Is uniroot() confusing the input values in R? - r

Question

I'm wondering in the following, why when I directly provide the value of q (see f2), uniroot() works perfectly fine BUT when instead I provide q as a function of other input values uniroot() (see f1) fails?
In the code, everything that has ...1 suffix (e.g., f1) relates to when I indirectly provide q. And everything that has ...2 suffix (e.g., f2) relates to when I directly provide q.
My goal is to solve for df2 such that y = .15 (correct answer is ~ 336.3956). (please just run the entire code below.)
alpha = c(.025, .975); df1 = 3; q = 48.05649 ; peta = .3 # input values
f1 <- function(alpha, q, df1, df2, ncp){ # Objective function (`q` indirectly)
alpha - suppressWarnings(pf(q = (peta / df1) / ((1 - peta)/df2), df1, df2,
ncp, lower.tail = FALSE))
}
f2 <- function(alpha, q, df1, df2, ncp){ # Objective function (`q` directly)
alpha - suppressWarnings(pf(q = q, df1, df2, ncp, lower.tail = FALSE))
}
ncp1 <- function(df2){ # root finding
b <- sapply(c(alpha[1], alpha[2]),
function(x) uniroot(f1, c(0, 1e7), alpha = x, q = peta, df1 = df1, df2 = df2)[[1]])
b / (b + (df2 + 4))
}
ncp2 <- function(df2){ # root finding
b <- sapply(c(alpha[1], alpha[2]),
function(x) uniroot(f2, c(0, 1e7), alpha = x, q = q, df1 = df1, df2 = df2)[[1]])
b / (b + (df2 + 4))
}
m1 <- function(df2, y){ # A Utility function
abs(abs(diff(ncp1(df2))) - y)
}
m2 <- function(df2, y){ # A Utility function
abs(abs(diff(ncp2(df2))) - y)
}
optimize(m1, c(1, 1e7), y = .15)[[1]] # Incorrect answer: 1e+07
optimize(m2, c(1, 1e7), y = .15)[[1]] # Correct answer: 336.3956

Answer 1

In ncp1
you have q = peta which then gets passed on to f1 but then does not actually get used, as pf takes q as (peta / df1) / ((1 - peta)/df2).
In ncp2
you have q = peta which then gets passed on to f2 and in turn to pf.
So the bottom line is you use different values for q in pf. If you re-active warnings, you will see that f1 as part of ncp1 fails to reach convergence.