YLL – Part 2 (Generalized Linear Mixed Model)

Generalized Linear Mixed Models (GLMMs) are a statistical modeling technique that combines elements of Generalized Linear Models (GLMs) and mixed effects models to:

1.  GLMMs are used to analyze data with non-normal distributions, correlations, or hierarchical structures.
2. They incorporate fixed effects for modeling relationships with predictors and random effects to account for unexplained variability, often found in clustered or repeated-measures data.
3. GLMMs are effective for data with nested or hierarchical structures, such as repeated measurements within individuals or groups.
4. Parameters are estimated using maximum likelihood or restricted maximum likelihood, providing a robust and flexible framework for statistical inference.
5. Like GLMs, GLMMs employ link functions to relate the response variable to the predictors and random effects, depending on the type of data being modeled.

Applications of Generalized Linear Mixed Models (GLMMs) in police fatal shootings:

1. GLMMs can be used to investigate whether there are demographic disparities in police fatal shootings, specifically focusing on factors such as race, gender, age, and socioeconomic status. This analysis can provide insights into potential biases in law enforcement actions.
2. They can be employed to examine temporal patterns in police fatal shootings, including the analysis of trends over time, seasonality, and day-of-week effects. Understanding temporal patterns can help identify periods of increased risk and inform law enforcement strategies.
3. Spatial GLMMs can be used to analyze the geographic distribution of police fatal shootings, identifying spatial clusters or areas with higher incident rates. This information can guide resource allocation and community policing efforts.
4. They can help identify and quantify risk factors and covariates associated with police fatal shootings. This may include factors such as the presence of weapons, mental health conditions, prior criminal history, and the characteristics of the officers involved.
5. They can be applied to evaluate the impact of policy changes and reforms within law enforcement agencies on the occurrence of fatal shootings. By comparing data before and after policy changes, it becomes possible to assess the effectiveness of new practices and procedures in reducing fatal incidents.