4 Example Articles

4.1 Cross-sectional: clustered or hierarchical

Efficacy Study of Zearn Math in a Large Urban School District

Note: The schools chose where to implement the ‘treatment’ (n = 15) or not (n = 20).

Concept	Article Details
Terms	hierarchical linear modeling (HLM)
Samples	Level 2: schools (n = 35) Level 1: students (n = 8718)
Missing	none noted
Centering	none noted
Components	descriptives, HLM, followup subgroup analysis (seems link only random intercepts)
Results	No plots, only tables presenting the main effect (treatment) and excluding covariates and variance components, effect sizes looks like the are Cohen’s d?
Software	Stata

Parent couples’ participation in speech-language therapy for school-age children with autism spectrum disorder in the United States

Concept	Article Details
Terms	ICC, multilevel models
Samples	Level 2: child (n = 40) Level 1: parent, mother and father (n = 80)
Missing	Only a small proportion of missing data, so composite variables were imputed using the expectation–maximization (EM) algorithm
Centering	Binary variables were entered uncentered Continuous variables were grand mean centered
Components	Null for ICC, Random intercepts (no random slopes), residual diagnostics
Results	Table with 3 MLM models, discussed moderation
Software	HLM (Version 7.01) using restricted maximum likelihood

County-level social factors and schizophrenia: A multilevel study of 1.9 million Chinese adults

Concept	Article Details
Terms	multilevel logistic regression
Samples	Level 2: county (n = 734) Level 1: person (n = 1,909,205) Note: further nesting in 771,797 households, 2980 towns (streets) and 5964 communities (villages) from 31 province was not modeled
Missing	-not mentioned-
Centering	-not mentioned-
Components	ICC, adjusted odds ratios from GzLMM, subgroup analysis by gender
Results	Tables of un-adjusted and adjusted odds ratios
Software	Stata version 13.0 for Windows

One-to-one iPad echnology in the Middle School Mathematics and Science Classrooms

Concept	Article Details
Terms	hierarchical linear modeling (HLM)
Samples	Level 2: students (n = 112) Level 1: up to 6 observations across 2 years (n = 8718) Note: further nesting among 10 teachers in 3 schools was not modeled
Time	Unclear, but assume time is treated as 6 equally spaced intervals (t = numeric: 0, 1, 2, 3, 4, 5)
Missing	Students were not eliminated if they did not have six scores since HLM allows for missing data at the first level (i.e. complete case analysis)
Centering	grand mean centering for the MAP test scores
Components	Single-level OLS, Null model HLM, RIAS (random slope for time), add covars
Results	Table showing design, nested equations, several ‘final’ model tables of results
Software	SPSS

Examining the Links Between Received Network Support and Marital Quality Among Mothers of Children with ASD: A Longitudinal Mediation Analysis

Concept	Article Details
Terms	multilevel modeling (MLM), conditional growth model, longitudinal multiple mediation models
Samples	Level 2 = mother/child (n = 96) Level 1 = time point/age (n = 3 x 96 ? )
Time	Unclear, assume time is measured in years at study years 5, 7, and 9 (t = numeric age at each observation)
Missing	Assumed data was missing at random, so complete-case analysis
Centering	Time-varying predictors and mediators were disaggregated into their constituent within and between-person effects. To assess within-person effects, Level 1 predictors were created by person-mean centering each predictor or mediator (i.e., subtracting each mother’s cross-time mean score on a predictor from her actual score on that measure). Level 2 predictors were created by first computing a cross-time mean score on a predictor for each mother and then grand-mean centering that score. Finally, baseline child problem behavior severity was grand-mean centered with a mean of zero.
Components	Bivariate correlation matrix at baseline, Null for ICC, add fixed effects, mediation
Results	MLM only reported in text. All tables and figures apply to the mediation
Software	SPSS 25.0 with MLmed, a macro which tests for mediation and moderated mediation in multilevel data, Restricted maximum likelihood, 95% confidence intervals (CIs) based on Monte Carlo bootstrapping estimates

Disability multilevel modelling in first episodes of psychosis at 3-year follow-up

Concept	Article Details
Terms	multilevel modeling statistical approach to repeated measures data, growth model
Samples	Level 2: participants (n = 449) Level 1: observations = baseline, 1 year, and 3 years later (n = 3 x 449 = 1347)
Time	Very unclear, but it does include “linear time” in the results
Missing	Only patients providing data for all the study variables during follow-up, and those who were assessed from the beginning of the study to the 1-year and 3-year follow-up were finally analyzed.
Centering	-not mentioned-
Components	group comparisons with Cohen’s d effect sizes, and decrease in Bayesian Information Criterion adjusted to sample size (SABIC) used to assess significance when comparing models, RIAS: Random intercepts and slope of time, assumption checking
Results	Table comparing nested models
Software	Mplus 6.11

Concept	Article Details
Terms
Samples	Level 2: child (n = 40) Level 1: parent, mother and father (n = 80)
Missing
Centering
Components
Results
Software