In mathematical or statistical modeling a threshold model is any model where a threshold value, or set of threshold values, is used to distinguish ranges of values where the behaviour predicted by the model varies in some important way. A particularly important instance arises in toxicology, where the model for the effect of a drug may be that there is zero effect for a dose below a critical or threshold value, while an effect of some significance exists above that value. Certain types of regression model may include threshold effects.
Threshold models are often used to model the behavior of groups, ranging from social insects to animal herds to human society.
Classic threshold models were introduced by Sakoda, in his 1949 dissertation and the Journal of Mathematical Sociology (JMS vol 1 #1, 1971).
They were subsequently developed by Schelling, Axelrod, and Granovetter to model collective behavior. Schelling used a special case of Sakoda's model to describe the dynamics of segregation motivated by individual interactions in America (JMS vol 1 #2, 1971) by constructing two simulation models. Schelling demonstrated that “there is no simple correspondence of individual incentive to collective results,” and that the dynamics of movement influenced patterns of segregation. In doing so Schelling highlighted the significance of “a general theory of ‘tipping’”.
Mark Granovetter, following Schelling, proposed the threshold model (Granovetter & Soong, 1983, 1986, 1988), which assumes that individuals’ behavior depends on the number of other individuals already engaging in that behavior (both Schelling and Granovetter classify their term of “threshold” as behavioral threshold.). He used the threshold model to explain the riot, residential segregation, and the spiral of silence. In the spirit of Granovetter's threshold model, the “threshold” is “the number or proportion of others who must make one decision before a given actor does so”.
It is necessary to emphasize the determinants of threshold. Different individuals have different thresholds.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Measures of surprise have been recently studied in statistics. This new concept can be used as the first exploratory tool to verify if a model under the null hypothesis fits appropriately. As no alter