Empirical variogram for longitudinal data

Calculates the variogram for observed measurements, with two components, the total variability in the data, and the variogram for all time lags in all individuals.

Usage

variogram(indv, time, Y)

Arguments

indv: vector of individual identification, as in the longitudinal data, repeated for each time point.
time: vector of observation time, as in the longitudinal data.
Y: vector of observed measurements. This can be a vector of longitudinal data, or residuals after fitting a model for the mean response.

Value

An object of class vargm and list with two elements. The first svar is a matrix with columns for all values \((u_ijk,v_ijk)\), and the second sigma2 is the total variability in the data.

Details

The empirical variogram in this function is calculated from observed half-squared-differences between pairs of measurements, \(v_ijk = 0.5 * (r_ij-r_ik)^2\) and the corresponding time differences \(u_ijk=t_ij-t_ik\). The variogram is plotted for averages of each time lag for the \(v_ijk\) for all \(i\).

Note

There is a function plot.vargm which should be used to plot the empirical variogram.

Author

Ines Sousa

Examples

data(mental)
mental.unbalanced <- to.unbalanced(mental, id.col = 1,
                                   times = c(0, 1, 2, 4, 6, 8),
                                   Y.col = 2:7,
                                   other.col = c(8, 10, 11))
names(mental.unbalanced)[3] <- "Y"

vgm <- variogram(indv = tail(mental.unbalanced[, 1], 30),
                 time = tail(mental.unbalanced[, 2], 30),
                 Y = tail(mental.unbalanced[, 3], 30))