Q.reg | R Documentation |

Use this function to adequately confer the `formula`

in VGAM when fitting quantile regression models.

```
Q.reg(y, pvector = NULL, length.arg = NULL)
```

`y` |
Numeric, a vector or a matrix. It is the response or dependent
variable in the |

`pvector` |
A prototype vector. Entries are the conditional |

`length.arg` |
A length–1 positive integer. It is the number of |

Conditional quantile regression can be carried out using family
functions in VGAM and VGAMextra.
The `formula`

must be set up using this function, `Q.reg`

.
Here, the `p`

–quantiles of interest may be entered via
`pvector`

. Alternatively, use argument `length.arg`

by
establishing the length of `pvector`

.

Besides, the corresponding link must be entered.
For example, `gamma1Qlink`

is the proper link to fit models of conditional quantiles for
data distributed as Gamma via the family function
`gamma1`

.

See examples for further details.

A matrix, each column adequately arranged for regression on conditional quantiles, conforming with VGAM.

Indeed, this is equivalent to `cbind(y, y, ...)`

, where the
total number of columns is, either the length of `pvector`

, or
`length.arg`

.

Link functions for quantile regression in VGAM require the
vector of `p`

–quantiles of interest via the argument `p`

.
See `normal1sdQlink`

or
`maxwellQlink`

for instance.

Therefore, the integer entered at `length.arg`

in this function,
if utilized, must match the length of the vector `p`

. Else,
it will be recycled.

V. Miranda and T. W. Yee.

`normal1sdQlink`

,
`maxwellQlink`

,
`gamma1Qlink`

,
`gamma1`

,
`vglm`

,
`vgam`

```
### Quantile regression with data distributed as Maxwell(s) ###
set.seed(12073)
x2 <- seq(0, 100,length.out = 100) # independent variable
b0 <- 0.5 # true intercept
b1 <- 0.25 # true slope
b2 <- 0.02 # true second order coef.
alpha <- b0 + b1 * x2 + b2 * x2^2 # Quadratically modelling the parameters
nn <- 100 # Sample size
# The data as a data frame. #
mdata <- data.frame(y = rmaxwell(n = nn, rate = alpha), x2 = x2, x3 = x2^2)
# Quantile regression using our link function maxwellQlink(). #
# Quantiles 25%, 50%, 75% are of interest #
my.p <- c(0.25, 0.50, 0.75)
fit <- vglm(Q.reg(y, pvector = my.p) ~ x2 + x3,
# OPTIONALLY Q.reg(y, length = length(my.p)) ~ x2 + x3
maxwell(link = maxwellQlink(p = my.p)),
data = mdata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
summary(fit)
head(predict(fit))
constraints(fit)
```

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