Advanced statistical modeling

Model clustered, nested, and repeated data without pretending observations are independent

Multilevel and mixed-effects models can represent dependence across students, schools, sites, people, teams, or repeated observations when the design and sample support them.

QuestionDesignDataModelDiagnosticsInterpretation

Start with the source of dependence

The first decision is not random intercept versus random slope. It is which observations share information, at what level, and how the research question crosses those levels.

  • Map units and levels
  • Distinguish nesting from crossing
  • Identify within- and between-unit questions

Specify variation the design can support

Random effects, time trends, covariance structures, and cross-level terms add meaning only when supported by the design and data. Singular fits and unstable variance estimates are evidence to investigate.

  • Compare defensible specifications
  • Check residual and influence patterns
  • Use sensitivity analysis for key choices

Interpret at the correct level

A within-person change is not automatically a between-person difference. Centering, coding, and interaction choices determine the meaning of coefficients and should be documented.

  • Coefficient interpretation map
  • Variance and uncertainty summary
  • Prediction or marginal-effect display
Start with the decision

Review my multilevel design

Bring the research question, design, or existing output. A first review can identify the next statistical decision and the information needed to scope it.