下午好： 我有30年的guanacos人口数据和矩阵模拟模型;我想通过最小化残差平方和（Sum（obs-pred）^ 2）来估计使用optim的R中模型参数的12的最佳值。我用模型创建了一个函数。模型工作正常，因为如果我使用固定参数值调用函数，我会得到执行结果。当我使用sewt的初始参数和函数调用optim时，我得到以下错误消息：＆＃34;参数a13不存在，没有遗漏值＃34 ;; 还有：丢失警告消息：在if（SSQ == 0）{： 条件的长度> 1，只使用第一个元素 来自：顶级（自由译自西班牙语）。
请在下面的三个部分中找到R代码：（1）首先使用功能＆＃34; guafit＆＃34;声明，（2）使用模型的独立运行调用＆＃34; guafit＆＃34;，以及（3）调用＆＃34; optim＆＃34;及其起始参数值。
谢谢你，Jorge Rabinovich
# Section (1):
# Clean all
rm(list=ls())
#####################################################################
####################### Function "guafit" ##########################
#####################################################################
guafit <- function(SSQ,a13,a21,a32,a33,ad1,ad2,ad3,ad4,bd1,bd2,bd3,bd4) {
# Create the field population (a 30-years time series)
# ====================================================
tfield <- c(12334,10670,19078,11219,11771,12323,13027,14094,14604,17775,20774,16410,17626,21445,21111,20777,28978,27809,28935,38841,38363,32273,43128,58597,52456,33125,61334,60488,44773,56973)
# Assign values to the vector of the initial population
# =====================================================
G <- matrix(c(0,0,0),ncol=3, nrow=1)
G[1]= 1542
G[2]= 740
G[3]= 3885
# Load the matrices with their initial values for all 30 time units (years)
# =========================================================================
if (SSQ == 0) {
a<-array(0,dim=c(3,3,30))
for(i in 1:29) {
a[1,3,i]= a13
a[2,1,i]= a21
a[3,2,i]= a32
a[3,3,i]= a33
}
}
# Initialize some variables
# ==========================
tmod<-array(1,dim=c(1,30)); tmod <- as.numeric(tmod)
densprop<-array(1,dim=c(1,30)); densprop <- as.numeric(densprop)
FdeltaFe<-array(1,dim=c(1,30)); FdeltaFe <- as.numeric(FdeltaFe)
FdeltaSc<-array(1,dim=c(1,30)); FdeltaSc <- as.numeric(FdeltaSc)
FdeltaSj<-array(1,dim=c(1,30)); FdeltaSj <- as.numeric(FdeltaSj)
FdeltaSa<-array(1,dim=c(1,30)); FdeltaSa <- as.numeric(FdeltaSa)
# N0 is the initial population vector
# It is multiplied by 2 to represewnt both sexes
# ===============================================
# Transfer guanacos (G) as a vector with the three age classes
N0 <- G
tmod[1] <- (N0[1]+N0[2]+N0[3]) * 2
# Declaration of the initial simulation conditions
# ================================================
# ng is the number of female individuals per age class (dim 3x30)
# tmod is the total (both sexes) population (sum of the three age classes * 2)
ng <- matrix( 0, nrow= 3, ncol=30)
ng[,1] <- N0
# We assume a constant carrying capacity (K= 60000 individuals)
carcap= 60000
# Start simulation for 30 years
for(i in 1:29) {
#Set up the density-dependent coefficients
densprop[i] <- tmod[i] / carcap
# Calculate the density-dependent factors
FdeltaFe[i]= 1/(1+exp((densprop[i]-ad1)*bd1))
FdeltaSc[i]= 1/(1+exp((densprop[i]-ad2)*bd2))
FdeltaSj[i]= 1/(1+exp((densprop[i]-ad3)*bd3))
FdeltaSa[i]= 1/(1+exp((densprop[i]-ad4)*bd4))
# Apply the density-dependent factors to each coefficient in its own age class
a[1,3,i]= a[1,3,i] * FdeltaFe[i]
a[2,1,i]= a[2,1,i] * FdeltaSc[i]
a[3,2,i]= a[3,2,i] * FdeltaSj[i]
a[3,3,i]= a[3,3,i] * FdeltaSa[i]
# Project the total population with the matrix operation
ng[,i+1] <- a[,,i]%*%ng[,i]
tmod[i+1] <- (ng[1,i+1] + ng[2,i+1] + ng[3,i+1]) * 2
# End of the 30-years simulation loop
}
# Calculate the residual sum of squares (SSQ)
SSQ = sum((tmod - tfield)^2)
return(list(outm=tmod, outc=tfield, elSSQ=SSQ, matrices=a, losgua=G, losguaxe=ng))
# End of function guafit
}
#################################################################################
# Section (2):
# Initialize conditions and parameters before calling function guafit
SSQ <- 0
# Initialize the 8 density-dependent coefficients (2 coefficients per age class)
# ==============================================================================
ad1= 1.195680167
ad2= 1.127219245
ad3= 1.113739384
ad4= 1.320456815
bd1= 10.21559509
bd2= 9.80201883
bd3= 9.760834107
bd4= 10.59390027
# Assign initial values to the transition matrix coefficients
# ============================================================
a21= 0.6
a32=0.8
a33=0.9
a13=0.37
# Initialization of conditions is finished, we can call function guafit
# As a test, we call function guafit only once to check for results
myresults <- guafit(SSQ,a13,a21,a32,a33,ad1, ad2, ad3, ad4, bd1, bd2, bd3, bd4)
# We save the results of interest of function guafit with new variables
restmod <- myresults$outm
tfield <- myresults$outc
SSQvalue <- myresults$elSSQ
lasmatrices <- myresults$matrices
reslosgua <- myresults$losgua
reslosguaxe <- myresults$losguaxe
SSQvalue
# Graph the results
axisx <- c(1982:2011)
plot(axisx,tfield)
lines(axisx,restmod)
#################################################################################
# Section (3):
# I try the optim function
# First creating the initial parameter values variable to pass as an argument
startparam <- c(SSQ, a13,a21,a32,a33,ad1, ad2, ad3, ad4, bd1, bd2, bd3, bd4)
optim(startparam, guafit)
# and I got error message mentioned above.
# I also tried calling as:
optim(par=startparam, fn=guafit)
# and I got the same error message
# I also tried calling optim but passing the values directly as a list of values:
startparam <- c(SSQ=0, a13=0.37, a21=0.6, a32=0.8, a33=0.9, ad1=1.1, ad2=1.1, ad3=1.1, ad4=1.1, bd1=10, bd2=10, bd3=10, bd4=10)
optim(startparam, guafit)
optim(par=startparam, fn=guafit)
# and I got the same error message
答案 0 :(得分：0)
我运行了代码，但我不确定它是否返回正确的参数估计值。我尝试了两种不同的方法。
采用第一种方法，我做了以下事情：
optim声明中删除了常量ad1，ad2，ad3和ad4是常量，而不是要估算的参数。我猜你可以说我假设ad1，ad2，ad3和ad4是不变的偏差。第一种方法返回了与您的初始值非常匹配的bd1，bd2，bd3和bd4的估算值。
采用第二种方法，我做了以下几点：
optim声明中删除了常量ad1，ad2，ad3和ad4是要估算的参数。第二种方法返回了所有八个参数的估算值：ad1，ad2，ad3，ad4，bd1，bd2，{ {1}}和bd3但我不认为估算值是正确的。请注意，Hessian中的两列都是bd4。无法使用第二种方法估算SE，0，bd1，bd2和bd3的估算值与初始值不相符。
两种方法的bd4代码如下。检查代码以查看是否有任何方法正在执行您想要的操作。如果将R，ad1，ad2和ad3视为参数至关重要，则可能需要修改模型代码。
以下是第一种方法的ad4代码和输出：
R以下是第一种方法的输出：
set.seed(2345)
guafit <- function(param) {
bd1 <- param[1]
bd2 <- param[2]
bd3 <- param[3]
bd4 <- param[4]
# Start simulation for 30 years
for(i in 1:29) {
# Set up the density-dependent coefficients
densprop[i] <- tmod[i] / carcap
# Calculate the density-dependent factors
FdeltaFe[i]= 1/(1+exp((densprop[i]-ad1)*bd1))
FdeltaSc[i]= 1/(1+exp((densprop[i]-ad2)*bd2))
FdeltaSj[i]= 1/(1+exp((densprop[i]-ad3)*bd3))
FdeltaSa[i]= 1/(1+exp((densprop[i]-ad4)*bd4))
# Apply density-dependent factors to each coefficient in its own age class
a[1,3,i]= a[1,3,i] * FdeltaFe[i]
a[2,1,i]= a[2,1,i] * FdeltaSc[i]
a[3,2,i]= a[3,2,i] * FdeltaSj[i]
a[3,3,i]= a[3,3,i] * FdeltaSa[i]
# Project the total population with the matrix operation
ng[,i+1] <- a[,,i]%*%ng[,i]
tmod[i+1] <- (ng[1,i+1] + ng[2,i+1] + ng[3,i+1]) * 2
# End of the 30-years simulation loop
}
# Calculate the residual sum of squares (SSQ)
SSQ = sum((tmod - tfield)^2)
# End of function guafit
}
# Create the field population (a 30-years time series)
# ====================================================
tfield <- c(12334,10670,19078,11219,11771,12323,13027,14094,14604,17775,
20774,16410,17626,21445,21111,20777,28978,27809,28935,38841,
38363,32273,43128,58597,52456,33125,61334,60488,44773,56973)
# Initialize conditions and parameters before calling function guafit
SSQ <- 0
# Assign initial values to the transition matrix coefficients
# ============================================================
a21 = 0.6
a32 = 0.8
a33 = 0.9
a13 = 0.37
# Assign values to the vector of the initial population
# =====================================================
G <- matrix(c(0,0,0),ncol=3, nrow=1)
G[1] = 1542
G[2] = 740
G[3] = 3885
# Load the matrices with their initial values for all 30 time units (years)
# =========================================================================
a <- array(0,dim=c(3,3,30))
for(i in 1:29) {
a[1,3,i]= a13
a[2,1,i]= a21
a[3,2,i]= a32
a[3,3,i]= a33
}
# Initialize some variables
# ==========================
tmod<-array(1,dim=c(1,30)); tmod <- as.numeric(tmod)
densprop <- array(1,dim=c(1,30))
densprop <- as.numeric(densprop)
FdeltaFe <- array(1,dim=c(1,30))
FdeltaFe <- as.numeric(FdeltaFe)
FdeltaSc <- array(1,dim=c(1,30))
FdeltaSc <- as.numeric(FdeltaSc)
FdeltaSj <- array(1,dim=c(1,30))
FdeltaSj <- as.numeric(FdeltaSj)
FdeltaSa <- array(1,dim=c(1,30))
FdeltaSa <- as.numeric(FdeltaSa)
ng <- matrix( 0, nrow= 3, ncol=30)
# We assume a constant carrying capacity (K= 60000 individuals)
carcap= 60000
# N0 is the initial population vector
# It is multiplied by 2 to represewnt both sexes
# ===============================================
# Transfer guanacos (G) as a vector with the three age classes
N0 <- G
tmod[1] <- (N0[1]+N0[2]+N0[3]) * 2
# Declaration of the initial simulation conditions
# ================================================
# ng is the number of female individuals per age class (dim 3x30)
# tmod is total (both sexes) population (sum of the three age classes * 2)
ng[,1] <- N0
ad1 <- 1.195680167
ad2 <- 1.127219245
ad3 <- 1.113739384
ad4 <- 1.320456815
fit <- optim ( c(10.21559509,
9.80201883,
9.760834107,
10.59390027), fn=guafit, method='BFGS', hessian=TRUE)
fit
以下是四个参数估计值及其标准误差：
$par
[1] 11.315899 11.886347 11.912239 9.675885
$value
[1] 1177381086
$counts
function gradient
150 17
$convergence
[1] 0
$message
NULL
$hessian
[,1] [,2] [,3] [,4]
[1,] 417100.8 306371.2 326483.2 941186.8
[2,] 306371.2 516636.4 370602.5 1061540.5
[3,] 326483.2 370602.5 577929.7 1135695.9
[4,] 941186.8 1061540.5 1135695.9 3720506.4
以下是第二种方法的 mle se
[1,] 11.315899 0.002439888
[2,] 11.886347 0.002240669
[3,] 11.912239 0.002153876
[4,] 9.675885 0.001042035
代码，用于估算八个参数。用第二种方法无法估计SE：
R以下是第二种方法的输出：
set.seed(2345)
guafit <- function(param) {
ad1 <- param[1]
ad2 <- param[2]
ad3 <- param[3]
ad4 <- param[4]
bd1 <- param[5]
bd2 <- param[6]
bd3 <- param[7]
bd4 <- param[8]
# Start simulation for 30 years
for(i in 1:29) {
# Set up the density-dependent coefficients
densprop[i] <- tmod[i] / carcap
# Calculate the density-dependent factors
FdeltaFe[i]= 1/(1+exp((densprop[i]-ad1)*bd1))
FdeltaSc[i]= 1/(1+exp((densprop[i]-ad2)*bd2))
FdeltaSj[i]= 1/(1+exp((densprop[i]-ad3)*bd3))
FdeltaSa[i]= 1/(1+exp((densprop[i]-ad4)*bd4))
# Apply the density-dependent factors to each coefficient in its own age class
a[1,3,i]= a[1,3,i] * FdeltaFe[i]
a[2,1,i]= a[2,1,i] * FdeltaSc[i]
a[3,2,i]= a[3,2,i] * FdeltaSj[i]
a[3,3,i]= a[3,3,i] * FdeltaSa[i]
# Project the total population with the matrix operation
ng[,i+1] <- a[,,i]%*%ng[,i]
tmod[i+1] <- (ng[1,i+1] + ng[2,i+1] + ng[3,i+1]) * 2
# End of the 30-years simulation loop
}
# Calculate the residual sum of squares (SSQ)
SSQ = sum((tmod - tfield)^2)
# End of function guafit
}
# Create the field population (a 30-years time series)
# ====================================================
tfield <- c(12334,10670,19078,11219,11771,12323,13027,14094,14604,17775,
20774,16410,17626,21445,21111,20777,28978,27809,28935,38841,
38363,32273,43128,58597,52456,33125,61334,60488,44773,56973)
# Initialize conditions and parameters before calling function guafit
SSQ <- 0
# Assign initial values to the transition matrix coefficients
# ============================================================
a21 = 0.6
a32 = 0.8
a33 = 0.9
a13 = 0.37
# Assign values to the vector of the initial population
# =====================================================
G <- matrix(c(0,0,0),ncol=3, nrow=1)
G[1] = 1542
G[2] = 740
G[3] = 3885
# Load the matrices with their initial values for all 30 time units (years)
# =========================================================================
a <- array(0,dim=c(3,3,30))
for(i in 1:29) {
a[1,3,i]= a13
a[2,1,i]= a21
a[3,2,i]= a32
a[3,3,i]= a33
}
# Initialize some variables
# ==========================
tmod<-array(1,dim=c(1,30)); tmod <- as.numeric(tmod)
densprop <- array(1,dim=c(1,30))
densprop <- as.numeric(densprop)
FdeltaFe <- array(1,dim=c(1,30))
FdeltaFe <- as.numeric(FdeltaFe)
FdeltaSc <- array(1,dim=c(1,30))
FdeltaSc <- as.numeric(FdeltaSc)
FdeltaSj <- array(1,dim=c(1,30))
FdeltaSj <- as.numeric(FdeltaSj)
FdeltaSa <- array(1,dim=c(1,30))
FdeltaSa <- as.numeric(FdeltaSa)
ng <- matrix( 0, nrow= 3, ncol=30)
# We assume a constant carrying capacity (K= 60000 individuals)
carcap= 60000
# N0 is the initial population vector
# It is multiplied by 2 to represewnt both sexes
# ===============================================
# Transfer guanacos (G) as a vector with the three age classes
N0 <- G
tmod[1] <- (N0[1]+N0[2]+N0[3]) * 2
# Declaration of the initial simulation conditions
# ================================================
# ng is the number of female individuals per age class (dim 3x30)
# tmod is the total (both sexes) population (sum of the three age classes * 2)
ng[,1] <- N0
fit <- optim ( c( 1.195680167,
1.127219245,
1.113739384,
1.320456815,
10.21559509,
9.80201883,
9.760834107,
10.59390027), fn=guafit, method='BFGS', hessian=TRUE)
fit
答案 1 :(得分：0)
2015年4月27日，星期一
亲爱的马克：万分感谢您为我的问题投入的工作和想法。
一些评论和补充：
（1）必须估算所有8个参数ad1，ad2，ad3，ad4，bd1，bd2，bd3和bd4（正如您在第二种方法中所做的那样）。
（2）但另外30周期3x3矩阵[a（3x3x30）]有四个元素（a13，a21，a32和a33）也必须通过优化来估算。< / p>
（3）这就是我将矩阵a [,, i]作为参数传递的原因;也许当你删除[,, i]作为调用optim的参数时，问题就消失了。
（4）也许这是我原来的问题开始的地方;我记得曾经读过某个地方，因为参数有尺寸，优化存在问题;你认为我的错误信息与参数列表中的[,, i]作为参数有关吗？
（5）我知道我有点雄心勃勃：我要求优化以最小化我的SSQ（场和群体向量之间的残差平方和）改变总共128个参数（4x30 = 120为a [,, i]矩阵，以及（1）中提到的八个附加参数。
（6）如果问题是由参数列表中的[,, i]作为参数引起的，如果我在调用时替换参数列表中的矩阵a [,, i]，你认为它会消失吗？优先列出120个单独的值？
（7）另一个重要问题：我需要在拟合完成后将模型种群向量（tmod）作为来自optim的输出变量;我插入你的脚本（方法＃1）命令＆＃34; return（restmod = tmod）＆＃34;就在计算SSQ之前，我得到一条错误消息，说明＆＃34;在optim中的目标函数评估大小30不是1＆＃34;。请求此输出时我犯了错误吗？
（8）最后，还有一个非常重要的问题：我忘了提到我的参数必须是约束条件;它们非常简单：a [i]矩阵的所有非零系数（即a [1,3，i] = a13，a [2,1，i] = a21，a [3,2， i] = a32，a [3,3，i] = a33）必须<= 1，除了a13必须<= 0.5（其他8个参数不受约束）。你如何通过优化必要的约束？
再次，非常感谢，
豪尔赫