Identifying uniroot for multiple independent variables in R

Question

I am trying to calculate the value of x where y = 0. I could able to do it for single x using the following code

lm.model <- lm(y ~ x)
cc <- coef(lm.model)

f <- function(x) cc[2]*x + cc[1] 
plot(x, y)
abline(coef(lm.model))
abline(h=0, col="blue")

(threshold <- uniroot(f, interval = c(0, 100))$root)
abline(v=threshold, col="blue")

x = c(33.05, 14.22, 15.35, 13.52, 8.7, 13.73, 8.28, 21.02, 9.97, 
11.98, 12.87, 5.05, 11.23, 11.65, 10.05, 12.58, 13.88, 9.66, 
4.62, 4.56, 5.35, 3.7, 3.29, 4.87, 3.75, 6.55, 4.51, 7.77, 4.7, 
4.18, 25.14, 18.08, 10.41)
y = c(16.22699279, 15.78620732, 9.656361014, -17.32805679, -20.85685895, 
7.601993251, -4.776053714, 10.50972236, 3.853479771, 7.713563136, 
8.579366561, 14.16989395, 7.484692081, -1.2807472, -12.13759458, 
-0.29138513, -5.238157067, -2.033194068, -38.12157566, -33.61912493, 
-9.763657548, -0.240863712, 9.090638907, 7.345492608, 6.949676888, 
-19.94866471, 0.995659732, -1.162616185, 5.497998429, 1.656653092, 
2.116687436, 22.23175649, 10.33039543)

But I have multiple x variables. Now how can I apply it for multiple x variables at a time? Here is an example data

df = structure(list(y = c(16.2269927925813, 15.7862073196372, 9.65636101412767, 
-17.3280567922775, -20.8568589521297, 7.6019932507973, -4.77605371404423, 
10.5097223644541, 3.85347977129367, 7.71356313645697, 8.57936656085966, 
14.1698939499927, 7.4846920807874, -1.28074719969249, -12.1375945758837, 
-0.291385130176774, -5.23815706681139, -2.03319406769161, -38.1215756639013, 
-33.6191249261727, -9.76365754821171, -0.240863712421707, 9.09063890677045, 
7.34549260800693, 6.94967688778232, -19.9486647079697, 0.995659731521127, 
-1.16261618452931, 5.49799842947493, 1.65665309209479, 2.11668743610013, 
22.2317564898722, 10.3303954315884), x1 = c(8.56, 8.66, 9.09, 
8.36, 8.3, 8.63, 8.78, 8.44, 8.34, 8.46, 8.33, 8.19, 8.58, 8.65, 
8.75, 8.34, 8.77, 9.06, 9.31, 9.11, 9.26, 9.81, 9.68, 9.79, 9.26, 
9.53, 8.89, 8.89, 10.37, 9.58, 10.27, 10.16, 10.27), x2 = c(164, 
328.3, 0, 590.2, 406.6, 188.4, 423.8, 355.3, 337.6, 0, 0, 200.1, 
0, 315.8, 547.5, 225.6, 655.7, 387.2, 0, 487.4, 400.4, 0, 234.9, 
275.5, 0, 0, 613.2, 207.4, 184.4, 162.8, 220, 174.8, 0), x3 = c(4517.7, 
2953.4, 2899.3, 2573.8, 3310.7, 3880.3, 3016.8, 3552.3, 2960.1, 
323, 2638.5, 3343.1, 3274.7, 3218, 3268.3, 3507.9, 3709.2, 3537.5, 
2634.4, 1964.6, 3333.7, 2809.7, 3326.8, 3524.5, 3893.9, 3166.7, 
3992.1, 4324.7, 3077.9, 3069.9, 4218.9, 3897.4, 2693.9), x4 = c(14.7, 
14.5, 15.5, 17, 16.2, 15.9, 15.7, 15.3, 13.5, 14, 15.4, 16.2, 
15.6, 15.7, 15.1, 15.8, 15.3, 14.9, 15.7, 16.3, 15.21000004, 
16.7, 15.6, 16.2, 15.7, 16.3, 17.3, 16.9, 15.7, 14.9, 13.81999969, 
14.90754509, 12.42847157), x5 = c(28.3, 29.1, 28.3, 29.1, 28.7, 
29.3, 28.9, 28.4, 29.3, 29.3, 29.1, 29, 29.9, 29.5, 28.4, 30.3, 
29.1, 29.1, 29, 29.5, 29.3, 28.5, 29, 28.7, 29.4, 28.8, 29.2, 
30.1, 28.3, 28.7, 24.96999931, 25.79496384, 25.3072052), x6 = c(33.05, 
14.22, 15.35, 13.52, 8.7, 13.73, 8.28, 21.02, 9.97, 11.98, 12.87, 
5.05, 11.23, 11.65, 10.05, 12.58, 13.88, 9.66, 4.62, 4.56, 5.35, 
3.7, 3.29, 4.87, 3.75, 6.55, 4.51, 7.77, 4.7, 4.18, 25.14, 18.08, 
10.41), x7 = c(13.8425, 11.1175, 8.95, 13.5375, 5.4025, 13.5625, 
13.735, 14.14, 8.0875, 5.565, 12.255, 3.3075, 6.345, 4.8125, 
4.0325, 11.475, 10.32, 17.71, 2.3375, 3.92, 5.7, 2.42, 8.3075, 
7.4725, 7.7925, 10.8725, 8.005, 11.7475, 13.405, 8.425, 47.155, 
26.1, 6.6675), x8 = c(0.95, 3.01, 1.92, 1.51, 2.61, 1.32, 3.55, 
1.21, 2.14, 1.1, 1.32, 0.76, 1.34, 5.41, 9.38, 6.55, 4.44, 7.37, 
9.84, 12.68, 15.52, 23.01, 18.59, 21.64, 19.69, 25.22, 22.38, 
25.03, 37.42, 22.26, 2.1, 3.01, 0.82), x9 = c(26.2, 25.8, 25.8, 
25.5, 26, 24.7, 22.9, 25.3, 26.3, 26.1, 22.5, 25.9, 26.4, 25.2, 
25.8, 25.4, 25, 23.2, 26.4, 25.8, 26.6, 26.2, 25.8, 26.8, 25, 
25.4, 25.6, 26.1, 25.7, 25.8, 24.78000069, 24.98148918, 26.39899826
), x10 = c(35.4, 39, 37.5, 36.4, 37.1, 36.2, 37.3, 36.4, 37.5, 
36, 36.6, 35.6, 37.3, 38.3, 37, 37.5, 37.5, 39.6, 37.8, 36.8, 
36.6, 38.4, 38.9, 38.4, 38.4, 37.7, 39.1, 37.7, 37.8, 39.4, 36.25, 
35.57029343, 35.57416534), x11 = c(653.86191565, 383.1, 457.1, 
591.4, 549.2, 475.2, 626.4, 308.8, 652.4, 77, 380.9, 530.5, 393, 
712.1, 623.4, 515.7, 706.4, 713.4, 343.7, 559.5, 630.1, 292.3, 
578.6, 628.88904574, 480.96959685, 591.35600287, 804.8, 419.6, 
403.7, 361.2, 515.07101438, 434.66682808, 299.9531298), x12 = c(163.9793854, 
167.9, 135, 215.8, 213, 188.4, 260.6, 191.8, 337.6, 55, 147.6, 
200.1, 140.7, 315.8, 189.6, 225.6, 469.3, 201.8, 140, 297.2, 
204.6, 142.5, 234.9, 275.494751, 153.7796173, 147.6174622, 433.6, 
207.4, 184.4, 162.8, 219.9721832, 174.8355713, 106.8163605), 
    x13 = c(92, 67, 67, 50, 70, 87, 68, 86, 70, 11, 66, 79, 70, 
    61, 75, 78, 78, 77, 69, 35, 72, 76, 69, 84, 93, 73, 81, 99, 
    80, 76, 101, 86, 80), x14 = c(70, 42, 46, 34, 55, 60, 51, 
    65, 49, 1, 40, 56, 54, 41, 48, 57, 46, 50, 41, 22, 47, 47, 
    49, 57, 70, 52, 56, 70, 48, 50, 74, 66, 47), x15 = c(21, 
    12, 13, 10, 14, 16, 10, 13, 10, 0, 9, 14, 16, 20, 14, 14, 
    13, 15, 10, 7, 17, 8, 14, 14, 14, 11, 17, 19, 12, 11, 17, 
    17, 9), x16 = c(1076.8, 783.7, 711.8, 1041.9, 957.4, 939.3, 
    662.9, 768.1, 770.3, 0, 399.2, 606.2, 724.1, 960.8, 943.8, 
    737.8, 1477.4, 1191.7, 371.3, 956.4, 1251.7, 345.7, 1210.7, 
    845, 598.1, 821.7, 1310.6, 940.1, 581, 520, 313.5, 606.8, 
    201.2), x17 = c(163.9793854, 167.9, 128.4, 215.8, 213, 188.4, 
    260.6, 191.8, 337.6, 55, 147.6, 200.1, 140.7, 315.8, 189.6, 
    225.6, 469.3, 201.8, 140, 297.2, 204.6, 142.5, 234.9, 157.7472534, 
    153.7796173, 147.6174622, 133.1873627, 150.2, 184.4, 162.8, 
    219.9721832, 174.8355713, 106.8163605)), row.names = c(NA, 
33L), class = "data.frame")

Answer 1

You can use purrr::map to loop through every x.

library(dplyr)
library(purrr)

thresholds <- df %>%
  select(-y) %>%
  map_dbl(function(x){
    lm.model <- lm(df$y ~ x)
    cc <- coef(lm.model)
    
    f <- function(x) cc[2]*x + cc[1] 
    plot(x, df$y)
    abline(coef(lm.model))
    abline(h=0, col="blue")
    
    threshold <- tryCatch(uniroot(f, interval = c(0, 100))$root, error = function(cond){NA})
    abline(v=threshold, col="blue")
    
    return(threshold)})

For some x's, uniroot(f, interval = c(0, 100))$root yields an error: Error

in uniroot(f, interval = c(0, 100)) : f() values at end points not of opposite sign

So the tryCatch is used to return NA for the threshold associated with that x, instead of breaking the code.

Result:

> thresholds
       x1        x2        x3        x4        x5        x6        x7        x8        x9 
 9.023314        NA        NA 15.459841 28.727293 10.514728 10.493577  9.669244 25.522480 
      x10       x11       x12       x13       x14       x15       x16       x17 
37.370852        NA        NA 73.398380 50.239522 13.022176        NA        NA

Edit: binding the graphs together

graphs <- df %>%
  select(-y) %>%
  imap(function(x, name){
    lm.model <- lm(df$y ~ x)
    cc <- coef(lm.model)
    
    f <- function(x) cc[2]*x + cc[1] 
    threshold <- tryCatch(uniroot(f, interval = c(0, 100))$root, error = function(cond){NA})
    
    g = ggplot(mapping = aes(x)) +
      geom_point(aes(y = df$y)) +
      geom_line(aes(y = cc[2]*x + cc[1])) +
      geom_hline(yintercept = 0, color = "blue") +
      labs(title = name, y = "y", x = "x")
    
    if(!is.na(threshold)) {g = g + geom_vline(xintercept = threshold, color = "blue")}
    
    return(g)})

ggpubr::ggarrange(plotlist = graphs)

Result:

Obs2: i assumed that you don't need the thresholds vector defined in the first attempt, if you still need it, it's easy to add it back to the answer
Obs1: let me know if you want any aesthetic change on the graphs

Edit 2: graph with common axis

To use a common axis is better to use facets instead of ggarrange. In order to do that, we need to first save the fitted data for all variables, then plot, so the ggplot expression goes out of the map. Also, we now save the treshold info.

graphs <- df %>%
  select(-y) %>%
  imap(function(x, name){
    lm.model <- lm(df$y ~ x)
    cc <- coef(lm.model)
  
    f <- function(x) cc[2]*x + cc[1] 
    threshold <- tryCatch(uniroot(f, interval = c(0, 100))$root, error = function(cond){NA})
    
    list(threshold = threshold,
         data = tibble(y = df$y, "name" = name, "x" = x, "fitted" = cc[2]*x + cc[1]))})

Now we use the purrr::transpose() function to build a dataset for the data and other for the treshold. This functions does something like:

list(x1 = list(treshold, data), x2 = ...) >>> list(treshold = list(x1, x2, ...), data = list(x1, x2, ...))

df2 = graphs %>%
  transpose() %>%
  `$`(data) %>%
  bind_rows() %>%
  mutate(name = factor(name, paste0("x", 1:17)))

thresholds = graphs %>%
  transpose() %>%
  `$`(threshold) %>%
  {tibble(int = as.numeric(.), name = names(.))} #both datasets have the name column, to be used inside `facet_wrap()`
  
ggplot(df2, aes(x)) +
  geom_point(aes(y = y)) +
  geom_line(aes(y = fitted)) +
  facet_wrap(vars(name), scales = "free_x") +
  geom_hline(yintercept = 0, color = "blue") +
  geom_vline(aes(xintercept = int), thresholds, color = "blue", linetype = 2) +
  geom_label(aes(label = round(int, 2), x = int*1, y = min(df$y)), thresholds, size = 4)

Result:

Obs1: the labels position and size can be easily altered. Another option is using the thresholds as a axis break Obs2: this method can be slow for large datasets. A more efficient option is to save only threshold and cc inside map, and then building the dataset after it.