Trivariate Normal Distribution Family Function
Maximum likelihood estimation of the nine parameters of a trivariate normal distribution.
trinormal(zero = c("sd", "rho"), eq.mean = FALSE,
eq.sd = FALSE, eq.cor = FALSE,
lmean1 = "identitylink", lmean2 = "identitylink",
lmean3 = "identitylink",
lsd1 = "loglink", lsd2 = "loglink", lsd3 = "loglink",
lrho12 = "rhobitlink", lrho23 = "rhobitlink", lrho13 = "rhobitlink",
imean1 = NULL, imean2 = NULL, imean3 = NULL,
isd1 = NULL, isd2 = NULL, isd3 = NULL,
irho12 = NULL, irho23 = NULL, irho13 = NULL, imethod = 1)lmean1, lmean2, lmean3, lsd1, lsd2, lsd3 |
Link functions applied to the means and standard deviations.
See |
lrho12, lrho23, lrho13 |
Link functions applied to the correlation parameters.
See |
imean1, imean2, imean3, isd1, isd2, isd3 |
See |
irho12, irho23, irho13, imethod, zero |
See |
eq.mean, eq.sd, eq.cor |
Logical. Constrain the means or the standard deviations or correlation parameters to be equal? |
For the trivariate normal distribution,
this fits a linear model (LM) to the means, and
by default,
the other parameters are intercept-only.
The response should be a three-column matrix.
The three correlation parameters are prefixed by rho,
and the default gives them values between -1 and 1
however, this may be problematic when the correlation parameters
are constrained to be equal, etc..
The fitted means are returned as the fitted values, which is in
the form of a three-column matrix.
Fisher scoring is implemented.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
The default parameterization does not make the estimated
variance-covariance matrix positive-definite.
In order for the variance-covariance matrix to be positive-definite
the quantity
1 - rho12^2 - rho13^2 - rho23^2 + 2 * rho12 * rho13 * rho23
must be positive, and if eq.cor = TRUE then
this means that the rhos must be between -0.5 and 1.
T. W. Yee
set.seed(123); nn <- 1000
tdata <- data.frame(x2 = runif(nn), x3 = runif(nn))
tdata <- transform(tdata, y1 = rnorm(nn, 1 + 2 * x2),
y2 = rnorm(nn, 3 + 4 * x2),
y3 = rnorm(nn, 4 + 5 * x2))
fit1 <- vglm(cbind(y1, y2, y3) ~ x2, data = tdata,
trinormal(eq.sd = TRUE, eq.cor = TRUE), trace = TRUE)
coef(fit1, matrix = TRUE)
constraints(fit1)
summary(fit1)
## Not run: # Try this when eq.sd = TRUE, eq.cor = TRUE:
fit2 <- vglm(cbind(y1, y2, y3) ~ x2, data = tdata, stepsize = 0.25,
trinormal(eq.sd = TRUE, eq.cor = TRUE,
lrho12 = extlogitlink(min = -0.5),
lrho23 = extlogitlink(min = -0.5),
lrho13 = extlogitlink(min = -0.5)), trace = TRUE)
coef(fit2, matrix = TRUE)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.