Simulation Study

We perform simulation studies to visualize the ISRP estimates over time and the distribution of the estimates. We also check the accuracy of the delta method in approximating the sampling distribution of the estimates of the parameters. We simulated the growth trajectories for n = 1000 individuals for 20 times points where each trajectory was generated from the multivariate normal distribution with logistic mean function and variance-covariance matrix with Koopmans’ structure. Based on this data, we obtained an estimate of the parameters. The process was replicated 1000 times to visualize the sampling distribution of the estimate of the parameters by using the histogram. In addition, even if the data were simulated from the other growth model, the normal approximation of the sampling distribution of the estimators remains unchanged. For example, we carried out the same simulation study using the extended version of the logistic growth model with r(t) = r0*t^(c−1), and r(t) = r0*(1 + c*t) and evaluated the estimate of r under the assumption of the logistic model.