变长矢量的矢量化和

我试图通过以下方程模拟y的观测结果:

对于X的所有可能值和参数贝塔的随机值以及参数德尔塔的矢量。

使用来自tidyverse的R和包,这是我迄今为止得到的:

library(tidyverse)
library(extraDistr)
n <- 100
x_max <- 4

set.seed(1)
data <- 
    tibble(
        id = 1:100,
        beta = rnorm(100, mean = 0, sd = 1/(x_max - 1)),
        delta = cbind(0, rdirichlet(n, rep(1, x_max - 1)))
    ) %>% 
    expand_grid(x = 1:x_max)

data

# A tibble: 400 × 4
      id    beta delta[,1]   [,2]    [,3]   [,4]     x
   <int>   <dbl>     <dbl>  <dbl>   <dbl>  <dbl> <int>
 1     1 -0.209          0 0.169  0.170   0.661      1
 2     1 -0.209          0 0.169  0.170   0.661      2
 3     1 -0.209          0 0.169  0.170   0.661      3
 4     1 -0.209          0 0.169  0.170   0.661      4
 5     2  0.0612         0 0.0962 0.00297 0.901      1
 6     2  0.0612         0 0.0962 0.00297 0.901      2
 7     2  0.0612         0 0.0962 0.00297 0.901      3
 8     2  0.0612         0 0.0962 0.00297 0.901      4
 9     3 -0.279          0 0.241  0.714   0.0451     1
10     3 -0.279          0 0.241  0.714   0.0451     2
# ℹ 390 more rows
# ℹ Use `print(n = ...)` to see more rows

我被困在从上面的公式计算y值的部分。挑战在于在计算增量参数的总和时使用x作为索引变量。我要找的是这样的东西:

data %>% 
    rowwise() %>% 
    mutate(
        y = beta * sum(c_across(delta[,1]:delta[,x]))
    )

但是,此代码不起作用,我收到以下错误消息:

Error in `mutate()`:
ℹ In argument: `y = beta * sum(c_across(delta[, 1]:delta[, x]))`.
ℹ In row 1.
Caused by error in `c_across()`:
! Problem while evaluating `delta[, 1]`.
Caused by error:
! object 'delta' not found

我知道嵌套矩阵一定有问题 delta 。然而,我仍然觉得 dplyr 应该能够支持矢量化索引操作吗?

从上面的例子中,我希望得到的结果是:

# A tibble: 400 × 5
# Rowwise: 
      id    beta delta[,1]   [,2]    [,3]   [,4]     x        y
   <int>   <dbl>     <dbl>  <dbl>   <dbl>  <dbl> <int>    <dbl>
 1     1 -0.209          0 0.169  0.170   0.661      1  0      
 2     1 -0.209          0 0.169  0.170   0.661      2 -0.0352 
 3     1 -0.209          0 0.169  0.170   0.661      3 -0.0708 
 4     1 -0.209          0 0.169  0.170   0.661      4 -0.209  
 5     2  0.0612         0 0.0962 0.00297 0.901      1  0      
 6     2  0.0612         0 0.0962 0.00297 0.901      2  0.00589
 7     2  0.0612         0 0.0962 0.00297 0.901      3  0.00607
 8     2  0.0612         0 0.0962 0.00297 0.901      4  0.0612 
 9     3 -0.279          0 0.241  0.714   0.0451     1  0      
10     3 -0.279          0 0.241  0.714   0.0451     2 -0.0671 
# ℹ 390 more rows
# ℹ Use `print(n = ...)` to see more rows