uninormal: Univariate Normal Distribution

Description

Maximum likelihood estimation of the two parameters of a univariate normal distribution.

Usage

uninormal(lmean = "identitylink", lsd = "loge", lvar = "loge",
          var.arg = FALSE, imethod = 1, isd = NULL, parallel = FALSE,
          smallno = 1e-05, zero = -2)

Arguments

lmean, lsd, lvar

Link functions applied to the mean and standard deviation/variance. See Links for more choices. Being positive quantities, a log link is the default for the standard deviation and variance (see va

var.arg

Logical. If TRUE then the second parameter is the variance and lsd and esd are ignored, else the standard deviation is used and lvar and evar are ignored.

smallno

Numeric, positive but close to 0. Used specifically for quasi-variances; if the link for the mean is explink then any non-positive value of eta is replaced by this quantity (hopefully,

imethod, parallel, isd, zero

See CommonVGAMffArguments for more information. If lmean = loge then try imethod = 2. If parallel = TRUE then the parallelism constraint is not app

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

Warning

uninormal() is the new name; normal1() is old and will be decommissioned soon.

Details

This fits a linear model (LM) as the first linear/additive predictor. So, by default, this is just the mean. By default, the log of the standard deviation is the second linear/additive predictor. The Fisher information matrix is diagonal. This VGAM family function can handle multiple responses.

References

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011) Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

Examples

Run this code

udata <- data.frame(x2 = rnorm(nn <- 200))
udata <- transform(udata,
                   y1  = rnorm(nn, m = 1 - 3*x2, sd = exp(1 + 0.2*x2)),
                   y2a = rnorm(nn, m = 1 + 2*x2, sd = exp(1 + 2.0*x2)^0.5),
                   y2b = rnorm(nn, m = 1 + 2*x2, sd = exp(1 + 2.0*x2)^0.5))
fit1 <- vglm(y1 ~ x2, uninormal(zero = NULL), data = udata, trace = TRUE)
coef(fit1, matrix = TRUE)
fit2 <- vglm(cbind(y2a, y2b) ~ x2, data = udata, trace = TRUE,
             uninormal(var = TRUE, parallel = TRUE ~ x2,
                       zero = NULL))
coef(fit2, matrix = TRUE)

# Generate data from N(mu = theta = 10, sigma = theta) and estimate theta.
theta <- 10
udata <- data.frame(y3 = rnorm(100, m = theta, sd = theta))
fit3a <- vglm(y3 ~ 1, uninormal(lsd = "identitylink"), data = udata,
             constraints = list("(Intercept)" = rbind(1, 1)))
fit3b <- vglm(y3 ~ 1, uninormal(lsd = "identitylink", parallel = TRUE ~ 1,
                                zero = NULL), data = udata)
coef(fit3a, matrix = TRUE)
coef(fit3b, matrix = TRUE)  # Same as fit3a

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