige12', 'sige22', 'sigx_w',
                                    'n', 'nrep', 'alpha', 'b', 'nb', 'pop.cov',
                                    'method', 'mu', 'w_value'), envir = environment())
@@ -175,4 +175,3 @@ power3 is the power of moderation on the path x to m."), class = "webpower")
 
 
 
-
diff --git a/R/model8.R b/R/model8.R
index a02d4e5..5a3ca1a 100644
--- a/R/model8.R
+++ b/R/model8.R
@@ -4,13 +4,13 @@
 #'
 #' power analysis of model 8 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 #'
-#' @param beta1 regression coefficient of mediator (m) on predictor (x)
-#' @param beta2 regression coefficient of outcome (y) on predictor (m)
-#' @param beta3 regression coefficient of outcome (y) on mediator (x)
-#' @param a1 regression coefficient of mediator (m) on moderator (w)
-#' @param a2 regression coefficient of mediator (y) on moderator (w)
-#' @param c1 regression coefficient of mediator (m) on the product (xw)
-#' @param c2 regression coefficient of mediator (y) on the product (xw)
+#' @param a1 regression coefficient of mediator (m) on predictor (x)
+#' @param cp regression coefficient of outcome (y) on predictor (m)
+#' @param b1 regression coefficient of outcome (y) on mediator (x)
+#' @param c1 regression coefficient of mediator (m) on moderator (w)
+#' @param d1 regression coefficient of mediator (y) on moderator (w)
+#' @param c2 regression coefficient of mediator (m) on the product (xw)
+#' @param d2 regression coefficient of mediator (y) on the product (xw)
 #' @param sigx2 variance of predictor (x)
 #' @param sigw2 variance of moderator (w)
 #' @param sige12 variance of error in the first regression equation
@@ -31,42 +31,42 @@
 #' @export
 #' @examples
 #' # usage of wp.modmed.m8
-#' test = wp.modmed.m8(beta1 = 0.2, beta2 = 0.2, beta3 = 0.2,
-#'                    a1 = 0.2, a2=0.2, c1 = 0.2, c2 = 0.2,
+#' test = wp.modmed.m8(a1 = 0.2, cp = 0.2, b1 = 0.2,
+#'                    c1 = 0.2, d1=0.2, c2 = 0.2, d2 = 0.2,
 #'                    sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
 #'                    n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 #' print(test)
-wp.modmed.m8 <- function (beta1 = 0.2, beta2 = 0.75, beta3 = 0.8,
-                  a1 = 0.6, a2 = 0.3, c1 = 0.8, c2 = 0.79,
+wp.modmed.m8 <- function (a1 = 0.2, cp = 0.75, b1 = 0.8,
+                  c1 = 0.6, d1 = 0.3, c2 = 0.8, d2 = 0.79,
                   sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
-                  n = 100, nrep = 1000, alpha = 0.05, b = 1000, nb = n,
+                  n = 100, nrep = 100, alpha = 0.05, b = 1000, nb = n,
                   w_value = 0, method = "value", ncore = 1,
                   pop.cov = NULL, mu = NULL, varnames = c('y','x','w','m','xw'))
 {
   if (is.null(pop.cov) || is.null(mu)){
     sigxw2 = sigx2*sigw2 + sigx_w^2
-    sigm_xw = c1*sigxw2
-    sigy_xw = (beta2*c1 + c2)*sigxw2
-    sigm_x = a1*sigx_w + beta1*sigx2
-    sigm_w = beta1*sigx_w+a1*sigw2
-    sigy_x = (a2 + a1*beta2)*sigx_w + (beta3 + beta1*beta2)*sigx2
-    sigy_w = (a2+a1*beta2)*sigw2 + (beta3 + beta1*beta2)*sigx_w
-    sigy2 = (a2 + a1*beta2)^2*sigw2 + (beta3 + beta1*beta2)^2*sigx2 + beta2^2*sige12 +
-      (beta2*c1 + c2)^2*sigxw2 + sige22 + 2*(a2 + a1*beta2)*(beta3 + beta1*beta2)*sigx_w
-    sigm2 = beta1^2*sigx2 + a1^2*sigw2 + c1^2*sigxw2 + sige12 + 2*beta1*a1*sigx_w
-    sigy_m = a2*sigm_w + beta3*sigm_x + beta2*sigm2 + c2*sigm_xw
-    pop.cov = array(c(sigy2, sigy_x, sigy_w, sigy_m, sigy_xw, beta2*sige12, sige22,
+    sigm_xw = c2*sigxw2
+    sigy_xw = (cp*c2 + d2)*sigxw2
+    sigm_x = c1*sigx_w + a1*sigx2
+    sigm_w = a1*sigx_w+c1*sigw2
+    sigy_x = (d1 + c1*cp)*sigx_w + (b1 + a1*cp)*sigx2
+    sigy_w = (d1+c1*cp)*sigw2 + (b1 + a1*cp)*sigx_w
+    sigy2 = (d1 + c1*cp)^2*sigw2 + (b1 + a1*cp)^2*sigx2 + cp^2*sige12 +
+      (cp*c2 + d2)^2*sigxw2 + sige22 + 2*(d1 + c1*cp)*(b1 + a1*cp)*sigx_w
+    sigm2 = a1^2*sigx2 + c1^2*sigw2 + c2^2*sigxw2 + sige12 + 2*a1*c1*sigx_w
+    sigy_m = d1*sigm_w + b1*sigm_x + cp*sigm2 + d2*sigm_xw
+    pop.cov = array(c(sigy2, sigy_x, sigy_w, sigy_m, sigy_xw, cp*sige12, sige22,
                     sigy_x, sigx2, sigx_w, sigm_x, 0, 0, 0,
                     sigy_w, sigx_w, sigw2, sigm_w, 0, 0, 0,
                     sigy_m, sigm_x, sigm_w, sigm2, sigm_xw, sige12, 0,
                     sigy_xw, 0, 0, sigm_xw, sigxw2, 0, 0,
-                    beta2*sige12, 0, 0, sige12, 0, sige12, 0,
+                    cp*sige12, 0, 0, sige12, 0, sige12, 0,
                     sige22, 0, 0, 0, 0, 0, sige22),
                     dim = c(7, 7))
     pop.cov = pop.cov[1:5,1:5]
     u_xw = sigx_w
-    u_m = c1*u_xw
-    u_y = beta2*u_m + c2*u_xw
+    u_m = c2*u_xw
+    u_y = cp*u_m + d2*u_xw
     colnames(pop.cov) = rownames(pop.cov) = c('y','x','w','m','xw')
     mu = c(u_y, 0, 0, u_m, u_xw)
   }else{
@@ -89,32 +89,32 @@ wp.modmed.m8 <- function (beta1 = 0.2, beta2 = 0.75, beta3 = 0.8,
       test_boot2 = lm(y ~ x + m + w + xw,data = boot_data)
       boot_CI = (test_boot1$coefficients[2] + test_boot1$coefficients[4]*w_value)*test_boot2$coefficients[3]
       boot_CD = test_boot2$coefficients[2] + test_boot2$coefficients[5]*w_value
-      boot_c1 = as.numeric(test_boot1$coefficients[4])
-      boot_c2 = as.numeric(test_boot2$coefficients[5])
+      boot_c2 = as.numeric(test_boot1$coefficients[4])
+      boot_d2 = as.numeric(test_boot2$coefficients[5])
       boot_CI1 = (test_boot1$coefficients[2] + test_boot1$coefficients[4]*w_value)
       boot_CI2 = test_boot2$coefficients[3]
-      return(list(boot_CI, boot_CD, boot_c1, boot_c2, boot_CI1, boot_CI2))
+      return(list(boot_CI, boot_CD, boot_c2, boot_d2, boot_CI1, boot_CI2))
     }
     boot_effect = lapply(1:b, bootstrap)
     boot_CI = matrix(0, ncol = 1, nrow = b)
     boot_CD = matrix(0, ncol = 1, nrow = b)
-    boot_c1 = matrix(0, ncol = 1, nrow = b)
     boot_c2 = matrix(0, ncol = 1, nrow = b)
+    boot_d2 = matrix(0, ncol = 1, nrow = b)
     boot_CI1 = matrix(0, ncol = 1, nrow = b)
     boot_CI2 = matrix(0, ncol = 1, nrow = b)
 
     boot_CI = t(sapply(1:b, function(i) unlist(boot_effect[[i]][1])))
     boot_CD = t(sapply(1:b, function(i) unlist(boot_effect[[i]][2])))
-    boot_c1 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][3])))
-    boot_c2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][4])))
+    boot_c2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][3])))
+    boot_d2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][4])))
     boot_CI1 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][5])))
     boot_CI2 = t(sapply(1:b, function(i) unlist(boot_effect[[i]][6])))
 
 
     interval_CI = matrix(0, ncol = 1, nrow = 2)
     interval_CD = matrix(0, ncol = 1, nrow = 2)
-    interval_c1 = matrix(0, ncol = 1, nrow = 2)
     interval_c2 = matrix(0, ncol = 1, nrow = 2)
+    interval_d2 = matrix(0, ncol = 1, nrow = 2)
     interval_CI1 = matrix(0, ncol = 1, nrow = 2)
     interval_CI2 = matrix(0, ncol = 1, nrow = 2)
 
@@ -125,10 +125,10 @@ wp.modmed.m8 <- function (beta1 = 0.2, beta2 = 0.75, beta3 = 0.8,
     interval_CD[, 1] = quantile(boot_CD,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
-    interval_c1[, 1] = quantile(boot_c1,
+    interval_c2[, 1] = quantile(boot_c2,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
-    interval_c2[, 1] = quantile(boot_c2,
+    interval_d2[, 1] = quantile(boot_d2,
                                 probs = c(alpha / 2, 1 - alpha / 2),
                                 names = T)
     interval_CI1[, 1] = quantile(boot_CI1,
@@ -141,17 +141,17 @@ wp.modmed.m8 <- function (beta1 = 0.2, beta2 = 0.75, beta3 = 0.8,
 
     r_CI = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_CI[1,i], interval_CI[2,i])))
     r_DI = as.numeric(!sapply(1,function(i) dplyr::between(0,interval_CD[1,i], interval_CD[2,i])))
-    r_c1 = as.numeric(!sapply(1, function(i) dplyr::between(0,interval_c1[1,i], interval_c1[2,i])))
     r_c2 = as.numeric(!sapply(1, function(i) dplyr::between(0,interval_c2[1,i], interval_c2[2,i])))
+    r_d2 = as.numeric(!sapply(1, function(i) dplyr::between(0,interval_d2[1,i], interval_d2[2,i])))
     if (method == "joint"){
       r_CI = as.numeric(!dplyr::between(0, interval_CI1[1,1], interval_CI1[2,1]))*as.numeric(!dplyr::between(0, interval_CI2[1,1], interval_CI2[2,1]))
     }
-    power=c(r_CI, r_DI, r_c1, r_c2)
+    power=c(r_CI, r_DI, r_c2, r_d2)
     return(power)
   }
   if (ncore > 1){
     CL1 = parallel::makeCluster(ncore)
-    parallel::clusterExport(CL1, c('beta1', 'beta2', 'beta3', 'a1', 'a2', 'c1','c2',
+    parallel::clusterExport(CL1, c('a1', 'cp', 'b1', 'c1', 'd1', 'c2','d2',
                                    'sigx2', 'sigw2', 'sige12', 'sige22', 'sigx_w',
                                    'n', 'nrep', 'alpha', 'b', 'nb', 'pop.cov',
                                    'mu', 'w_value', 'method'), envir = environment())
@@ -182,3 +182,5 @@ power4 is the power of moderation on the path x to y."), class = "webpower")
   return(power.structure)
 
 }
+
+
diff --git a/man/wp.modmed.m14.Rd b/man/wp.modmed.m14.Rd
index 8df034a..c18e70d 100644
--- a/man/wp.modmed.m14.Rd
+++ b/man/wp.modmed.m14.Rd
@@ -6,17 +6,17 @@
 \usage{
 wp.modmed.m14(
   a1 = 0.2,
-  cc = 0.2,
+  cp = 0.2,
   b1 = 0.5,
-  c1 = 0.5,
-  c2 = 0.2,
+  d1 = 0.5,
+  b2 = 0.2,
   sigx2 = 1,
   sigw2 = 1,
   sige12 = 1,
   sige22 = 1,
   sigx_w = 0.5,
   n = 100,
-  nrep = 1000,
+  nrep = 100,
   alpha = 0.05,
   b = 1000,
   nb = n,
@@ -31,13 +31,13 @@ wp.modmed.m14(
 \arguments{
 \item{a1}{regression coefficient of mediator (m) on predictor (x)}
 
-\item{cc}{regression coefficient of outcome (y) on predictor (x)}
+\item{cp}{regression coefficient of outcome (y) on predictor (x)}
 
 \item{b1}{regression coefficient of outcome (y) on mediator (m)}
 
-\item{c1}{regression coefficient of outcome (y) on moderator (w)}
+\item{d1}{regression coefficient of outcome (y) on moderator (w)}
 
-\item{c2}{regression coefficient of outcome (y) on the product (mw)}
+\item{b2}{regression coefficient of outcome (y) on the product (mw)}
 
 \item{sigx2}{variance of predictor (x)}
 
@@ -79,9 +79,9 @@ power analysis of model 14 in Introduction to Mediation, Moderation, and Conditi
 }
 \examples{
 \donttest{
-test = wp.modmed.m14(a1 = 0.2, cc = 0.2, b1 = 0.5, c1 = 0.5, c2 = 0.2, sigx2 = 1,
-                     sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5, n = 50,
-                     nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
+test = wp.modmed.m14(a1 = 0.2, cp = 0.2, b1 = 0.5, d1 = 0.5, b2 = 0.2, sigx2 = 1,
+                    sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5, n = 50,
+                    nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 print(test)
 }
 }
diff --git a/man/wp.modmed.m15.Rd b/man/wp.modmed.m15.Rd
index 8326882..130df5d 100644
--- a/man/wp.modmed.m15.Rd
+++ b/man/wp.modmed.m15.Rd
@@ -6,18 +6,18 @@
 \usage{
 wp.modmed.m15(
   a1 = 0.6,
-  c = 0.2,
+  cp = 0.2,
   b1 = 0.3,
   b2 = 0.5,
-  c1 = 0.2,
-  c2 = 0.1,
+  d1 = 0.2,
+  d2 = 0.1,
   sigx2 = 1,
   sigw2 = 1,
   sige12 = 1,
   sige22 = 1,
   sigx_w = 0.4,
-  n = 500,
-  nrep = 1000,
+  n = 100,
+  nrep = 100,
   alpha = 0.05,
   b = 1000,
   nb = n,
@@ -32,15 +32,15 @@ wp.modmed.m15(
 \arguments{
 \item{a1}{regression coefficient of mediator (m) on predictor (x)}
 
-\item{c}{regression coefficient of outcome (y) on predictor (x)}
+\item{cp}{regression coefficient of outcome (y) on predictor (x)}
 
 \item{b1}{regression coefficient of outcome (y) on mediator (m)}
 
 \item{b2}{regression coefficient of outcome (y) on the product (mw)}
 
-\item{c1}{regression coefficient of outcome (y) on moderator (w)}
+\item{d1}{regression coefficient of outcome (y) on moderator (w)}
 
-\item{c2}{regression coefficient of outcome (y) on the product (xw)}
+\item{d2}{regression coefficient of outcome (y) on the product (xw)}
 
 \item{sigx2}{variance of predictor (x)}
 
@@ -80,12 +80,11 @@ power of indirect effect, direct effect, and moderation
 \description{
 power analysis of model 15 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 }
-
 \examples{
 \donttest{
-test = wp.modmed.m15(a1 = 0.6, c = 0.2, b1 = 0.3, b2 = 0.2, c1 = 0.2, c2 = 0.1,
-                      sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.4,
-                      n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
+test = wp.modmed.m15(a1 = 0.6, cp = 0.2, b1 = 0.3, b2 = 0.2, d1 = 0.2, d2 = 0.1,
+                     sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.4,
+                     n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 print(test)
 }
 }
diff --git a/man/wp.modmed.m58.Rd b/man/wp.modmed.m58.Rd
index 6728062..ad83319 100644
--- a/man/wp.modmed.m58.Rd
+++ b/man/wp.modmed.m58.Rd
@@ -5,20 +5,20 @@
 \title{model58}
 \usage{
 wp.modmed.m58(
-  a1 = 0.5,
-  b1 = 0.75,
-  c1 = 0.1,
-  a2 = 0.4,
-  b2 = 0.6,
+  c1 = 0.5,
+  a1 = 0.75,
   c2 = 0.1,
-  b3 = 0.5,
+  d1 = 0.4,
+  b1 = 0.6,
+  b2 = 0.1,
+  cp = 0.5,
   sigx2 = 1,
   sigw2 = 1,
   sige12 = 1,
   sige22 = 1,
   sigx_w = 0.4,
-  n = 500,
-  nrep = 1000,
+  n = 100,
+  nrep = 100,
   alpha = 0.05,
   b = 1000,
   nb = n,
@@ -27,23 +27,23 @@ wp.modmed.m58(
   ncore = 1,
   pop.cov = NULL,
   mu = NULL,
-  varnames =  c('x', 'w', 'm', 'xw', 'mw', 'y')
+  varnames = c("x", "w", "m", "xw", "mw", "y")
 )
 }
 \arguments{
-\item{a1}{regression coefficient of outcome (m) on moderator (w)}
+\item{c1}{regression coefficient of outcome (m) on moderator (w)}
 
-\item{b1}{regression coefficient of mediator (m) on predictor (x)}
+\item{a1}{regression coefficient of mediator (m) on predictor (x)}
 
-\item{c1}{regression coefficient of outcome (m) on the product (xw)}
+\item{c2}{regression coefficient of outcome (m) on the product (xw)}
 
-\item{a2}{regression coefficient of outcome (y) on moderator (w)}
+\item{d1}{regression coefficient of outcome (y) on moderator (w)}
 
-\item{b2}{regression coefficient of outcome (y) on mediator (m)}
+\item{b1}{regression coefficient of outcome (y) on mediator (m)}
 
-\item{c2}{regression coefficient of outcome (y) on the product (mw)}
+\item{b2}{regression coefficient of outcome (y) on the product (mw)}
 
-\item{b3}{regression coefficient of outcome (y) on predictor (x)}
+\item{cp}{regression coefficient of outcome (y) on predictor (x)}
 
 \item{sigx2}{variance of predictor (x)}
 
@@ -83,13 +83,12 @@ power of indirect effect, direct effect, and moderation
 \description{
 power analysis of model 58 in Introduction to Mediation, Moderation, and Conditional Process Analysis
 }
-
 \examples{
 \donttest{
-test = wp.modmed.m58(a1 = 0.2, b1 = 0.2, c1 = 0.1, c2 = 0.1,
-      b2 = 0.2, b3 = 0.2, a2 = 0.2,
-      sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
-      n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
+test = wp.modmed.m58(c1 = 0.2, a1 = 0.2, c2 = 0.1, b2 = 0.1,
+     b1 = 0.2, cp = 0.2, d1 = 0.2,
+     sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
+     n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 print(test)
 }
 }
diff --git a/man/wp.modmed.m7.Rd b/man/wp.modmed.m7.Rd
index 476f59e..a43568d 100644
--- a/man/wp.modmed.m7.Rd
+++ b/man/wp.modmed.m7.Rd
@@ -5,18 +5,18 @@
 \title{model7}
 \usage{
 wp.modmed.m7(
-  beta1 = 0.39,
-  beta2 = 0.2,
-  beta3 = 0.3,
   a1 = 0.39,
-  c1 = 0.2,
+  cp = 0.2,
+  b1 = 0.3,
+  c1 = 0.39,
+  c2 = 0.2,
   sigx2 = 1,
   sigw2 = 1,
   sige12 = 1,
   sige22 = 1,
   sigx_w = 0.5,
-  n = 500,
-  nrep = 1000,
+  n = 100,
+  nrep = 100,
   alpha = 0.05,
   b = 1000,
   nb = n,
@@ -29,15 +29,15 @@ wp.modmed.m7(
 )
 }
 \arguments{
-\item{beta1}{regression coefficient of mediator (m) on predictor (x)}
+\item{a1}{regression coefficient of mediator (m) on predictor (x)}
 
-\item{beta2}{regression coefficient of outcome (y) on predictor (x)}
+\item{cp}{regression coefficient of outcome (y) on predictor (x)}
 
-\item{beta3}{regression coefficient of outcome (y) on mediator (m)}
+\item{b1}{regression coefficient of outcome (y) on mediator (m)}
 
-\item{a1}{regression coefficient of mediator (m) on moderator (w)}
+\item{c1}{regression coefficient of mediator (m) on moderator (w)}
 
-\item{c1}{regression coefficient of mediator (m) on the product (xw)}
+\item{c2}{regression coefficient of mediator (m) on the product (xw)}
 
 \item{sigx2}{variance of predictor (x)}
 
@@ -80,10 +80,10 @@ power analysis of model 7 in Introduction to Mediation, Moderation, and Conditio
 \examples{
 \donttest{
 # usage of wp.modmed.m7
-test = wp.modmed.m7(beta1 = 0.39, beta2 = 0.2, beta3 = 0.3, a1 = 0.39,
-          c1 = 0.2, sigx2 = 1, sigw2 = 1, sige12 = 1,
-          sige22 = 1, sigx_w = 0.5, n = 50, nrep = 100,
-          alpha = 0.05, b = 1000, ncore = 1)
+test = wp.modmed.m7(a1 = 0.39, cp = 0.2, b1 = 0.3, c1 = 0.39,
+          c2 = 0.2, sigx2 = 1, sigw2 = 1, sige12 = 1,
+         sige22 = 1, sigx_w = 0.5, n = 50, nrep = 100,
+         alpha = 0.05, b = 1000, ncore = 1)
 print(test)
 }
 }
diff --git a/man/wp.modmed.m8.Rd b/man/wp.modmed.m8.Rd
index 2b34082..1f2b2a1 100644
--- a/man/wp.modmed.m8.Rd
+++ b/man/wp.modmed.m8.Rd
@@ -5,20 +5,20 @@
 \title{model8}
 \usage{
 wp.modmed.m8(
-  beta1 = 0.2,
-  beta2 = 0.75,
-  beta3 = 0.8,
-  a1 = 0.6,
-  a2 = 0.3,
-  c1 = 0.8,
-  c2 = 0.79,
+  a1 = 0.2,
+  cp = 0.75,
+  b1 = 0.8,
+  c1 = 0.6,
+  d1 = 0.3,
+  c2 = 0.8,
+  d2 = 0.79,
   sigx2 = 1,
   sigw2 = 1,
   sige12 = 1,
   sige22 = 1,
   sigx_w = 0.5,
   n = 100,
-  nrep = 1000,
+  nrep = 100,
   alpha = 0.05,
   b = 1000,
   nb = n,
@@ -31,19 +31,19 @@ wp.modmed.m8(
 )
 }
 \arguments{
-\item{beta1}{regression coefficient of mediator (m) on predictor (x)}
+\item{a1}{regression coefficient of mediator (m) on predictor (x)}
 
-\item{beta2}{regression coefficient of outcome (y) on predictor (m)}
+\item{cp}{regression coefficient of outcome (y) on predictor (m)}
 
-\item{beta3}{regression coefficient of outcome (y) on mediator (x)}
+\item{b1}{regression coefficient of outcome (y) on mediator (x)}
 
-\item{a1}{regression coefficient of mediator (m) on moderator (w)}
+\item{c1}{regression coefficient of mediator (m) on moderator (w)}
 
-\item{a2}{regression coefficient of mediator (y) on moderator (w)}
+\item{d1}{regression coefficient of mediator (y) on moderator (w)}
 
-\item{c1}{regression coefficient of mediator (m) on the product (xw)}
+\item{c2}{regression coefficient of mediator (m) on the product (xw)}
 
-\item{c2}{regression coefficient of mediator (y) on the product (xw)}
+\item{d2}{regression coefficient of mediator (y) on the product (xw)}
 
 \item{sigx2}{variance of predictor (x)}
 
@@ -86,10 +86,10 @@ power analysis of model 8 in Introduction to Mediation, Moderation, and Conditio
 \examples{
 \donttest{
 # usage of wp.modmed.m8
-test = wp.modmed.m8(beta1 = 0.2, beta2 = 0.2, beta3 = 0.2,
-                    a1 = 0.2, a2=0.2, c1 = 0.2, c2 = 0.2,
-                    sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
-                    n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
+test = wp.modmed.m8(a1 = 0.2, cp = 0.2, b1 = 0.2,
+                   c1 = 0.2, d1=0.2, c2 = 0.2, d2 = 0.2,
+                   sigx2 = 1, sigw2 = 1, sige12 = 1, sige22 = 1, sigx_w = 0.5,
+                   n = 50, nrep = 100, alpha = 0.05, b = 1000, ncore = 1)
 print(test)
 }
 }