Multilevel Modelling in School Research

Data in school research are rarely independent. Students sit in classes, classes belong to schools, and teachers who answer a questionnaire about their principal are answering about the same person as their colleagues down the corridor. Multilevel modelling (also called hierarchical linear modelling, mixed-effects or random-coefficient modelling) is the family of regression models built for this structure. It lets you separate variation within schools from variation between schools, estimate how school-level conditions such as leadership or climate relate to teacher-level outcomes, and obtain standard errors that respect the fact that your observations come in clusters. In educational administration the method is now routine in studies using international datasets such as TALIS and PISA, and increasingly common in thesis work based on teacher surveys.

When to use it

Use a multilevel model when your observations are grouped and the grouping is part of the story. Typical cases in our field include teachers nested in schools (job satisfaction, self-efficacy, commitment), students nested in classes or schools (achievement, belonging), and repeated measurements nested in individuals.

The practical reason is statistical. Teachers in the same school share a principal, a staff room and a local context, so their answers tend to resemble one another. Ordinary regression treats each teacher as a fresh, independent piece of information. When that assumption fails, the standard errors are too small, confidence intervals are too narrow and too many effects look significant (Hox et al., 2018). The problem is worst for predictors measured at school level, because a sample of 600 teachers from 30 schools contains only 30 independent pieces of information about anything that varies between schools.

There is also a substantive reason: questions such as “do schools with stronger distributed leadership have more collaborative staff?” are school-level questions, and a multilevel model makes the level of each claim explicit.

Key concepts

Concept	What it means	Why it matters in a thesis
Level 1 / level 2	The lower unit (teacher, student) and the cluster it belongs to (school, class)	Every variable must be assigned to a level before modelling
ICC (intraclass correlation)	Share of total outcome variance lying between clusters, estimated from a model with no predictors	Tells you how much the clustering matters
Design effect	Factor by which clustering inflates sampling variance compared with a simple random sample	Shows how much your “effective” sample shrinks
Random intercept	School averages on the outcome are allowed to differ	The basic multilevel model
Random slope	The relationship between a level-1 predictor and the outcome is allowed to differ across schools	Needed before testing cross-level interactions
Centring	Re-expressing predictors as deviations from the grand mean or from each school’s mean	Changes what coefficients mean
rwg, ICC(1), ICC(2)	Indices of within-school agreement, non-independence and reliability of school means	Justify aggregating teacher perceptions to school level

The design effect for a two-stage sample is usually written as one plus the ICC multiplied by the average cluster size minus one (Hox et al., 2018). Suppose a thesis surveys 20 teachers in each of 30 schools and the ICC is .10. The design effect is 1 + (19 × .10) = 2.9, so the 600 responses carry roughly the information of 207 independent observations. Even a modest ICC therefore has large consequences when clusters are big.

Step by step

Map the levels before you collect data

Decide what each variable describes. Experience and self-efficacy are teacher characteristics (level 1); school size and location are school characteristics (level 2). Perceived leadership and climate are measured from teachers but often theorised as properties of the school. This decision shapes both your sampling plan and your model.

Fit the empty model and report the ICC

Start with a random-intercept model containing no predictors. From its two variance components (between-school and within-school) compute the ICC. A non-trivial ICC confirms that a multilevel model is warranted; a value near zero does not automatically license ordinary regression if your hypotheses concern school-level predictors, but it does tell you that schools explain little of the outcome.

Justify any aggregation of teacher perceptions

If you average teachers’ ratings of leadership or climate to create a school-level variable, you need evidence that the average represents something shared. Three indices are commonly reported. The rwg family (James et al., 1984) compares the observed variance of ratings within a school with the variance expected if teachers had answered at random; rwg(j) is the multi-item version. ICC(1) indicates how much of the variance in individual ratings is attributable to school membership. ICC(2) estimates the reliability of the school means, and it rises with the number of respondents per school (Bliese, 2000).

Cut-offs need care. A value of .70 for rwg is widely used, but O’Neill (2017) shows that it goes back to an informal recommendation rather than any formal derivation and warns against applying it mechanically. LeBreton and Senter (2008) instead propose graded bands: up to .30 indicating lack of agreement, .31 to .50 weak, .51 to .70 moderate, .71 to .90 strong and above .90 very strong. For ICC(2), values around .70 are often quoted as a benchmark, but this is a rule of thumb, and because ICC(2) depends on how many teachers answered in each school, a low value may simply reflect small groups. Shieh (2016) also points out that the usual ICC(2) estimator is only one of several possible indices of the reliability of group means and compares alternatives on bias and precision. Report the mean or median rwg across schools, the share of schools below your chosen value, and both ICCs, and say which null distribution you assumed for rwg.

Choose a centring strategy that matches the question

Enders and Tofighi (2007) show that centring is a substantive decision. Centring within cluster (subtracting each school’s mean) yields a pure within-school effect for a level-1 predictor and is preferred when you estimate random slopes or test cross-level interactions, since grand-mean centring can blend within- and between-school variation and produce misleading interactions. Grand-mean centring is better suited when the aim is the effect of a level-2 predictor after adjusting for level-1 covariates. If you want to know whether a predictor works differently within and between schools (a contextual effect), add the school means as a level-2 predictor alongside the level-1 variable and compare the within-school and between-school coefficients.

Add predictors and consider random slopes

Add level-1 predictors, then level-2 predictors, and compare models. A random slope asks whether, say, the link between collaboration and job satisfaction is stronger in some schools than in others. Only test cross-level interactions (for example, whether school climate moderates that link) when there is a theoretical reason, and remember that variance components for slopes are the parameters most demanding of level-2 sample size.

Plan the number of schools, not just the number of teachers

The number of clusters is usually the binding constraint. In Maas and Hox’s (2005) simulation, which compared 30, 50 and 100 groups, regression coefficients, variance components and the standard errors of the fixed effects were essentially unbiased, but the standard errors of the level-2 variances were underestimated when there were 50 or fewer groups. The problem was clearest with 30 groups, where these standard errors were roughly 15% too small. If school-level variances or random slopes are themselves of interest, their results argue for clearly more than 50 schools. With fewer clusters, restricted maximum likelihood (REML) combined with a Kenward-Roger correction to the degrees of freedom helps keep tests of fixed effects honest (McNeish, 2017).

This is where many theses run into trouble. A typical design collects 300 to 500 teacher questionnaires from 8 to 15 schools. Such data can support teacher-level analyses with the clustering properly handled, but they say very little about school-level effects, and random slope variances will be poorly estimated. Be candid about this in the limitations section, or redesign the sample to include more schools with fewer teachers in each.

Software

HLM, the program associated with Raudenbush and Bryk (2002) and distributed by Scientific Software International, is dedicated to hierarchical models. Mplus handles two-level models through TYPE = TWOLEVEL (with RANDOM for random slopes), offers grand-mean and group-mean options through CENTER in the DEFINE command, and, unless a covariate is declared as within-only, splits a level-1 covariate into latent within and between parts, which helps when school means are based on few teachers. In R, the lme4 package fits mixed models with lmer(), using REML by default (Bates et al., 2015); the lmerTest package adds Satterthwaite or Kenward-Roger degrees of freedom to the summary.

What to report

• The nesting structure: number of schools, number of teachers, and the range of teachers per school.
• The empty model’s variance components and ICC.
• For aggregated variables: rwg(j) summary, ICC(1), ICC(2), and the cut-offs you used with their sources.
• The centring choice for each predictor and the reason for it.
• Estimation method (ML or REML), software and version, and any small-sample correction.
• Fixed effects with standard errors or confidence intervals, variance components at each level, and the proportion of variance explained at each level.
• How model comparisons were made (deviance or information criteria) and how missing data were handled.

Common mistakes

• Running ordinary regression or SEM on teacher data from a handful of schools and reporting school-level conclusions.
• Averaging teacher perceptions to school level without reporting agreement or reliability.
• Treating the .70 rwg threshold as a pass mark rather than a convention with known weaknesses.
• Leaving centring unreported, so readers cannot tell what a coefficient means.
• Estimating random slopes and cross-level interactions with 10 to 20 schools.
• Calling an analysis “multilevel” when only a cluster-robust standard error was applied. That correction is defensible, but it is a different approach and should be named as such.

Examples from Turkish research

Turkish researchers have used multilevel models both with national TALIS samples and with locally collected teacher surveys. These studies are useful models for theses on distributed leadership, teacher collaboration and school climate, and more summaries appear in our research digests.

• Duyar, Gümüş and Bellibaş (2013) analysed TALIS data from 2,967 teachers in 178 Turkish lower secondary schools with two-level HLM, finding that aspects of principal leadership and, above all, teacher collaboration predicted teachers’ self-efficacy and job satisfaction (International Journal of Educational Management).
• Bellibaş, Karadağ and Gümüş (2021) surveyed 598 teachers in 50 schools in Adıyaman and Konya and used HLM to relate teacher agency and school characteristics to collective teacher efficacy (Başkent University Journal of Education).
• Özdemir, Kılınç, Polatcan, Turan and Bellibaş (2023) used Türkiye’s TALIS lower secondary data (3,223 teachers, 192 schools) in a multilevel latent profile analysis, showing that distributed leadership was linked to teacher collaboration, which in turn related to teachers’ instructional practice profiles (Educational Administration Quarterly).

Key takeaways

• Teachers in the same school are not independent observations; ignoring this shrinks standard errors and overstates school-level effects.
• Report the ICC and design effect first, then justify any school-level aggregation with rwg, ICC(1) and ICC(2), naming the source of each cut-off.
• Centring changes what coefficients mean: centre within schools for level-1 and cross-level effects, at the grand mean for level-2 effects adjusted for teacher covariates.
• The number of schools limits what you can claim; with few schools, focus on teacher-level questions and use REML with small-sample corrections.

References

• Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01
• Bellibaş, M. Ş., Karadağ, N., & Gümüş, S. (2021). Kolektif öğretmen yeterliği ile öğretmen failliği arasındaki ilişkinin incelenmesi: Hiyerarşik lineer modelleme (HLM) analizi [Examining the relationship between collective teacher efficacy and teacher agency: A hierarchical linear modelling (HLM) analysis]. Başkent University Journal of Education, 8(1), 160–168.
• Bliese, P. D. (2000). Within-group agreement, non-independence, and reliability: Implications for data aggregation and analysis. In K. J. Klein & S. W. J. Kozlowski (Eds.), Multilevel theory, research, and methods in organizations: Foundations, extensions, and new directions (pp. 349–381). Jossey-Bass.
• Duyar, I., Gumus, S., & Bellibas, M. S. (2013). Multilevel analysis of teacher work attitudes: The influence of principal leadership and teacher collaboration. International Journal of Educational Management, 27(7), 700–719. https://doi.org/10.1108/IJEM-09-2012-0107
• Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12(2), 121–138. https://doi.org/10.1037/1082-989X.12.2.121
• Hox, J. J., Moerbeek, M., & van de Schoot, R. (2018). Multilevel analysis: Techniques and applications (3rd ed.). Routledge.
• James, L. R., Demaree, R. G., & Wolf, G. (1984). Estimating within-group interrater reliability with and without response bias. Journal of Applied Psychology, 69(1), 85–98. https://doi.org/10.1037/0021-9010.69.1.85
• LeBreton, J. M., & Senter, J. L. (2008). Answers to 20 questions about interrater reliability and interrater agreement. Organizational Research Methods, 11(4), 815–852. https://doi.org/10.1177/1094428106296642
• Maas, C. J. M., & Hox, J. J. (2005). Sufficient sample sizes for multilevel modeling. Methodology, 1(3), 86–92. https://doi.org/10.1027/1614-2241.1.3.86
• McNeish, D. (2017). Small sample methods for multilevel modeling: A colloquial elucidation of REML and the Kenward-Roger correction. Multivariate Behavioral Research, 52(5), 661–670. https://doi.org/10.1080/00273171.2017.1344538
• O’Neill, T. A. (2017). An overview of interrater agreement on Likert scales for researchers and practitioners. Frontiers in Psychology, 8, Article 777. https://doi.org/10.3389/fpsyg.2017.00777
• Özdemir, N., Kılınç, A. Ç., Polatcan, M., Turan, S., & Bellibaş, M. Ş. (2023). Exploring teachers’ instructional practice profiles: Do distributed leadership and teacher collaboration make a difference? Educational Administration Quarterly, 59(2), 255–305. https://doi.org/10.1177/0013161X231159092
• Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Sage.
• Shieh, G. (2016). Choosing the best index for the average score intraclass correlation coefficient. Behavior Research Methods, 48(3), 994–1003. https://doi.org/10.3758/s13428-015-0623-y

Last reviewed: October 2026