Example

Consider the following example. We have two marginal characteristics defined in the control totals - persons and income. The dataset characteristics defines three categories - persons (3 groups), income (2 groups) and age of head (3 groups). A combination of those groups divides the space of households characteristics into 18 groups in total, as shown in Figure 8.2.

Figure: Example of dividing household characteristics into bins.

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
age_of_head           0         29
age_of_head          30         49
age_of_head          50         -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 bins defined by the marginal characteristics. In this case, it would iterate over the 6 groups marked by A,B,C,D,E,F in Figure 8.2, it would then determine the number of households that belong to each group in terms of their characteristics and compare it with the control total for that group. If for example in bin F (shaded area in the figure) there are 10 households to be created, the model would randomly sample (with replacement) 10 bins from the 3 bins within F (formed by groups on the axis ``age_of_head''), weighted by the number of existing households in those bins. These are categories of the 10 new households. Then for each of the 10 households it would randomly sample the actual value of each characteristics. For example, for the very front cube of F, it would sample income between 0 and $49,999$ (rounded to the nearest 10), number of persons between 4 and 8 and age of head between 15 and 29. If the difference between control total and the number of households in F would call for removing households, the model would randomly sample households belonging to F regardless to which bin within F they belong.