7.2.2 Building of an initial typology

• Selection of an initial configuration. Before starting the process of aggregating the cases, the program selects the initial configuration, i.e. t initial group profiles, in either one of the following ways:

· Case profiles of t cases, selected randomly (using random numbers), constitute the starting configuration; in order to obtain the initial configuration, the remaining cases are distributed into t-groups.

· Case profiles of t cases, selected in a stepwise manner, constitute the starting configuration; in order to obtain the initial configuration.

• The initial configuration is a set of group profiles calculated for cases distributed across categories of a key variable;
• The initial configuration is a set of a priori group profiles provided by the researcher.

When the construction starts from t case profiles, the program considers this set of t vectors as a set of t ‘starting cases’ and distributes the remaining cases according to their distance to each of the starting case.

Denote the set of t starting cases by

and the distance between groups and/or cases i and j by D(P_ii,P_j).

Note that D(P_i, P_j) can be any distance - City block distance, Euclidean distance or Chi-square distance.

For each case the program calculates

There are two possibilities:

1. b £ g : case i is assigned to the closest group, P_kj and the profile is recalculated

2. b > g : case i forms a new group which is added to the set P_starting, and the two closest profiles P_kj and P_kj’ are aggregated forming one group with the new profile

At the end of this procedure, the initial configuration is a set of t profiles

where P_j is a mean profile of all the cases belonging to the group j.

At this stage the program does not take into account weighting of cases, if any.

• Stabilization of the initial configuration. The initial configuration is stabilized by an iterative process. During each iteration, the program redistributes the cases among initial groups taking into account their distances to each group profile.

Here, again there are two possibilities:

1. when case and

then this case remains in the group P_j;

2. when case but

then the case i is moved from the group P_j to the group P_j, and the profiles of those two groups are recalculated as follows:

After this operation, the group P_j contains N_j-1 cases and the group P_j’ contains N_j+1 cases.

The procedure is repeated until the groups are stabilized or when the number of iterations fixed by the researcher is reached. Stability of groups is measured by the percentage of cases that do not change groups between two subsequent iterations.