Description Usage Arguments Details Value Note Author(s) References See Also Examples
Distribution–specified quantile regression.
An extension of uninormal
from VGAM.
It handles effectively uninormalQlink
via the first
linear predictor.
1 2 3 4 5 6 
uninormalff(link1 = "identitylink", lsd = "loglink",
percentile = 50,
imethod = 1, isd = NULL, parallel = FALSE,
smallno = 1.0e5, zero = "sd")

link1 
Link function for the first linear predictor.
By default

percentile 
Numeric. A vector with the percentiles of interest, between
0 and 100.
Used only when 
lsd, imethod, isd, parallel, smallno, zero 
Same as in

An extension of
uninormal
adapted to handle
uninormalQlink
,
for normal quantile regression (QR) via the first
linear predictor.
The standard deviation only can be estimated.
The second linear predictor is fixed to
η_2 = log σ, and
var.arg
is set internally to FALSE
.
Unlike usual QR where the distribution of YX is unspecified,
uninormalff()
estimates normal distributions at different
quantiles (as entered in percentile
)
of the YX. For this, set
link1 = uninormaQlink
. To mimic
uninormal
set
link1 = "identitylink"
(default).
Initial developments of this work are in
Miranda & Yee (2019).
See, e.g.,
weibullRff
,
for another example on distribution specified
quantile regression with the two–parameter Weibull
distribution.
An object of class "vglm"
.
See vglmclass
for full details.
Q.reg
must be used in
the vglm()
or vgam()
to enter the response.
See example below.
This VGAM family function does not handle censored data.
V. Miranda and Thomas W. Yee.
Miranda & Yee (2019) New Link Functions for Distribution–Specific Quantile Regression Based on Vector Generalized Linear and Additive Models. Journal of Probability and Statistics, Article ID 3493628.
Miranda & Yee (2021) Two–Parameter Link Functions, With Application to Negative Binomial, Weibull and Quantile Regression. In preparation.
uninormalQlink
,
uninormal
,
Q.reg
,
weibullQlink
,
weibullRff
,
CommonVGAMffArguments
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  ## Not run:
x2 < seq(0,10,length.out = 100) # independent variable
sig < exp(0.5 + 0.15*x2) # nonconstant variance
b_0 < 10 # true intercept
b_1 < 0.15 # true slope
set.seed(17221) # make the next line reproducible
e < rnorm(100,mean = 0, sd = sig) # normal random error with nonconstant variance
y < b_0 + b_1*x2 + e # dependent variable
## Data
ndata < data.frame(y = y, x2 = x2)
## Some percentiles of interest
percentile < c(10, 25, 50, 90)
## Normal quantile regression, zero = NULL
fit1 < vglm(Q.reg(y, length.arg = 4) ~ x2,
uninormalff(link1 = "uninormalQlink", percentile = percentile, zero = NULL),
data = ndata, trace = TRUE)
#summary(fit1)
( my.coef3Q < coef(fit1, mat = TRUE) )
## Plots  percentile curves.
plot(y ~ x2, pch = 19, ylim = c(1, 25),
main =" Normal quantile regression")
abline(h = 3:25, v = 0, col = "gray", lty = "dashed")
with(ndata, lines(x2, my.coef3Q[1, 1] + my.coef3Q[2, 1] * x2,
col = "red", lty = "dotted", lwd = 4))
with(ndata, lines(x2, my.coef3Q[1, 3] + my.coef3Q[2, 3] * x2,
col = "orange", lty = "dotted", lwd = 4))
with(ndata, lines(x2, my.coef3Q[1, 5] + my.coef3Q[2, 5] * x2,
col = "blue", lty = "dotted", lwd = 4))
with(ndata, lines(x2, my.coef3Q[1, 7] + my.coef3Q[2, 7] * x2,
col = "brown", lty = "dotted", lwd = 4))
legend("topleft", c("90th", "50th", "25th", "10th"),
col = c("brown", "blue", "orange", "red"), lty = rep("dotted", 4), lwd = rep(4, 4))
## Mimicking 'VGAM:uninormal'
fit2 < vglm(y ~ x2, uninormalff(link1 = "identitylink", percentile = NULL, zero = NULL),
data = ndata, trace = TRUE)
## End(Not run)

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