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Multidimensional Attitude Change Models. Galileo

The spatial models presented in this chapter include several classes of models: Multidimensional Attitude Change Models, Spring Models, Variable Mass Models, Spatial‐linkage Models and Hierarchical Models. All these models have been developed within the extended Galileo research framework for measurement of change in cognitive and cultural processes. What is specific to Galileo modelling is the approach to change in both cognitive and cultural processes in terms of the relationships among cognitive and cultural concepts viewed as ‘objects’ (Woelfel and Fink, 1980: preface, 10). Anything could be an ‘object’ in a cognitive space: attitude, belief, behaviour.

Attitude change is modelled as a cognitive process. Conclusions drawn from the multidimensional measurement of change in cognitive objects, like attitudes held by individuals or collectives (i.e., groups or society at large), have been generalized so as to give an account on the measurement of change in cultural objects (Woelfel and Fink, 1980: 32–37).

Galileo was originally conceived as a measurement model, and it is based on mathematical modelling. The computational dimension appears inherent due to complex mathematical calculations requested for the modelling of continuum and multidimensional aspects. As time passed and its complexity increased, the computational modelling character of the Galileo approach became more and more emphasized.

Measurement of attitude change in the Galileo modelling framework starts from the assumption that experience has a representation, and this representation should be based on objects and their relationships. From this point of view, Galileo is a model of relative representation (Woelfel, [n.d.]2009: 2) since each object is represented by means of all the rest of the objects which constitute the system being represented; that is, a cognitive system or a culture. As a difference from the Aristotelian categorical representation, the Galileo Model addresses the multidimensional representation: the representation space has as many dimensions as objects. An object in such a space could be an attitude, a belief, value or emotion, or any cultural object.

The Galileo Model was conceived and has been used for change measurement in attitude and cultural processes.

Conceptual Background

These classes of approaches are inspired by several classic modelling theories with concern to attitudes, communication and cognitive processes.

One source of inspiration is represented by Osgood’s concept of semantic space (Osgood, 1964: 171). He used connotative meanings of the objects in a semantic space to derive the attitudes toward particular objects. Inspired by this idea and by George Herbert Mead’s (1934) works on mind and self, Joseph Woelfel developed multidimensional models of attitude change which (a) define each concept by its dissimilarity (also called semantic ‘separation’ or ‘discrepancy’) to all the other concepts in the semantic space (Woelfel, 1980) and (b) evaluate this ‘dissimilarity’ in order to measure the attitude change (Woelfel, 1980: 99; [n.d.]2009: 2). The Galileo model is a relativistic model as its fundamental assumption is that an object (concept) gets a meaning only from relating it to other objects in a cognitive space (Woelfel and Fink, 1980: 145). The self is also considered an object in this space. The model approaches the issue of representation of cognitive and cultural experience.

Another conceptual background is provided by the Yale model (Hovland et al., 1953) on persuasive communication. Inspired by this model, the multidimensional attitude change model works with two types of variables: (a) the messages xi, viewed as ‘forces’ which make the attitude ‘move’ along the dimensions described by the other concepts (objects, attributes) with which they are linked; (b) the ‘difference’ or ‘dissimilarity’ (also called ‘separation’, ‘discrepancy’ or ‘distance’) between the recipient’s attitude and the concepts (i.e. stimuli) provided by the incoming (persuasive) message(s) in a communication process.

The notion of ‘discrepancy’ (‘dissimilarity’ or ‘separation’) in a semantic space is considered equivalent to the notion of ‘distance’ in a metric space. The semantic space could be considered a multidimensional space: each concept (object) introduces a new dimension along which the attitude change could develop. This change is determined by the most relevant concepts in the semantic space, namely, by the concepts which are closer to the ‘self’ or within a neighbourhood which defines the ‘self’.

As regards the ‘self’ issue, the authors of the Galileo Model found inspiration in Mead’s theory on mind and self (1934) as well as in Heider’s theory of balance (1958) and in Festinger’s theory of cognitive dissonance (1957). However, the model departs from its inspiring sources by considering that the ‘self’ is an information structure constructed dynamically in the so‐called ‘self‐process’. In the Galileo Model, the ‘self’ is defined as a set of relationships with all the other objects in a cognitive space. These relationships are modelled as distances between the ‘self’ and all the other objects. As an information structure, the ‘self’ is dynamically changing as a result of the changes induced in the cognitive space from processing the new information provided by the incoming messages. The change could also be induced from internal information processing (Woelfel and Fink, 1980: 145).

A third source of inspiration is represented by Newtonian mechanics. Each message is modelled as a ‘force’ whose effect on the actor’s attitude is to modify its location in the cognitive space and, therefore, its discrepancies from all the other concepts within the space. Each object in the attitude space has a location and a mass. The motion of an attitude in a multidimensional space is evaluated on the methodological background of the metric multidimensional scaling measurement methods (Young and Householder, 1938; Torgersen, 1958).

Formal Models Based on the Galileo Model

Stan Kaplowitz and Edward Fink (1982: 373–378) provided a review of the models developed on the Galileo theoretical and methodological background. Variable‐mass (VM) impulse models (Saltiel and Woelfel, 1975) include VM.1 models (Woelfel and Saltiel, 1978; Woelfel et al., 1980) and VM.2 models (Danes et al., 1978). These models are designed to show how the message’s force can influence the attitude trajectory. A change in attitude can be predicted by the mass of messages, that is, the configuration and amount of information (number of messages and content) necessary to move any object (concept) toward the person’s so‐called ‘self’ neighbourhood. Messages which identify two objects (concepts) or identify the similarity of two objects (concepts) are likely to be highly effective in making the receiver resistant to other (persuasive) incoming messages with a different content. Information of this type increases the concept’s mass and makes it resistant to high acceleration.

Fixed‐mass spring models assume that the information in the message works like a ‘spring’, in that it serves as the connection between two concepts identified by the message: the more information received about an object (concept), the stronger anchored the concept and, therefore, the more difficult it is to be moved (changed). More complex spring models assume that messages both create springs and add mass to the concepts. This may induce variability in a concept’s capacity to resist change (Kaplowitz and Fink, 1982).

Another model based on the Galileo approach is the Hierarchical model (Dinauer, 2003; Dinauer and Fink, 2005), which is designed for the measurement of inter‐attitudinal change.

Galileo Model

The Conceptual Model

The Galileo Model (Woelfel and Saltiel, 1978) provides for the cognitive theory underlying the multidimensional attitude change measurement model.

As a difference from the Aristotelian way of defining the experience based on the concept of ‘category’, the Galileo Model is concerned with the cognitive experience, which is modelled as a mathematical continuum. The Galileo Model works with the notions of ‘objects’ and their relationships in order to represent experience and to measure the change in attitudes. An ‘object’ is defined as a representation of experience (Woelfel, 1980: 2; Woelfel and Fink, 1980: 145). The cognitive space of a set of representations corresponding to the attitude domain is considered a multidimensional space. Since the cognitive space is viewed as a representation of experience, the attitude is a cognitive structure which could include (or not) an affective component, avoiding the idea of developing a measurement model based on affective dichotomies usually employed by the classic scale measurement models.

Attitude change is viewed as a cognitive process in this multidimensional cognitive space. As such, an attitude change is defined with respect to the concepts of ‘self’ and ‘object’. From a conceptual point of view, it is based on the notion of similarity/dissimilarity, which in operational terms is defined as ‘difference’ or ‘distance’.

The notion of ‘self’ is defined in the same paradigm: it is defined, like any other object in the attitude domain, in terms of its relationships with all the other objects in the cognitive space (Woelfel, 1980: 99). As it is defined by its dissimilarities with respect to all the other objects in this space, these pairwise separations are conceived as beliefs (Woelfel, 1980: 99).

Attitudes are defined as beliefs; that is, measured dissimilarities between the ‘self’ and any of the other objects in the cognitive space (Woelfel, 1980: 92).

The ways in which attitude change could be associated with a particular behaviour are derived from preliminary research concerning the predictive role of the socially relevant others who know and influence an individual actor’s behaviour (see the notion of ‘significant others’ in Haller and Woelfel (1972)).

Attitude change modelling has been addressed in the Hovland–Yale model of persuasive communication (Hovland et al., 1953; Anderson and Hovland, 1957), which assumes that the essential factors are the message, the source of the message and the recipient (audience) of the message. The model further assumes that four main elements which should be taken into consideration for the evaluation of an attitude change are: (i) the attitude of the source (i.e. as perceived by the receiver) with respect to the attitudinal object, (ii) the attitude advocated by the message, (iii) the initial and (iv) final attitudes of the receiver (i.e. as modified by the message). In unidimensional models, the values taken by these concepts always lie on a single axis, and their variation range is described by values which go from one end to the other of this axis. Classic measurement procedures, like the Likert scales, are based on this measurement principle.

An alternative to this unidimensional attitude change modelling approach is the multidimensional one. It is rooted in the idea introduced by Osgood et al. (1957) that variables describing attitude change can be measured with multidimensional methods. This was further extended by Joseph Woelfel et al. (1980: 153) in their modelling approach: attitudes can change on multiple dimensions, each dimension being associated with an object (concept) in the attitude domain.

Other theoretical roots of this approach can be found in the works of George Herbert Mead (1934). Mead’s view of the continuous interaction between the individual actor and the social environment was adapted and used by Woelfel and collaborators to develop a theory about the measurement of the dynamics of attitude change in social communication processes. Attitudes are defined by means of their global set of relationships to the concepts in the cognitive structure of the attitude domain (Woelfel, 1980: 92). Attitude change is therefore associated with the overall change in this global conceptual structure.

Woelfel describes it (Woelfel and Saltiel, 1978; Woelfel, 1980: 94) with an equation which models attitude change as depending on three main factors: (1) the number of old messages which contributed to the original attitude formation, (2) the number of new messages which contribute to the change of attitude and (3) the amount of discrepancy between the new and the old attitude (i.e. an averaged position between the positions advocated by each of the new persuasive messages).

The linear force aggregation theory – see Woelfel (1980: 94, equation 1) – is an attitude change measurement model. Attitude change is considered to be a cognitive process which can be described as a motion in a multidimensional space. The dimensions are the attributes of the object and the motion is defined with the Newtonian expression of relationship between force, mass and acceleration.

Attitude change is described as the outcome of the weighted sum of the ‘forces’ exerted by each message on the existing attitude towards a particular object such that a new attitude is issued after an interval of time (measurement time).

Adapting the original equation – see Woelfel and Saltiel (1978: equation 5), the model describes attitude change as a consequence of receiving new messages (new information) about the attitude:

(11.1) images

where images is the interval of time, new_att is the new attitude measured at time t1, old_att is the original attitude at time t0, m0 is the number of messages out of which the old attitude has been formed, m1 is the number of new messages received during the interval of time images and I is the amount of other messages received over the specified interval of time.

The force aggregation theory shows that the stability of attitudes increases in direct proportionality with the amount of information contained in all received messages (Woelfel, [n.d.]2009: 94).

The Operational Model

The Galileo Model operationalizes the definitions of attitude and belief so as to allow for an operationalization of their motion in the multidimensional space of objects and attributes. The operationalization of the attitude definition consists of replacing the classic association between an attitude object and an expression of affect (like/dislike) with the association between two points in the cognitive space of a set of representations: one point should be the ‘self’ point, while the other point could be any of the other ‘objects’’ points in the attitude domain. The association between the two points is defined as the distance between these points.

The operationalized definition of a belief is the distance between any two concept points (with the exception of the ‘self’ point) in the cognitive space of a set of representations such that one point is an attribute point.

At the operational level, the Galileo Model defines the cognitive change processes (attitude change) and cultural change processes (culture change) as changes in spatial locations within the cognitive or cultural space, respectively. The change in spatial location is assimilated with a ‘motion’ in the multidimensional space of a set of representations (Woelfel and Fink, 1980: 39). An attitude change, described as a cognitive process suffered by an object (i.e. attitude) in the cognitive space, is modelled as a motion of an object relative to the other objects in a physical space. The Galileo Model defines attitude change as a cognitive process which updates the relationships between all concepts in the cognitive space as new (persuasive) messages are received by an individual actor. These relationships are measured by pair comparison methods, and the dissimilarities are expressed as matrices which are evaluated by metric multidimensional scaling procedures. The typical outcome of such procedures is the representation of the cognitive objects (concepts or cultures) as points in a multidimensional space (Riemann space).

Once a cognitive space is defined for a set of objects (concepts or cultural objects), the laws of Newtonian physics could be addressed as laws of motion for all concepts within the space (Woelfel, [n.d.]2009).

As initially described by Woelfel and Fink (1980) (see also Kaplowitz et al., 1983: 234–235), the set of assumptions which allow for modelling the cognitive space and objects on a Newtonian mechanics basis are: (i) the concepts within a cognitive system have location and mass characteristics; (ii) attitude and belief change with regard to a particular object in the cognitive system is expressed as a motion in that space under Newtonian laws of physical motion; (iii) any incoming message received by a recipient is viewed as exerting a force which influences the current state of the cognitive system (as inspired from McGuire’s (1968: 257) idea); (iv) modelling the motion of a concept as a physical motion, the Galileo model assumes that the acceleration of the concept in the cognitive space is calculated by dividing the force induced by the message by the mass of the concept; (v) the mass of a concept is assumed to be represented as the cumulated amount of information received through the incoming messages.

The notion of reference frame is associated with the study of an object of perception by comparison with other objects in some experience. A reference frame is defined as a set of objects which are taken together to serve as a standard of reference in measuring the identity or activity of some (set of) object(s) (Woelfel and Fink, 1980: 53). There are several types of reference frames: (1) accidental (natural); (2) contrived (laboratory); and (3) the mathematical reference frame.

When the reference frame for experimental research differs across observers and/or time, a transformation is needed (objectivization principle). If the rules of transformation are not known, then the outcomes cannot avoid errors of interpretation affecting the validity of the experimental research. In order to avoid such problems, a mathematical reference frame is usually defined and constructed. It allows for the transformation of observations in one reference frame to another one in a general, abstract manner (Woelfel and Fink, 1980: 55). A reference frame, once established, (Woelfel, 1980: 108) provides for a description of the cognitive processes. The definition of a concept is given by its location (position vector) within the reference frame. Changes in the meaning of any concept are modelled as changes in the location or position vector.

The operationalization of a multidimensional attitude change process comprises two phases:

  • In the first phase, a reference frame is constructed. The aim of this phase is that of transforming the raw data by following the metric multidimensional scaling procedures.
  • The second phase is based on the measurement of change as a motion in a multidimensional space. The ‘force’ paradigm is applied since the force aggregation theory has a formal similarity to Newtonian mechanics. The attitude domain comprises multiple objects (beliefs, attitudes). Any object is viewed like a physical object in a physical space: they have location and mass attributes.

The metric multidimensional scaling procedure for establishing the coordinate reference frame on a set of objects consists of the following steps (Woelfel and Fink, 1980: 66):

  1. Identify the set of reference objects.
  2. Set up the standard separation (standard measure), that is, the separation between the two elements of an arbitrary chosen pair of objects in the set.
  3. Separation estimations for all pairs of the remaining objects; separations are estimated as ratios of the standard separation.
  4. A matrix of distances is obtained and converted into a deviation matrix with origin at the centroid of all the points (Torgersen’s method) or at an arbitrary point (Young and Householder’s method).
  5. The deviation matrix is converted into a matrix of scalar products.
  6. The scalar products matrix is transformed into the matrix R in which any concept P is represented by a position vector images, where images is a set of r orthonormal vectors.

The cross‐observer transformations (Woelfel, 1980: 105) consist of applying this procedure for obtaining the R matrix. The transformations over time consist of applying rotations and translations for the comparison of time‐ordered individual or aggregate coordinate frames (Woelfel, 1980: 106).

For a number n of observers, the R matrix (images matrix) will be obtained representing a non‐Euclidean system of coordinates (Riemann manifold). As multidimensional attitude change is modelled as the overall outcome of the external forces exerted by the incoming messages, this procedure provides for the description of their effect such that it can be measured (Woelfel and Fink, 1980: 155). Messages are represented as vectors in this space (Woelfel and Fink, 1980: 150). Concepts are represented as position vectors. Under the equal mass condition, each concept will converge on the centre of mass of the distribution of concepts. This means that the attitudes and beliefs of an individual actor are predicted by the average beliefs and attitudes indicated by the persons who are closer to that individual (i.e. these close persons are called ‘significant others’). An experiment focused on the measurement of political attitudes of elementary and high school actors showed that they were accurately predicted by the average political attitudes of the significant others (Woelfel and Fink, 1980: 153).

Implementation

Galileo is a complex commercial software platform which provides a multiple components package specialized in the measurement of cognitive processes and systems. It includes several generators of questionnaire patterns (automated and electronic questionnaire makers), a program for providing data entries and programs for text analysis.

Galileo includes neural network components for text analysis (CAPTAC).

For political attitude change measurements, Galileo includes programs used in electoral campaigns for generating electoral campaign strategies or for estimations of the vote percentages likely to be obtained by candidates (BALLOT).

Web Resources

Galileo

www.galileoco.com. Commercial site: includes a literature database, a technical documentation database and packages of software programs.

References

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