AdmArwiki

One feature of ADMB is that it can produce standard deviations of dependent variables as well as independent variables, so that the user does not need to employ the delta method or similar techniques. In this section we plot the corresponding confidence intervals for the models given in the section on real data.

In addition, each plot includes the corresponding VPA estimates for each population, for comparison.

We assume that from a numerical point of view, it is beneficial to estimate cohorts of large size. To get an idea of which cohorts are the largest we plot the survey indices, given below:

As can be seen, the cohorts born in 1994 to 1997 seem to be the strongest. Also, the curves are not monotoic, with the curve for the cohort born 1988 having a particularly challenging shape. This should be taken into consideration when designing the model.

This is the so-called simple model, defined here.

We estimate the four cohorts born 1994-1997, and get:

cod.par # Number of parameters = 7 Objective function value = -6.38904 Maximum gradient component = 1.21049e-05 # N0: 5.20885 8.70965 9.09365 9.14128 # q: 0.189709 # logs: -0.677473363133 # M: 0.499999941397

The solid curves with starred points are the VPA estimates, and the solid lines with error bars ending in circles are the estimates of our model, with the circles denoting the end of the 95% confidence intervals.

Note that the VPA estimates start at age 3.

As one can see, the VPA estimates are for the most part (for the red, green, and most of the blue trajectory) within the confidence intervals of our model. However, it seems the simple model overestimates the population size, compared with VPA.

In addition, note that the mortality M is at its upper bound of 0.5.