STATISTICAL METHOD
Linear Mixed Model Analysis
Statistical Consulting for Multilevel Data
We apply linear mixed model analysis within your design, specifying the random effects the data can support, choosing the estimation method for the question, and reporting fixed effects with 95% confidence intervals and variance components in publication-ready form.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is a Linear Mixed Model?
A linear mixed model, also called a multilevel model, analyzes a continuous outcome measured on grouped observations, such as repeated visits within patients or pupils within schools. Fixed effects give the average effects of predictors and time, while random effects describe how individuals or clusters depart from them in intercepts and, where the data allow, in slopes. Incomplete follow-up is handled when missingness depends only on observed information. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides linear mixed model analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is a Linear Mixed Model Appropriate?
A mixed model fits a continuous outcome with correlated observations, and these are the research situations in which researchers most often ask us to apply or confirm it.
Repeated Measures Over Time Participants are measured at several visits, possibly unevenly spaced or incomplete, and the question is how a continuous outcome changes over time or differs between groups.
Observations Nested in Clusters Pupils within schools, patients within clinics or staff within firms share a context, so their outcomes correlate and a single-level regression would misstate the standard errors.
Prespecified Analysis Plan A protocol names the longitudinal mixed model, such as a group-by-time interaction with random effects, and the covariance and estimation must be fixed before outcomes are seen.
Reviewing a Completed Analysis A mixed model has been run, perhaps with a singular fit warning, and a reviewer has questioned it. Independent Statistical Review re-examines the random-effects structure.
ANALYTICAL APPROACH
How We Apply the Linear Mixed Model
Within the family of Longitudinal & Multilevel Analysis, the model is specified only after the time structure, the clusters and the missing data have been examined.
Clusters and Level Structure We confirm the subject or cluster identifier and the level at which each predictor varies. With few clusters, variance estimates and degrees of freedom are fragile, and we say so.
Random-Effects Structure We start from the structure the design implies and simplify only as far as the data require. A singular fit or non-convergence often means the structure asks more than the data hold.
Within and Between Effects A time-varying predictor can act within persons and between them. We center it on the cluster mean, or use a Mundlak-type formulation, so the two effects are separated, not blended.
Estimation and Inference Variance components are estimated by REML, and models with different fixed effects are compared by ML. With few clusters, Kenward-Roger or Satterthwaite degrees of freedom apply.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the model is delivered with the estimates, checks and files needed to report and defend it.
Data & Variable Review Identifiers, time coding, observations per cluster, missing visits and the level of each predictor are reviewed, and duplicate subject-time rows are resolved before any model is fitted.
Method-Specific Checks Residual and random-effect plots, convergence and singular-fit messages are examined, and a simpler covariance structure is compared where the data cannot support the planned one.
Statistical Results Fixed-effect estimates with 95% confidence intervals, variance components and the intraclass correlation, with model comparisons made under the estimation method that suits each question.
Publication-Ready Tables & Figures Model tables and fitted-trajectory plots with confidence bands, formatted to APA 7, STROBE for cohort studies, CONSORT for trial reports or the journal's requirements, ready to insert.
Interpretation Effects are written with their uncertainty, within what the design supports, and the missing-at-random assumption and any sensitivity analysis for dropout are stated.
Reproducible Analysis Files R scripts using lme4 or nlme, Stata do-files, SAS or SPSS syntax are provided where applicable, so every estimate can be traced and rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
A linear mixed model suits a continuous outcome on repeated or nested data. These methods fit better for a non-normal outcome, many clusters with a marginal focus, latent change or complete balanced data.
01
Generalized Linear Mixed Models (GLMM)
When the outcome is binary, a count or another non-normal response, random effects are kept and a link function and a suitable distribution are added.
02
Generalized Estimating Equations (GEE)
For a continuous outcome both estimate the same average effects, but with many clusters GEE gives robust inference that does not rely on the covariance model.
03
Latent Growth Curve Modeling (LGM)
When the interest lies in latent intercepts and slopes, measurement error or growth linked to other latent variables, a structural equation framework fits better.
04
Repeated Measures ANOVA
With complete data on every participant, few occasions and a balanced design, repeated measures ANOVA can answer a simple within-subject question.
CASE EXAMPLE
How We Work in Practice
An illustration of how a repeated-measures question moves from a planned model to a reportable, defensible result.
ILLUSTRATIVE EXAMPLE · PEDIATRIC DEVELOPMENT RESEARCH · UNITED STATES
A pediatric developmental clinic followed children in an early language program and wanted to describe how a continuous language score changed across clinic visits, by program group.
The analysis plan named a linear mixed model with time, group and their interaction, a random intercept and a random slope for time. Visits were unevenly spaced and some children missed appointments, so dropping every child with a missed visit was ruled out. When fitted, the slope variance was close to zero and the fit was singular. Following the plan’s stated fallback, we dropped the random slope, compared residual covariance structures by AIC under REML, and tested the interaction with ML. We judged missing visits as plausibly missing at random, given earlier scores and age, and said so.
Outcome: The team received the group-by-time interaction with its 95% confidence interval, the variance components, a methods paragraph on the simplification, trajectory figures and the R scripts.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Mixed Models
Linear mixed models are run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Mixed Models Across Research Fields
Mixed effects regression appears wherever observations are repeated or nested, each field bringing its own clustering, time structure and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher who recognized the clustered structure of the data and needed a clear statement of what could be concluded.
“Our dataset looked straightforward until we got into Linear Mixed Models (Multilevel Modeling) and realized the clustered structure of the data rather than treating every row as independent. The team sorted out the analytical setup and gave us a clear explanation of what could and could not be concluded. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your mixed model, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your mixed model analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, the substantive meaning of the random effects, interpretation and conclusions remain with you, and our interpretation stays within what the design supports.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About the Linear Mixed Model
Short answers to what researchers ask before a mixed model analysis, from random effects and cluster numbers to confidentiality and the assessment process.
Do I need a random slope as well as a random intercept?
Not by default. A random slope is justified only when the effect of time or another predictor plausibly varies between clusters and the data can estimate that variance. Models that ask for more random effects than the data hold often return singular fits, so we start from the design, check convergence and the variance estimates, and simplify with the reasons recorded. Dropping a needed slope can make standard errors too small, so the choice is reported.
Should I use a mixed model or repeated measures ANOVA?
A mixed model is usually preferable when follow-up is incomplete, visits are unevenly timed, covariates change over time or there are several clustering levels, because it uses all observed data and models the covariance explicitly. Repeated measures ANOVA fits complete, balanced designs with few occasions. A mixed model is valid with missing data only when missingness depends on observed information, an assumption we state.
How many clusters do I need for a reliable mixed model?
There is no single threshold, but with fewer than roughly 30 clusters, variance estimates and standard errors can be unreliable, and random slopes or cross-level interactions need more. REML with Kenward-Roger or Satterthwaite degrees of freedom improves the inference, and with very few clusters, cluster fixed effects, or cluster-robust errors with a small-sample correction, may be more defensible.
Can you review an analysis that has already been completed?
Yes, we can review a completed mixed model before submission or a response to reviewers. We check the identifier and level structure, the random-effects specification and any singular or convergence warnings, the estimation method behind each comparison, the handling of missing data and how the effects were reported, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With a
Linear Mixed Model?
Share your research question, study design and data. We assess the clustering and time structure and confirm the modeling approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014