Warning message: Those produced when calculating confidence intervals

Question

I am trying to estimate the upper and lower limits using the 95% confidence interval, but the R returns the following message:

Warning message:
In rnorm(nrow(df), media/-0.832, media/-0.399) : NAs produzidos

Data frame I’m using:

y<-c(-1.0, -1.0, -1.0, -1.0, 0.769, 0.623, -1.0, 0.327, -1.0, -0.638,
   -1.0, -1.0, -0.618, -1.0, -0.670, -1.0, 0.028, -1.0, -1.0, -1.0,
   0.235, -0.286, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.148,
   0.857, -0.918)
df<-data.frame(y)

n<-length(df$y)
media<-mean(df$y)
var<-var(df$y)

ic<-media+qt(c(0.025, 0.975), df=n-1)*sqrt(var/length(df$y))

media<-abs(mean(df$y))
df$lim_inf<-df$y-rnorm(nrow(df), media/-0.832, media/-0.399)
df$lim_sup<-df$y+abs(rnorm(nrow(df), media/-0.832, media/-0.399))

How do I make R not return Nas?

Answer 1

I do not know if the following is what the question asks.

intconf <- function(x, nivel = 0.95, normal = FALSE){
  qq <- c((1 - nivel)/2, 1 - (1 - nivel)/2)
  n <- length(x)
  xbar <- mean(x)
  s2 <- var(x)
  ic <- if(normal && (n >= 30)){
    xbar + qnorm(qq)*sqrt(s2/n)
  } else {
    xbar + qt(qq, df = n - 1)*sqrt(s2/n)
  }
  setNames(ic, c("lim_inf", "lim_sup"))
}

This function calculates confidence intervals for the average. If the sample x for small, n < 30, uses the Student t distribution, otherwise and if the argument normal = TRUE uses the normal distribution. The 30 value is often considered to decide whether the sample is small (it does not come in the Wikipedia on this topic).

With the question data,

intconf(df$y)
#   lim_inf    lim_sup 
#-0.8479307 -0.4110068

As the sample has 32 elements one can use the normal distribution.

nrow(df)
#[1] 32

intconf(df$y, normal = TRUE)
#   lim_inf    lim_sup 
#-0.8394098 -0.4195277

To see these results, a histogram can be drawn with the vertical lines corresponding to the confidence intervals.

icdf <- rbind(
  intconf(df$y),
  intconf(df$y, normal = TRUE)
)

brks <- seq(min(df$y), max(df$y), length.out = 7)
hist(df$y, breaks = brks, freq = FALSE)
abline(v = icdf, col = c("red", "blue"))
legend("top", legend = c("t", "normal"), lty = 1, col = c("red", "blue"), horiz = TRUE)

Answer 2

Rui Barradas already gave a good answer on how to calculate the confidence interval, this is to understand what was doing wrong. Because it is not only a programming error, but understanding of the IC.

The error message

The error that R is returning comes from using a negative value for the standard deviation in the function rnorm:

> rnorm(5, -.4, .1)
[1] -0.4070113 -0.3860859 -0.3772370 -0.4746763 -0.3817434

> rnorm(5, -.4, -.1)
[1] NaN NaN NaN NaN NaN
Warning message:
In rnorm(5, -0.4, -0.1) : NAs produced

This is because standard deviation does not take negative values. But why are you using rnorm to calculate the limits? Why use the absolute value of the average?

Calculation of the CI

There is a reason that basic R packages do not have a function for computing IC. It is a measure of how reliable the estimate of a parameter is, how it is calculated depends on the parameter and the model assigned to the data.

Your formula is correct for mu estimated small sample (or large variance) following close to normal distribution. Compare with the result of a test t:

ic <- media + qt(c(0.025, 0.975), df = n-1) * sqrt(var/n)

> ic
[1] -0.8479307 -0.4110068

> t.test(dados$y)$conf.int
[1] -0.8479307 -0.4110068
attr(,"conf.level")
[1] 0.95

But are these good assumptions for your data? Contrast with the result of the @Rui-Barradas function. And compare with the result using different methods with the average estimated by bootstrap:

library(boot)

media.b <- boot(dados$y, function(x,i) mean(x[i]), 10000)

> boot.ci(media.b, conf = .95, type = c("norm","basic", "perc", "bca"))
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 10000 bootstrap replicates

CALL :
boot.ci(boot.out = media.b, conf = 0.95, type = c("norm", "basic",
    "perc", "bca"))

Intervals :
Level      Normal              Basic
95%   (-0.8366, -0.4206 )   (-0.8527, -0.4365 )

Level     Percentile            BCa
95%   (-0.8224, -0.4063 )   (-0.8041, -0.3735 )
Calculations and Intervals on Original Scale

Adding limits to the data

Once you have calculated the range, simply add/subtract the values of y:

df$lim_inf <- df$y - ic[1]
df$lim_sup <- df$y + ic[2]

But this is wrong. The confidence interval applies to the estimated parameter (the mean, in this case), not to the individual values. A more appropriate option is to use the standard error:

ep <- sqrt(var/n)

df$lim_inf <- df$y - ep
df$lim_sup <- df$y + ep