Group-based multivariate trajectories

The group-based trajectory model with several normal indicators per unit (Nagin 1999; Magrini 2022): given group k, the r indicators of a unit at period t are multivariate normal with mean B_k' x_t and covariance S_k, independently over periods. mvtll() evaluates the log-likelihood and posterior memberships; mvtem() fits by EM with closed-form steps from the values given. A period with any missing indicator is left out for that unit.

Usage

mvtll(y, x, beta, sig, prob)

mvtem(y, x, beta, sig, prob, maxit = 500, tol = 1e-08)

Arguments

y

The indicators: an array of units by periods by indicators; NA allowed, not infinite values.

x

The design: a matrix with one row per period.

beta

The coefficients: an array of design columns by indicators by groups.

sig

The covariances: an array of indicators by indicators by groups, each positive definite.

prob

The group shares: positive numbers summing to 1.

maxit

The most iterations: a whole number from 1.

tol

Stop when an iteration gains at most tol (1 + |ll|).

Value

mvtll(): a list of ll and post. mvtem(): a list of the fitted beta, sig, prob, post, ll and iter.

References

Magrini, A. (2022). Assessment of agricultural sustainability in European Union countries: a group-based multivariate trajectory approach. AStA Advances in Statistical Analysis, 106. doi:10.1007/s10182-022-00437-9

Examples

set.seed(1)
x <- cbind(1, 1:5)
y <- array(rnorm(40 * 5 * 2), c(40, 5, 2))
y[1:20, , 1] <- y[1:20, , 1] + 3
b <- array(c(0, 0, 0, 0, 3, 0, 0, 0), c(2, 2, 2))
s <- array(diag(2), c(2, 2, 2))
mvtem(y, x, b, s, prob = c(0.5, 0.5))$prob
#> [1] 0.5000024 0.4999976