Hierarchical models, also known as hierarchical linear models, are a type of statistical modeling technique used to analyze data that is structured in a hierarchical or nested format. These models are particularly useful for analyzing data that has multiple levels of nesting, such as data collected from multiple schools within multiple districts, or data collected from multiple employees within multiple departments within a company.

One common example of a hierarchical model is a multi-level model, which is used to analyze data that has multiple levels of nesting. For example, consider a study on student achievement in schools. The data for this study may be structured in a hierarchical format, with students nested within classrooms, classrooms nested within schools, and schools nested within districts. In this case, a multi-level model could be used to analyze the data and determine the effects of various factors (such as teacher quality or school resources) on student achievement.

Another example of a hierarchical model is a mixed effects model, which is used to analyze data that has both fixed and random effects. For example, consider a study on employee productivity in a company. The data for this study may be structured in a hierarchical format, with employees nested within departments, departments nested within divisions, and divisions nested within the overall company. In this case, a mixed effects model could be used to analyze the data and determine the effects of various factors (such as departmental policies or divisional strategies) on employee productivity.

Overall, hierarchical models are useful for analyzing complex data structures and accounting for the effects of nested factors on the outcome of interest. These models can help researchers better understand the relationships between different levels of data, and can provide valuable insights for making informed decisions and predictions.