Mixed Effects Models

Overview

Mixed Effects Models (also known as Multilevel or Hierarchical Models) are used when data is grouped or clustered. They extend standard regression by including both Fixed Effects (the conventional population-level relationships) and Random Effects (subject-specific deviations).

These models are essential when: - Repeated Measures: The same subject is measured multiple times (longitudinal data). - Nested Structures: Students within schools, patients within hospitals, or plants within plots. - Correlated Errors: The assumption of independent errors is violated because observations within a group are more similar to each other.

Types of Models

  • MIXED_LINEAR_MODEL: Linear Mixed Effects (LME). The standard model for continuous normal outcomes. (y = X\beta + Z\gamma + \epsilon).
  • GLMM_BINOMIAL: Generalized Linear Mixed Model for binary data. Example: Modeling the probability of a student passing a test, accounting for school-level quality (random effect).
  • GLMM_POISSON: GLMM for count data. Example: Modeling patient seizure counts given drug treatment, accounting for patient-specific susceptibility.
  • GEE_MODEL: Generalized Estimating Equations. An alternative to GLMMs for longitudinal data (“population-averaged” models). GEEs are robust to misspecification of the correlation structure and are often used in medical trials.
Figure 1: Fixed vs Random Effects: Fixed effects (dashed line) estimate the global trend. Random intercepts allow each group (colors) to have its own baseline, capturing the clustered nature of the data.

Native Excel Capabilities

Excel is incapable of performing Mixed Effects modeling natively: - No Functions: Functions like LINEST typically ignore grouping or treat groups as fixed dummy variables (which consumes degrees of freedom and cannot generalize to new groups). - Impossible for GEE/GLMM: Estimating non-normal mixed models requires complex numerical integration (e.g., adaptive quadrature) which is impossible to implement in standard Excel formulas. - Analysis Pattern: Users currently ignore clustering (leading to Type I errors/false positives) or aggregate data to the group level (losing information).

The functions in this section bring powerful statsmodels mixed-effects capabilities directly to Excel users, enabling correct analysis of hierarchical and longitudinal datasets.

Tools

Tool Description
GEE_MODEL Fits a Generalized Estimating Equations (GEE) model for correlated data.
GLMM_BINOMIAL Fits a Generalized Linear Mixed Model (GLMM) with binomial family for binary clustered data.
GLMM_POISSON Fits a Generalized Linear Mixed Model (GLMM) with Poisson family for count clustered data.
MIXED_LINEAR_MODEL Fits a Linear Mixed Effects Model (LMM) with random intercepts and slopes.