Deviance

Definition

Deviance refers to the difference between observed values and expected values within a statistical model, often used to measure how well a model fits the data. It plays a key role in assessing model performance and is connected to likelihood functions and goodness-of-fit measures, which help in determining how accurately the model represents the underlying data-generating process.

5 Must Know Facts For Your Next Test

1. Deviance can be thought of as a generalization of the concept of residual sum of squares, used for models based on exponential family distributions.
2. In generalized linear models (GLMs), deviance is calculated as twice the difference between the log-likelihood of the saturated model and the log-likelihood of the fitted model.
3. A lower deviance value indicates a better fit of the model to the data, whereas a higher deviance suggests that the model does not explain the data well.
4. Deviance is often used in hypothesis testing to compare nested models, helping to determine if adding additional parameters significantly improves model fit.
5. In Poisson regression, deviance can help identify overdispersion in count data by comparing observed and expected frequencies.

Review Questions

• How does deviance relate to the assessment of model fit in statistical modeling?
  • Deviance is crucial for assessing model fit as it quantifies how well a statistical model captures the observed data compared to what is expected. It helps identify whether the chosen model adequately represents the data by comparing the log-likelihood of the fitted model against that of a perfect or saturated model. A lower deviance indicates a better fit, while higher values suggest that there might be inadequacies in the model structure or assumptions.
• In what ways can deviance be utilized in hypothesis testing for nested models?
  • Deviance serves as a tool for hypothesis testing by allowing comparison between nested models—one that includes additional parameters and one that does not. By calculating the difference in deviance between these models, researchers can determine if including additional predictors significantly improves model performance. This comparison is typically analyzed using a chi-squared test, where a significant difference suggests that the more complex model provides a better explanation of the data.
• Evaluate how understanding deviance can influence decisions when modeling count data with Poisson regression.
  • Understanding deviance is essential when modeling count data with Poisson regression because it provides insights into how well the model fits observed counts. If deviance indicates overdispersion, meaning that variability exceeds what Poisson distribution assumes, this knowledge prompts consideration of alternative models such as quasi-Poisson or negative binomial regression. Consequently, evaluating deviance not only aids in fitting an appropriate model but also ensures valid conclusions are drawn from data analysis, ultimately influencing decisions about modeling strategy.

Related terms

Likelihood: A measure of how well a statistical model explains observed data, often used in maximum likelihood estimation.

Residuals:

The differences between observed values and predicted values from a model, used to assess model fit.

Overdispersion:

A condition where the observed variance in data is greater than what the model predicts, often requiring adjustments in modeling techniques.