trinormalCovff {VGAMextra}

Trivariate Normal Distribution Family Function

Description

Estimates the means and the upper-half of the (symmetric) covariance matrix of a trivariate normal distribution by maximum likelihood.

Usage

      trinormalCovff(zero = c("var", "cov"),
                     lmean = "identitylink",
                     lvar  = "loglink",
                     lcov  = "identitylink")
                    

Arguments

zero

The linear predictors modelled as intercept–only. See zero for further details.

lmean, lvar, lcov

Link functions applied to the means, variances (diagonal elements of the covariance matrix), and covariances (off-diagonal elements). See Links for more choices.

Details

This family function is similar to trinormal. The only difference is that the variances and covariances, instead of the standard deviations and correlation coefficients, are directly modelled and estimated. Similarly, trinormalCovff also fits linear models to the means of a trivariate normal distribution.

The fitted means are returned as the fitted values in the form of a three–column matrix. By default, the variances and covariances are modelled as intercept–only, where a loglink link is applied to the variances and an identitylink over the covariances.

Value

An object of class "vglmff" (see vglmff-class) to be used by VGLM/VGAM modelling functions, e.g., vglm or vgam.

Author(s)

Victor Miranda and Thomas Yee.

See Also

trinormal, zero, Links, vglm.

Examples

set.seed(123); nn <- 350
var1 <- exp(1.5); var2 <- exp(0.75); var3 <- exp(1.0)

### Artificial data, with two covariates.
tdata <- data.frame(x2 = runif(nn), x3 = runif(nn))
tdata <- transform(tdata,
                   y1 = rnorm(nn, 1 + 2 * x2, sd = sqrt(var1)),
                   y2 = rnorm(nn, 3 + 1 * x2, sd = sqrt(var2)),
                   y3 = rnorm(nn, 3 - 1 * x3, sd = sqrt(var2 * var3)))

### Fit the model using VGAMextra::trinormalCovff().
fit.trinormCovff <- vglm(cbind(y1, y2, y3) ~ x2 + x3,
                         trinormalCovff,
                         data = tdata, trace = TRUE)

summary(fit.trinormCovff)
vcov(fit.trinormCovff)
                         
### Fitting the model using VGAM::trinormal()
fit.trinormVGAM <- vglm(cbind(y1, y2, y3) ~ x2 + x3,
                        trinormal,
                        data = tdata, trace = TRUE)
                         
summary(fit.trinormVGAM)
vcov(fit.trinormVGAM)

                         
#### Compare the estimated coefficients. Note that 
#### trinormal() estimates the sd's and correlation coeffs.
coef(fit.trinormCovff, matrix = TRUE)
coef(fit.trinormVGAM, matrix = TRUE)