Deviance

Deviance may refer to:

See also

Deviance (statistics)

In statistics, deviance is a quality of fit statistic for a model that is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.

Definition

The deviance for a model M₀, based on a dataset y, is defined as:

Here denotes the fitted values of the parameters in the model M₀, while denotes the fitted parameters for the "saturated model": both sets of fitted values are implicitly functions of the observations y. Here the saturated model is a model with a parameter for every observation so that the data are fitted exactly. This expression is simply −2 times the log-likelihood ratio of the reduced model compared to the full model. The deviance is used to compare two models – in particular in the case of generalized linear models where it has a similar role to residual variance from ANOVA in linear models (RSS).

Suppose in the framework of the GLM, we have two nested models, M₁ and M₂. In particular, suppose that M₁ contains the parameters in M₂, and k additional parameters. Then, under the null hypothesis that M₂ is the true model, the difference between the deviances for the two models follows an approximate chi-squared distribution with k-degrees of freedom.

Deviance (sociology)

In sociology, deviance describes an action or behavior that violates social norms, including a formally enacted rule (e.g., crime), as well as informal violations of social norms (e.g., rejecting folkways and mores). It is the purview of sociologists, psychologists, psychiatrists, and criminologists to study how these norms are created, how they change over time and how they are enforced.

Norms are rules and expectations by which members of society are conventionally guided. Deviance is an absence of conformity to these norms. Social norms differ from culture to culture. For example, a deviant act can be committed in one society that breaks a social norm there, but may be normal for another society.

Viewing deviance as a violation of social norms, sociologists have characterized it as "any thought, feeling, or action that members of a social group judge to be a violation of their values or rules "or group" conduct, that violates definitions of appropriate and inappropriate conduct shared by the members of a social system. The departure of certain types of behavior from the norms of a particular society at a particular time and "violation of certain types of group norms where behavior is in a disapproved direction and of sufficient degree to exceed the tolerance limit of the community.