normal1sdff | R Documentation |

Maximum likelihood estimation of the standard deviation, including inference for conditional quantiles, of a univariate normal distribution.

```
normal1sdff(zero = NULL, link = "loglink",
fixed.mean = 0, p.quant = NULL,
var.arg = FALSE)
```

`zero` |
Allows to model the single linear predictor in this family function as intercept–only. See below for important details about this. |

`link` |
This is the link function applied to the standard deviation.
If |

`fixed.mean` |
Numeric, a vector or a matrix. It allocates the (fixed) mean of the response in the fitting process. See below for further details. |

`p.quant` |
Numeric. A prototype vector of probabilities indicating the quantiles of interest, when quantile regression is to be performed. |

`var.arg` |
If |

This family function is a variant of
`uninormal`

to estimate the standard deviation of a Normal distribution
with *known* mean. The estimated values are returned as
the fitted values, unlike some other family functions where the mean
is returned as *fitted values*. However, here the mean is
assumed to be known.

By default, the response is supposedly *centered* on its mean,
that is, `fixed.mean`

` = 0`

. Change this accordingly:
For a single response or multiple responses, `fixed.mean`

must
be a numeric vector where each entry is the mean of each response,
only *if* the mean is *fixed*. When the mean is not constant,
`fixed.mean`

must be matrix with the number of columns matching
the number of responses.

*Quantile regression:*
The (single) linear/additive predictor by default is the `log`

of the standard deviation. However, if quantile regression is of
primary interest, then the response must be entered using the function
`Q.reg`

, and the corresponding
`p`

–quantiles through `p.quant`

in the
`vglm`

or `vgam`

call.
Additionally, set `normalsdQlink`

as the link function via the argument `link`

.

This family VGAM function handles multiple responses.

An object of class `"vglmff"`

.
See `vglmff-class`

for further details.

Be aware of the argument `zero`

:
by default, the single linear/additive predictor in this family
function, say `\eta`

, can be modeled in terms of covariates,
i.e., `zero = NULL`

.
To model `\eta`

as intercept–only, set `zero = "sd"`

.

See `zero`

for more details about this.

V. Miranda.

`normal1sdQlink`

,
`loglink`

,
`uninormal`

,
`CommonVGAMffArguments`

,
`zero`

,
`vgam`

,
`vglm`

.

```
set.seed(121216)
my.mean <- -1 # Mean (CONSTANT)
my.sd <- 2.5
y <- rnorm(100, mean = my.mean, sd = 2.0) # Generate some data.
normdat <- data.frame(y = y) # Setting up our data.
# Plotting the data
plot(y, main = c("Y ~ Normal ( mean(known), sd = 2.5 ). "),
ylab = "The data", pch = 20,
xlim = c(0, 100), ylim = c(-7, 7), col = "blue")
abline(h = 0, v = 0, lwd = 2, col = "black")
### EXAMPLE 1. Estimate the SD with two responses. The mean is fixed. ###
fit1 <- vglm(cbind(y, y) ~ 1, family = normal1sdff(fixed.mean = my.mean),
data = normdat, trace = TRUE, crit = "coef")
Coef(fit1)
summary(fit1)
### EXAMPLE 2. Quantile regression. The link normal1sdQlink() is used. ###
my.p <- c(25, 50, 75) / 100 # Quantiles 25%, 50% and 75% are of interest.
fit2 <- vglm(Q.reg(y, length.arg = 3) ~ 1,
family = normal1sdff(fixed.mean = my.mean, p.quant = my.p,
link = normal1sdQlink),
data = normdat, trace = TRUE, crit = "coef")
summary(fit2)
head(predict(fit2))
constraints(fit2)
### EXAMPLE 3. Complete the plot. Quantiles matching. ###
( my.c3Q <- coef(fit2, matrix = TRUE) )
with(normdat, lines(rep(my.c3Q[1], 100), col = "tan" , lty = "dotted", lwd = 2))
with(normdat, lines(rep(my.c3Q[2], 100), col = "orange", lty = "dotted", lwd = 2))
with(normdat, lines(rep(my.c3Q[3], 100), col = "brown1", lty = "dotted", lwd = 2))
legend(20, 7.0, c("Percentil 75", "Percentil 50", "Percentil 25"),
col = c("brown1", "orange", "tan"),
lty = rep("dotted", 3), lwd = rep(2, 3), cex = 0.75)
```

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