R behavior of mutate and rnorm - r

Question

Hello I have the following code from a course
library(tidyverse)
library(dslabs)
data("polls_us_election_2016")
head(results_us_election_2016)
results_us_election_2016 %>% arrange(desc(electoral_votes)) %>% top_n(5, electoral_votes)
'Computing the average and standard deviation for each state'
polls <- polls_us_election_2016 %>%
filter(state != "U.S." &
!grepl("CD", "state") &
enddate >= "2016-10-31" &
(grade %in% c("A+", "A", "A-", "B+") | is.na(grade))) %>%
mutate(spread = rawpoll_clinton/100 - rawpoll_trump/100) %>%
group_by(state) %>%
summarize(avg = mean(spread), sd = sd(spread), n = n()) %>%
mutate(state = as.character(state))
# joining electoral college votes and results
results <- left_join(polls, results_us_election_2016, by="state")
head(results)
# states with no polls: note Rhode Island and District of Columbia = Democrat
results_us_election_2016 %>% filter(!state %in% results$state)
# assigns sd to states with just one poll as median of other sd values
results <- results %>%
mutate(sd = ifelse(is.na(sd), median(results$sd, na.rm = TRUE), sd))
#Calculating the posterior mean and posterior standard error
mu <- 0
tau <- 0.02
results %>% mutate(sigma = sd/sqrt(n),
B = sigma^2/ (sigma^2 + tau^2),
posterior_mean = B*mu + (1-B)*avg,
posterior_se = sqrt( 1 / (1/sigma^2 + 1/tau^2))) %>%
arrange(abs(posterior_mean))
#Monte Carlo simulation of Election Night results (no general bias)
mu <- 0
tau <- 0.02
clinton_EV <- replicate(1000, {
results %>% mutate(sigma = sd/sqrt(n),
B = sigma^2/ (sigma^2 + tau^2),
posterior_mean = B*mu + (1-B)*avg,
posterior_se = sqrt( 1 / (1/sigma^2 + 1/tau^2)),
simulated_result = rnorm(length(posterior_mean), posterior_mean, posterior_se),
clintonvotes = ifelse(simulated_result > 0, electoral_votes, 0)) %>% # award votes if Clinton wins state
summarize(clinton = sum(clintonvotes)) %>% # total votes for Clinton
.$clinton + 7 # 7 votes for Rhode Island and DC
})
mean(clinton_EV > 269) # over 269 votes wins election
I don't understand how this line works
simulated_result = rnorm(length(posterior_mean), posterior_mean, posterior_se)
length(posterior_mean) = 47, so rnorm should return a vector of size 47.
When I replace this with 1 each state gets the same result from rnorm although posterior_mean and posterior_se are diffent for each state. When I change it 46 I get an error.
So it seems to me that this line fills the whole column simulated_result (perhaps 47 times with the same results?). I would have expected that mutate uses the values of each row only to manipulate this particulate row.
Can perhaps someone explain this behavior to me or point me to a resource where this is explained?

Answer 1

For the rnorm function, if you check the vignette:
rnorm(n, mean = 0, sd = 1) Arguments
x, q :vector of quantiles.
p :vector of probabilities.
n :number of observations. If length(n) > 1, the length is taken to be the number required.
mean :vector of means.
sd :vector of standard deviations.
There are two ways to use it, one, you generate a vector of length n, coming from normal distribution of same mean and sd, for example:
set.seed(111)
rnorm(10,0,1)
[1] 0.2352207 -0.3307359 -0.3116238 -2.3023457 -0.1708760 0.1402782 -1.4974267 -1.0101884
[9] -0.9484756 -0.4939622
If you provide a vector that is as long as n, you are specifying the mean and sd for each entry, for example:
set.seed(111)
rnorm(10,1:10,1:10)
[1] 1.23522071 1.33852826 2.06512853 -5.20938263 4.14561978 6.84166935 -3.48198659 -0.08150735
[9] 0.46371956 5.06037783
In this case, you generate a vector of 10 random normal variable, first entry comes from mean=1, sd=1, 2nd entry mean=2, sd=2 and so on. We can also do something in between:
set.seed(111)
rnorm(10,1:10,1))
[1] 1.235221 1.669264 2.688376 1.697654 4.829124 6.140278 5.502573 6.989812 8.051524 9.506038
In this case, it returns a vector of length 10, first entry coming from mean = 1,sd=1, 2nd coming from mean =2,sd =1, and we can visualize this by re-running this:
t(replicate(10,rnorm(10,1:10,1)))
It's not very clear what you replaced with 1, but essentially the purpose of mutate is to assign a column with the values. And the simulated results columns work like the above.