r - `nlme` 具有交叉随机效应

Question

我正在尝试将交叉非线性随机效应模型拟合为前面提到的线性随机效应模型 in this question在这个 mailing list post使用 nlme 包。不过，无论我尝试什么，我都会收到错误。这是一个例子

library(nlme)

#####
# simulate data
set.seed(18112003)
na <- 30
nb <- 30

sigma_a <- 1
sigma_b <- .5
sigma_res <- .33

n <- na*nb

a <- gl(na,1,n)
b <- gl(nb,na,n)
u <- gl(1,1,n)

x <- runif(n, -3, 3)

y_no_noise <- x + sin(2 * x)
y <- 
  x + sin(2 * x) + 
  rnorm(na, sd = sigma_a)[as.integer(a)] + 
  rnorm(nb, sd = sigma_b)[as.integer(b)] + 
  rnorm(n, sd = sigma_res)

#####
# works in the linear model where we know the true parameter
fit <- lme(
  # somehow we found the right values
  y ~ x + sin(2 * x), 
  random = list(u = pdBlocked(list(pdIdent(~ a - 1), pdIdent(~ b - 1)))))
vv <- VarCorr(fit)
vv2 <- vv[c("a1", "b1"), ]
storage.mode(vv2) <- "numeric"
print(vv2,digits=4)
#R    Variance StdDev
#R a1    1.016 1.0082
#R b1    0.221 0.4701

#####
# now try to do the same with `nlme`
fit <- nlme(
  y ~ c0 + sin(c1),
  fixed = list(c0 ~ x, c1 ~ x - 1),
  random = list(u = pdBlocked(list(pdIdent(~ a - 1), pdIdent(~ b - 1)))), 
  start = c(0, 0.5, 1))
#R Error in nlme.formula(y ~ a * x + sin(b * x), fixed = list(a ~ 1, b ~  : 
#R    'random' must be a formula or list of formulae 

lme 示例类似于“S 和 S-PLUS 中的混​​合效应模型”第 163-166 页，只有 2 个随机效应，而不是 3 个。

Answer 1

我应该使用 help("nlme") 中编写的双面公式

fit <- nlme(
  y ~ c0 + c1 + sin(c2),
  fixed = list(c0 ~ 1, c1 ~ x - 1, c2 ~ x - 1),
  random = list(u = pdBlocked(list(pdIdent(c0 ~ a - 1), pdIdent(c1 ~ b - 1)))), 
  start = c(0, 0.5, 1))

# fixed effects estimates
fixef(fit)
#R c0.(Intercept)           c1.x           c2.x 
#R     -0.1788218      0.9956076      2.0022338

# covariance estimates
vv <- VarCorr(fit)
vv2 <- vv[c("c0.a1", "c1.b1"), ]
storage.mode(vv2) <- "numeric"
print(vv2,digits=4)
#R       Variance StdDev
#R c0.a1   0.9884 0.9942
#R c1.b1   0.2197 0.4688