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Group-based trajectory model for counts

Source: R/doss.R
zgll.Rd

The finite mixture of Nagin (1999) for counts over time, zero-inflated Poisson within groups (Lambert 1992; Nielsen et al. 2014): unit i belongs to group k with probability prob[k]; given k, its counts are independent Poisson with log mean off + x_t' beta_k and, when z is given, zero with extra probability plogis(z_t' gamma_k). zgll() evaluates the log-likelihood and the posterior memberships; zgem() fits by a generalised EM from the values given (the log-likelihood never decreases). One start per call: the model has local maxima, so several starts are the caller's loop, and the number of groups is the caller's choice (compare the log-likelihoods with a penalty such as BIC).

Usage

zgll(y, x, z = NULL, par, prob, off = NULL)

zgem(y, x, z = NULL, par, prob, off = NULL, maxit = 500, tol = 1e-08)

Arguments

y

Counts: a matrix with one row per unit and one column per period; NA or a negative value is a missing period.

x

The design of the Poisson part: a matrix with one row per period (columns 1, t, t^2, say).

z

NULL for a Poisson model, or the design of the zero-inflation part, one row per period.

par

The coefficients: a matrix with one row per column of x (then of z) and one column per group.

prob

The group shares: positive numbers summing to 1.

off

NULL, or log exposures with the dimensions of y.

maxit

The most iterations: a whole number from 1.

tol

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

Value

zgll(): a list of ll and post (a matrix of posterior memberships, one row per unit). zgem(): a list of the fitted par, prob, post, ll and iter (iterations made).

References

Nagin, D. S. (1999). Analyzing developmental trajectories: a semiparametric, group-based approach. Psychological Methods, 4(2), 139-157. doi:10.1037/1082-989X.4.2.139

Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1), 1-14. doi:10.2307/1269547

Examples

set.seed(1)
x <- cbind(1, (1:6 - 3.5) / 2.5)
b <- cbind(c(0.5, -1), c(1.5, 0.5))
y <- t(sapply(rep(1:2, each = 50),
              function(k) rpois(6, exp(x %*% b[, k]))))
f <- zgem(y, x, par = b + 0.2, prob = c(0.5, 0.5))
f$par
#>            [,1]     [,2]
#> [1,]  0.4069311 1.530861
#> [2,] -1.1301323 0.481301