PCSinR {PCSinR}

PCS: Parallel Constraint Satisfaction networks in R

Description

The PCS package contains all necessary functions for building and simulation Parallel Constraint Satisfaction (PCS) network models within R.

Details

PCS models are an increasingly used framework throughout psychology: They provide quantitative predictions in a variety of paradigms, ranging from word and letter recognition, for which they were originally developed (McClelland & Rumelhart, 1981; Rumelhart & McClelland, 1982), to complex judgments and decisions (Glöckner & Betsch, 2008; Glöckner, Hilbig, & Jekel, 2014), and many other applications besides.

Theoretical overview

PCS networks embody the concept of consistency maximization in perception and cognition, in that they assume that a cognitive system will attempt to achieve a coherent state, in which all available information is weighted to provide a maximally consistent representation of a given task. Their central qualitative prediction follows from this basic assumption, namely that the weights assigned to available information are reevaluated during the decision process. These coherence shifts are a unique prediction of PCS models, and have been found in multiple domains (c.f. Glöckner, Betsch, & Schindler, 2010; Holyoak & Simon, 1999, Simon & Holyoak, 2002).

PCS models are implemented as neural networks, though they do not assume a direct mapping from model nodes and connections onto neurons and dendrites. Instead, the nodes represent concepts, and the links between them the degree to which the concepts are compatible or reconcilable. The assumption is that a PCS network is instantiated whenever a decision maker faces a choice (Glöckner & Betsch, 2008).

At any given time, a node exhibits a certain level of activation, which it passes through any present links to other nodes. If the level is positive, the node is activated, otherwise it is labelled inhibited. Activation is passed between nodes along the links, to varying degrees depending on their strength and nature, which determines the spread of activation in the network. Links can be excitatory, in that an activated node on one side leads to an increasing activation of any connected node, or inhibitory, in which connected nodes assume the opposite activation level. Thus, nodes can be mutually supportive regarding their level of activation, or restrain one another. Besides this qualitative difference, links also differ in their weight, a number which denotes the proportion of activation that is passed along the link. A link's magnitude captures the connection weight, and its sign the qualitative type of influence (excitatory or inhibitory). Links are always bidirectional, in that both nodes reciprocally influence one another, in the same manner and to the same extent.

Within the network, processing occurs in discontinuous cycles, iterations. In each cycle anew, nodes pass a proportion of their activation level along the links to connected siblings. At each receiving node, the total arriving activation is termed the total input. Because the amount of activation passed through a link is multiplied by the link weight, the total input is a weighted sum of the activation of all connected nodes. The input does not, however, influence the node directly, but instead is subject to two additional influences: First, the activation of each node is reduced by a fixed proportion at each iteration, so that the activation level decays to a fixed neutral point. Second, the current activation level of the node determines the influence of the arriving input: A node that is already active is less susceptible to further excitatory input, and more so to external inhibition. The converse holds for an inhibited node: Excitatory input is amplified, and further inhibition dampened. These forces constrain the activation between a floor and ceiling value.

Together, these two forces determine the reaction of a node to input. In particular, from their joint activity a non-linear activation function emerges: The level of activation a node approches over many interations is an s-shaped function of the input for excitatory links, concave for positive and convex for negative input. For an inhibitory link, this relationship is inverted.

Activation initially enters a network through the source node, which provides a constant level of activation. As activation enters the network and is passed between nodes, the properties sketched above ensure that the relationships between the concepts represented will increasingly be satisfied, and after some time, the network reaches a stable state in which nodes connected by excitatory links will share broadly similar levels of activation, and those connected by inhibitory links dissimilar states. Thus, the constraints represented in the network will be increasingly satisfied (giving the model family its name), and the representation will become coherent.

When a network has converged into this state, behavioral predictions can be derived: The number of iterations that passed during processing is used as a proxy for decision time, of the nodes representing choice alternatives, the one with the highest activation is assumed to be the chosen one, and the difference between the activations of these nodes is used to predict the confidence with which a decision is made or a course of action taken.

Package contents

This package contains all necessary simulation code to build and run PCS models. In particular, it contains a full, optimized implementation of the core model as specified by McClelland and Rumelhart (1981) as well as Glöckner and Betsch (2008), as well as several variants commonly used in the literature so that existing findings may be replicated.

PCS_run is the central function provided by the package. It creates, and runs, a model of a PCS network given a connection matrix and the necessary parameters.

Please see the function-specific documentation for additional information

References

PCS

Glöckner, A., & Betsch, T. (2008). Modeling option and strategy choices with connectionist networks: Towards an integrative model of automatic and deliberate decision making. Judgment and Decision Making, 3(3), 215–228.

Glöckner, A., Betsch, T., & Schindler, N. (2010). Coherence shifts in probabilistic inference tasks. Journal of Behavioral Decision Making, 23(5), 439–462. doi:10.1002/bdm.668

Glöckner, A., Hilbig, B. E., & Jekel, M. (2014). What is adaptive about adaptive decision making? A parallel constraint satisfaction account. Cognition, 133(3), 641–666. doi:10.1016/j.cognition.2014.08.017

Holyoak, K. J., & Simon, D. (1999). Bidirectional reasoning in decision making by constraint satisfaction. Journal of Experimental Psychology: General, 128(1), 3–31.

McClelland, J. L., & Rumelhart, D. E. (1981). An interactive activation model of context effects in letter perception: I. An account of basic findings. Psychological Review, 88(5), 375–407.

Rumelhart, D. E., & McClelland, J. L. (1982). An interactive activation model of context effects in letter perception: II. The contextual enhancement effect and some tests and extensions of the model. Psychological Review, 89(1), 60–94.

Simon, D., & Holyoak, K. (2002). Structural dynamics of cognition: From consistency theories to constraint satisfaction. Personality and Social Psychology Review, 6(4), 283–294.