We therefore see that the ‘representation of Spanish’ variable always takes first place, followed by representation of Catalan, even though it does not appear in regression analysis. Social network in Catalan takes second place in regression analysis and third in the other two. Social network in the other language, Spanish, also appears in all three techniques: it takes third place in regression analysis and comes fourth in the other two. Finally, reference group only appears in regression analysis; this variable also formed part of our model, the outline of which is illustrated in Figure 1.

5.2.2 Graph-induction techniques (SIPINA)

In addition to analyses of data we have termed "explanatory", such as those we have just seen (correlations, discriminatory and multiple regression analyses), we have used another technique, proposed by Rakotomalala (1997 and 2000). This will be very useful because it will enable us to explain a qualitative variable using explanatory variables, which are themselves discretized, qualitative variables. Here, we are referring to knowledge through graph-induction. This method involves constructing a predictive function in the form of a graph and a decision tree; it allows us to explain or predict the value taken by a particular "endogenous" variable, from a series of "exogenous" variables. We discussed the features of this technique elsewhere in this journal (Querol, 2001a).

We will now characterise the four linguistic groups that we have defined:

-Exclusive speakers of Catalan (ECAT);
-More Catalan-speaking (+CAT);
-More Spanish-speaking (+CAS);
-Exclusive speakers of Spanish (ECAS);

using some of the variables that we have introduced into the research:

Represent = Representation
Transmission L.= Language transmitted by the parents
Ident. = Identity
Ins. Mot. cat. = Instrumental motivations regarding Catalan
Int. Mot. = integrative motivations
Net = Social network
Fear = Fear of being assimilated
Bil / U = Bilingual / Unilingual
Cat. , Ct. = Catalan
Span., Sp. = Spanish
Eur = European

The procedure is actually similar to that of discriminatory analysis. Figure 2 illustrates the overall results using this new technique.

The following figure reveals the segments that will allow us to identify each group better. The first is representation of Spanish. The next two factors dividing the two preceding groups are: transmission of the language, i.e. whether or not the parents spoke to the pupil in Catalan, and the representation of Catalan. Once more, we see that the variable differentiating groups the most is representation, which bears out our hypotheses.

The third factors dividing these subgroups are: Spanish identity, European identity and, on two other occasions, language transmission. At the fourth level, the following come into play: instrumental motivations in Catalan; social network in Spanish; social network in Catalan; representation of Spanish, and the fear of being assimilated by Spanish-speakers. At the fifth level, we find the instrumental motivations in Spanish and Spanish identity. If we narrow down further the Catalan-speaking group, we see that the following are still involved: identity with language (chosen from a scale of which the two extremes were: Catalan language/Spanish language), bilingual / unilingual identity. Finally, we see the fear of being assimilated by Spanish-speakers and integrative motivations in Spanish.

Thus, we see that, of the variables of our hypotheses (excluding reference group, which was not a numerical variable), both representation of languages and social network are always found at the fourth level or lower. That is, we have discovered a new way of confirming our proposal by the use of induction graphs. This new knowledge technique enables us to outline the features of each group. We shall see this in Table 5, which reveals the segments that best allow us to identify each group. We will comment on the segments containing a sufficient number of pupils, allowing us to best isolate the group we want to describe (these were marked in Figure 2). The number of pupils analysed is 357, the percentages shown relate to each of the groups and all scales used are from 1 to 10.