Description Usage Arguments Details Value References See Also Examples
Evaluate the functions b and s, as specified by the vector
(b(d/6),b(2d/6),...,b(5d/6),s(0),s(d/6),...,s(5d/6)) computed using
bsciuupi2
, alpha
, m
and natural
at x
.
1 | bsspline2(x, bsvec, alpha, m, natural = 1)
|
x |
A value or vector of values at which the functions b and s are to be evaluated |
bsvec |
The vector (b(d/6), b(2d/6), …, b(5d/6), s(0), s(d/6),
…, s(5d/6)) computed using |
alpha |
The minimum coverage probability is 1 - |
m |
Degrees of freedom |
natural |
Equal to 1 (default) if the b and s functions are evaluated by
natural cubic spline interpolation or 0 if evaluated by clamped cubic spline
interpolation. This parameter must take the same value as that used in
|
The function b is an odd continuous function and the function s is an
even continuous function. In addition, b(x)=0 and s(x) is equal to the
1 - α/2 quantile of the t distribution with m
degrees of freedom for all |x| greater than or equal to d, where d is a
sufficiently large positive number (chosen by the function
bsciuupi2
). The values of these functions in the interval
[-d,d] are specified by the vector (b(d/6), b(2d/6), …,
b(5d/6), s(0), s(d/6), …, s(5d/6)) as follows. By assumption,
b(0)=0 and b(-i)=-b(i) and s(-i)=s(i) for
i=d/6,...,d. The values of b(x) and s(x) for any x
in the interval [-d,d] are found using cubic spline interpolation for
the given values of b(i) and s(i) for
i=-d,-5d/6,...,0,d/6,...,5d/6,d. The choices of d for m =
1, 2 and >2 are d=20, 10 and 6 respectively.
The vector (b(d/6), b(2d/6), …, b(5d/6), s(0), s(d/6), …,
s(5d/6)) that specifies the Kabaila and Giri(2009) confidence interval that
utilizes uncertain prior information (CIUUPI), with minimum coverage
probability 1 - alpha
, is obtained using
bsciuupi2
.
In the examples, we continue with the same 2 x 2 factorial example described
in the documentation for find_rho
.
A data frame containing x
and the corresponding values of the
functions b and s.
Kabaila, P. and Giri, R. (2009). Confidence intervals in regression utilizing prior information. Journal of Statistical Planning and Inference, 139, 3419-3429.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | alpha <- 0.05
m <- 8
# Find the vector (b(d/6),...,b(5d/6),s(0),...,s(5d/6)) that specifies the
# Kabaila & Giri (2009) CIUUPI for the first definition of the
# scaled expected length (default) (takes about 30 mins to run):
bsvec <- bsciuupi2(alpha, m, rho = -0.7071068)
# The result bsvec is (to 7 decimal places) the following:
bsvec <- c(-0.0287487, -0.2151595, -0.3430403, -0.3125889, -0.0852146,
1.9795390, 2.0665414, 2.3984471, 2.6460159, 2.6170066, 2.3925494)
# Graph the functions b and s
x <- seq(0, 8, by = 0.1)
splineval <- bsspline2(x, bsvec, alpha, m)
plot(x, splineval[, 2], type = "l", main = "b function",
ylab = " ", las = 1, lwd = 2, xaxs = "i", col = "blue")
plot(x, splineval[, 3], type = "l", main = "s function",
ylab = " ", las = 1, lwd = 2, xaxs = "i", col = "blue")
|
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