• Global, regional, and national liver cancer attributable to smoking and alcohol use burden, 1990-2021: analysis for the global burden of disease 2021 study
• Deep linear matrix approximate reconstruction with integrated BOLD signal denoising reveals reproducible hierarchical brain connectivity networks from multiband multi-echo fMRI
• Influence of apolipoprotein E genotype on the proteomic profile in cerebral microdialysis after human severe traumatic brain injury: a prospective observational study
• The Histological and Mechanical Behavior of Skin During Puncture for Different Impactor Sizes and Loading Rates
• Marital Stability During the Year After Traumatic Brain Injury in an Ecuadorian Sample: A Repeated-Measures Study
• Preoperative cognitive profile predictive of cognitive decline after subthalamic deep brain stimulation in Parkinson's disease
• The impact of mental health on health-related quality of life in patients with NF2-related Schwannomatosis
• Factors associated with mathematical capacity in children with Developmental Coordination Disorder

Hierarchical Linear Modeling (HLM), also known as multilevel modeling or mixed-effects modeling, is a statistical technique used to analyze data that is organized at more than one level. It is particularly useful for analyzing data with a nested structure, such as students within classrooms, patients within hospitals, or repeated measures within individuals.

• Hierarchical Data Structure:
  • Data is organized into levels. For example, in educational research:
    • Level 1: Individual students (within classrooms).
    • Level 2: Classrooms (within schools).
    • Level 3: Schools (within districts).
• Random Effects and Fixed Effects:
  • Fixed Effects: Parameters that are constant across all units (e.g., the effect of a treatment).
  • Random Effects: Parameters that vary across units or groups (e.g., differences between schools or classrooms).
• Modeling Variance:
  • HLM accounts for variance at each level of the hierarchy.
  • For example, in the student-classroom model, HLM estimates:
    • Variance among students within classrooms.
    • Variance among classrooms.
• Cross-level Interactions:
  • HLM allows for the examination of interactions between variables at different levels (e.g., how classroom-level characteristics influence the relationship between student-level predictors and outcomes).

• Level-1 Model:
  • Describes the relationships among variables within the lowest-level units (e.g., students).
  • Example: \\( Y_{ij} = \beta_{0j} + \beta_{1j}X_{ij} + e_{ij} \\)
    • \\( Y_{ij} \\): Outcome for individual \\( i \\) in group \\( j \\).
    • \\( \beta_{0j} \\): Intercept for group \\( j \\).
    • \\( \beta_{1j} \\): Slope for predictor \\( X \\).
    • \\( e_{ij} \\): Residual error for individual \\( i \\).
• Level-2 Model:
  • Models variation in Level-1 parameters across higher-level units (e.g., classrooms).
  • Example:
    • \\( \beta_{0j} = \gamma_{00} + \gamma_{01}W_j + u_{0j} \\)
    • \\( \beta_{1j} = \gamma_{10} + \gamma_{11}W_j + u_{1j} \\)
    • \\( W_j \\): Predictor at the group level (e.g., classroom characteristics).
• Combined Model:
  • Integrates Level-1 and Level-2 models into a single equation.

• Education:
  • Assessing how school-level policies influence student-level outcomes.
  • Analyzing teacher effects within schools.
• Healthcare:
  • Evaluating patient outcomes within hospitals or clinics.
  • Studying the effects of treatments across different patient populations.
• Psychology:
  • Examining repeated measures data (e.g., longitudinal studies).
• Sociology:
  • Understanding neighborhood effects on individual behavior.

• Accounts for nested data structures, avoiding biases in standard regression models.
• Handles unbalanced data (e.g., different numbers of students in classrooms).
• Estimates group-level and individual-level effects simultaneously.
• Allows for the examination of cross-level interactions.

• Specialized Software:
  • HLM software by SSI.
• General Statistical Software:
  • R (packages like lme4 and nlme).
  • Python (libraries like statsmodels).
  • SPSS (Mixed Models).
  • SAS (PROC MIXED).
  • Stata (Mixed Effects).

If you have a specific dataset or research question in mind, I can help with further guidance on implementing HLM. Let me know!