Example

Consider the following example. We have two marginal characteristics defined in the control totals - persons and income. The dataset characteristics defines two categories - persons (3 groups) and income (2 groups). A combination of those groups divides the space of households characteristics into 6 groups in total.

The table for the control totals dataset can be defined as follows:

year       persons      income     total_number_of_households
2006         0             0                100100
2006         1             0                230000
2006         2             0                 10000
2006         0             1                150000
2006         1             1                250000
2006         3             1                  5000
2007         0             0                110000
  .
  .
  .

The characteristics table defines the groups of each characteristics:

characteristic      min        max
persons               0          2
persons               2          4
persons               4         -1
income                0      49999
income            50000         -1

Note that $-1$ stands for $\infty$ . The values in the control totals table denotes the index (starting from 0) of the particular group within the characteristics table. E.g. the first line in the control totals table refers to the persons group $[0,2]$ and income group $[0,49999]$ .

The model iterates over the 6 bins defined by the marginal characteristics. For each of them, it determines the number of households that belong to that group in terms of their characteristics and compares it with the control total for that group. If for example in one of the bins there are 10 households to be created, the model would randomly sample (with replacement) 10 existing households from that bin and duplicate them. If the difference between control total and the number of households in a bin would call for removing households, the model would randomly sample households belonging to that bin and delete them.