interdependent_rows.R

library(tidyverse)

first_year <- tibble(year = 2010, z = 1, x = 2, y = 3)

all_years <- first_year %>%
  bind_rows(tibble(year = 2011:2015))

all_years
#> # A tibble: 6 x 4
#>    year     z     x     y
#>   <dbl> <dbl> <dbl> <dbl>
#> 1  2010     1     2     3
#> 2  2011    NA    NA    NA
#> 3  2012    NA    NA    NA
#> 4  2013    NA    NA    NA
#> 5  2014    NA    NA    NA
#> 6  2015    NA    NA    NA

# Panel data relationships:
# - Z is caused by previous X
# - X is caused by current Z and previous Y
# - Y is caused by previous X

# z = (β * lag(x))
# x = (β * z) + (β * lag(y))
# y = (β * lag(x))

# Sadly doesn't work
all_years %>% 
  mutate(z = 0.5 * lag(x)) %>% 
  mutate(x = 0.5 * z + 0.5 * lag(y)) %>% 
  mutate(y = 0.25 * lag(x))
#> # A tibble: 6 x 4
#>    year     z     x     y
#>   <dbl> <dbl> <dbl> <dbl>
#> 1  2010    NA    NA  NA  
#> 2  2011     1     2  NA  
#> 3  2012    NA    NA   0.5
#> 4  2013    NA    NA  NA  
#> 5  2014    NA    NA  NA  
#> 6  2015    NA    NA  NA


# This works, but it is ew
for (i in 2:nrow(all_years)) {
  all_years[i, "z"] <- 0.5 * all_years[i - 1, "x"]
  all_years[i, "x"] <- (0.5 * all_years[i, "z"]) + (0.5 * all_years[i - 1, "y"])
  all_years[i, "y"] <- 0.25 * all_years[i - 1, "x"]
}

all_years
#> # A tibble: 6 x 4
#>    year     z     x      y
#>   <dbl> <dbl> <dbl>  <dbl>
#> 1  2010 1     2     3     
#> 2  2011 1     2     0.5   
#> 3  2012 1     0.75  0.5   
#> 4  2013 0.375 0.438 0.188 
#> 5  2014 0.219 0.203 0.109 
#> 6  2015 0.102 0.105 0.0508

I cracked the summarise approach, making the unnest unnecessary:

library(tidyverse)

first_year <- tibble(year = 2010, z = 1, x = 2, y = 3)

all_years <- first_year %>%
    bind_rows(tibble(year = 2011:2015))

all_years %>%
    summarise(
        year = year,
        accumulate(
            .init = tibble(
                x = first(all_years$x),
                y = first(all_years$y),
                z = first(all_years$z)
            ),
            .x = seq(length(z) - 1), # because we're supplying 1 row in init - tripped me up
            .f = function(inputs, x_ignored) {
                tibble(
                    z = 0.5 * inputs$x,
                    x = 0.5 * z + 0.5 * inputs$y,
                    y = 0.25 * inputs$x
                )
            }
        ) %>%
        bind_rows()
    )
#> # A tibble: 6 x 4
#>    year     x      y     z
#>   <dbl> <dbl>  <dbl> <dbl>
#> 1  2010 2     3      1    
#> 2  2011 2     0.5    1    
#> 3  2012 0.75  0.5    1    
#> 4  2013 0.438 0.188  0.375
#> 5  2014 0.203 0.109  0.219
#> 6  2015 0.105 0.0508 0.102

^{Created on 2021-01-09 by the reprex package (v0.3.0)}