Interpreting Fixed Effects and Random Effects in Mixed Models

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-22

Key Takeaways

• Fixed effects estimate population-level relationships (e.g., treatment efficacy averaged across all subjects), while random effects model structured variation from clustering (e.g., inter-subject variability in baseline gene expression).
• The Intraclass Correlation Coefficient (ICC) quantifies the proportion of total variance attributable to grouping factors (e.g., between-patient variation in drug response), guiding the necessity of mixed models over simpler analyses like ANOVA.
• Interpretation requires assessing model convergence and variance component estimates; a singular fit (zero variance for a random effect) or negative variance components indicate model misspecification or data issues, potentially requiring simplification of the random structure.
• Random intercepts account for baseline differences between groups (e.g., varying basal metabolic rates across animal litters), while random slopes capture heterogeneity in predictor effects across groups (e.g., differing dose-response curves for a therapeutic agent in distinct patient cohorts).
• Residual diagnostics (normality, homoscedasticity) and random effect diagnostics (normality of random effects) are crucial for validating model assumptions, analogous to checking for normality of residuals in linear regression or assessing the distribution of viral loads in infected populations.
• A structured decision framework, involving questions about the exhaustiveness of predictor levels and scientific interest, aids in correctly classifying predictors as fixed or random, preventing misinterpretations of treatment effects or biological variability.

Quick Answer

• Fixed effects estimate population-level relationships between predictors and the response, while random effects model structured variation from clustering variables like subject, batch, or site.
• Use the intraclass correlation coefficient (ICC) to quantify how much of the total variance is attributable to random grouping factors, guiding whether a mixed model is necessary.
• Interpretation requires checking model convergence, variance component estimates, and residual diagnostics, a singular fit or zero variance indicates the random structure may be misspecified.

At a Glance

The Core Distinction Between Fixed and Random Effects

Mixed-effects models, also called hierarchical or multilevel models, partition the total variation in a response variable into components attributable to fixed effects and random effects. The fixed effects are the population-level parameters that describe the average relationship between predictors and the response. Random effects describe how individual groups, such as subjects, experimental batches, or sampling sites, deviate from that population average.

A fixed effect is a predictor whose levels are of direct interest and are assumed to be reproducible. For example, a researcher comparing three drug doses treats dose as a fixed effect because the specific doses are the focus of inference. The estimated coefficient for each dose level represents the mean difference in the response relative to a reference level, averaged across all groups in the study.

A random effect is a predictor whose levels are a sample from a larger population of possible levels. The goal is not to estimate the effect of each specific level but to estimate the variance among levels. For example, if a study uses 10 mice per treatment group, the mice are a random sample from a larger population of mice. The random effect for mouse accounts for the fact that observations from the same mouse are correlated.

The distinction matters for inference. Fixed effects are estimated with standard errors that reflect sampling uncertainty. Random effects are summarized by variance components, which describe how much of the total variation is associated with the grouping structure. The variance components are the basis for calculating the intraclass correlation coefficient (ICC), which is the proportion of total variance explained by the grouping factor.

Why Biologists Need Mixed Models

Biological data frequently have a hierarchical or clustered structure. Observations are not independent because they come from the same subject, the same experimental batch, the same field plot, or the same laboratory session. Ignoring this clustering can lead to incorrect standard errors and inflated false-positive rates.

Consider a study measuring gene expression in tissue samples from multiple patients. Samples from the same patient are more similar to each other than to samples from different patients. A model that treats all samples as independent ignores this correlation. A mixed model with patient as a random effect accounts for the within-patient correlation and produces valid inference for the fixed effects.

Mixed models also allow researchers to estimate the magnitude of between-group variation. This is often of scientific interest in its own right. For example, a plant biologist might want to know how much of the variation in yield is due to differences between fields versus differences within fields. The variance components from a mixed model provide this decomposition.

The National Library of Medicine hosts authoritative biomedical texts that describe the rationale for mixed models in research settings. These resources emphasize that the choice of model must reflect the design of the study and the source of correlation in the data.

The Mathematical Structure of a Mixed Model

A linear mixed model can be written in matrix notation as:

y = Xβ + Zb + ε

where y is the vector of responses, X is the design matrix for fixed effects, β is the vector of fixed-effect coefficients, Z is the design matrix for random effects, b is the vector of random-effect deviations, and ε is the vector of residual errors.

The random effects b are assumed to follow a normal distribution with mean zero and variance-covariance matrix G. The residuals ε are assumed to follow a normal distribution with mean zero and variance-covariance matrix R. The total variance of the response is the sum of the variance contributions from the random effects and the residuals.

The variance-covariance matrix of the response is V = ZGZ' + R. This structure allows the model to account for correlation among observations within the same group. Observations from the same group share the same random-effect deviation, which induces positive correlation.

Variance Components

The variance components are the parameters that describe the magnitude of the random effects. For a model with a single random intercept, the variance components are the between-group variance and the within-group variance. The between-group variance is the variance of the random intercepts. The within-group variance is the residual variance.

The ICC is the ratio of the between-group variance to the total variance:

ICC = σ²_between / (σ²_between + σ²_within)

The ICC ranges from 0 to 1. An ICC of 0 indicates that there is no between-group variation and all observations are independent. An ICC of 1 indicates that all observations within a group are identical and all variation is between groups.

Random Intercepts and Random Slopes

A random intercept model allows each group to have its own intercept. The fixed-effect intercept is the average intercept across all groups. The random intercept variance describes how much the group-specific intercepts vary around this average.

A random slope model allows each group to have its own slope for a predictor. The fixed-effect slope is the average slope across all groups. The random slope variance describes how much the group-specific slopes vary around this average.

Models can include both random intercepts and random slopes. The random intercept and random slope can be correlated. The correlation between the random intercept and random slope describes whether groups with higher intercepts tend to have steeper or shallower slopes.

Interpreting Fixed Effect Coefficients

The fixed-effect coefficients are the primary output for testing hypotheses about predictors. Each coefficient represents the expected change in the response for a one-unit change in the predictor, holding all other predictors constant.

For a continuous predictor, the coefficient is the slope of the relationship between the predictor and the response. For a categorical predictor, the coefficient for each level is the difference between that level and the reference level.

The standard error of the coefficient reflects the uncertainty in the estimate. The standard error accounts for the clustering structure through the variance-covariance matrix V. The degrees of freedom for the test statistic are not always straightforward in mixed models, and different software packages use different approximations.

Confidence Intervals

The confidence interval for a fixed effect coefficient is the estimate plus or minus a multiple of the standard error. The multiple is based on the t-distribution with the appropriate degrees of freedom. The confidence interval provides a range of plausible values for the true coefficient.

A confidence interval that does not include zero indicates that the effect is statistically significant at the chosen level. The width of the confidence interval reflects the precision of the estimate. Larger sample sizes and more balanced designs produce narrower confidence intervals.

Effect Size

The coefficient alone does not indicate the practical importance of an effect. The effect size should be interpreted in the context of the measurement scale and the biological relevance. A small coefficient may be important if the response variable has a small range, and a large coefficient may be unimportant if the response variable has a large range.

Standardized coefficients can be used to compare the relative importance of predictors measured on different scales. Standardization involves dividing the coefficient by the standard deviation of the response or the predictor.

Interpreting Random Effect Variance

The random effect variance components are the key output for understanding the clustering structure of the data. The variance of the random intercept describes the between-group variability. A large variance relative to the residual variance indicates that groups differ substantially.

The variance components are estimated using restricted maximum likelihood (REML) or maximum likelihood (ML). REML is preferred for estimating variance components because it accounts for the loss of degrees of freedom from estimating the fixed effects.

The Intraclass Correlation Coefficient

The ICC is the most direct summary of the random effect variance. It describes the proportion of total variance that is due to between-group differences. The ICC is also the correlation between two observations from the same group.

An ICC of 0.05 means that 5 percent of the total variance is between groups. An ICC of 0.30 means that 30 percent of the total variance is between groups. The ICC is used to justify the use of a mixed model and to interpret the magnitude of the clustering effect.

Variance of Random Slopes

The variance of a random slope describes how much the effect of a predictor varies across groups. A variance of zero means that the effect is the same in all groups. A large variance means that the effect differs substantially across groups.

The variance of the random slope is often of direct scientific interest. For example, a researcher might want to know whether the effect of a drug varies across patients. The random slope variance provides this information.

Practical Workflow for Fitting a Mixed Model

The workflow for fitting a mixed model involves several steps. Each step requires a decision that affects the interpretation of the results.

Step 1: Define the Research Question

The research question determines which predictors are fixed and which are random. The fixed effects are the predictors of interest. The random effects are the grouping factors that induce correlation in the data.

The research question should specify whether the interest is in the average effect of a predictor or in the variation of the effect across groups. This distinction determines whether a random intercept or a random slope is needed.

Step 2: Specify the Model

The model specification includes the fixed effects, the random effects, and the residual structure. The fixed effects are specified as a linear combination of predictors. The random effects are specified by the grouping factors and the structure of the random terms.

The model should include all predictors that are scientifically relevant. The random effects should include all grouping factors that induce correlation. The model should be as simple as possible while still capturing the structure of the data.

Step 3: Fit the Model

The model is fit using a statistical software package. The fitting algorithm estimates the fixed effects and the variance components. The algorithm iterates between estimating the fixed effects and the variance components until convergence.

The convergence of the algorithm should be checked. A model that does not converge may have a poorly specified structure or a problem with the data.

Step 4: Check the Model

The model should be checked for violations of the assumptions. The residuals should be examined for normality and homoscedasticity. The random effects should be examined for normality.

The model fit should be compared to alternative models. The comparison can be based on the likelihood ratio test or the Akaike information criterion (AIC).

Step 5: Interpret the Results

The fixed effects are interpreted as the population-level effects. The random effects are interpreted as the variance components. The ICC is calculated from the variance components.

The results should be reported with the estimates, the standard errors, and the confidence intervals. The variance components should be reported with their estimates and the ICC.

Options and Tradeoffs in Model Specification

The choice of the random effect structure is a critical decision. The model can include random intercepts, random slopes, or both. The model can also include multiple random grouping factors.

Random Intercept Only

The simplest random effect structure is a random intercept for each group. This model assumes that the effect of the predictor is the same in all groups and that the groups differ only in their baseline level.

The random intercept model is appropriate when the scientific question is about the average effect of the predictor and the grouping is a nuisance factor. The model is simple and easy to interpret.

Random Intercept and Random Slope

The random intercept and random slope model allows the effect of the predictor to vary across groups. The model estimates the variance of the intercepts, the variance of the slopes, and the correlation between the intercepts and the slopes.

The random slope model is appropriate when the scientific question is about the variation of the effect across groups. The model is more complex and requires more data to estimate the additional variance components.

Nested Random Effects

Nested random effects occur when one grouping factor is nested within another. For example, animals are nested within litters, and litters are nested within treatments. The nested structure is specified in the model.

The nested structure is important for the correct estimation of the variance components. The variance of the nested factor is the variance within the higher-level factor.

Crossed Random Effects

Crossed random effects occur when two grouping factors are not nested. For example, a study might have subjects and items, and each subject is measured on each item. The crossed structure is specified in the model.

The crossed random effects are important for the correct estimation of the variance components. The variance of each factor is estimated separately.

Observations and Measurements for Model Validation

The validation of a mixed model requires the examination of the residuals and the random effects. The residuals are the differences between the observed and the predicted values. The random effects are the estimated deviations for each group.

Residual Diagnostics

The residuals should be examined for the normality and the homoscedasticity. The residuals should be plotted against the fitted values. The residuals should be plotted against each predictor.

A pattern in the residuals indicates a problem with the model. The pattern could be a nonlinear relationship, a heteroscedasticity, or an outlier.

Random Effect Diagnostics

The random effects should be examined for the normality. The random effects should be plotted as a histogram or a quantile-quantile plot. The random effects should be checked for the outliers.

A group with an extreme random effect may be an outlier. The group may have a different relationship than the other groups.

Model Comparison

The model should be compared to the alternative models. The comparison can be based on the likelihood ratio test or the AIC. The likelihood ratio test compares the fit of the nested models. The AIC compares the fit of the non-nested models.

The model with the lower AIC is preferred. The likelihood ratio test is used to test the significance of the random effects.

Records and Documentation

The documentation of the model is important for the reproducibility of the analysis. The documentation should include the data, the model specification, the fitting algorithm, and the results.

Data Records

The data should be documented with the variables, the units, and the structure. The data should be stored in a format that can be read by the software.

Model Records

The model specification should be documented with the fixed effects, the random effects, and the residual structure. The fitting algorithm should be documented with the software and the version.

Results Records

The results should be documented with the estimates, the standard errors, and the confidence intervals. The variance components should be documented with the ICC.

The National Institutes of Health data management and sharing policy requires that the data and the analysis be documented for the reproducibility of the research. The documentation should be sufficient for another researcher to reproduce the analysis.

Common Failure Patterns in Mixed Model Interpretation

Several common problems can arise in the interpretation of mixed models. These problems can lead to incorrect conclusions.

Singular Fit

A singular fit occurs when the estimated variance of a random effect is zero or the correlation between the random effects is estimated to be one. The singular fit indicates that the random effect structure is too complex for the data.

The singular fit can be addressed by simplifying the random effect structure. The random slope can be removed, or the correlation between the random intercept and the random slope can be removed.

Non-Convergence

Non-convergence occurs when the fitting algorithm fails to find a stable solution. The non-convergence can be caused by a complex model, a small sample size, or a poorly scaled variable.

The non-convergence can be addressed by simplifying the model, increasing the number of iterations, or rescaling the variables.

Overfitting

Overfitting occurs when the model is too complex for the data. The overfitting can lead to the unstable estimates and the poor prediction.

The overfitting can be addressed by simplifying the model or by using a regularization method.

Misinterpretation of the ICC

The ICC is often misinterpreted as the proportion of the variance explained by the random effect. The ICC is the proportion of the variance that is due to the between-group differences. The ICC does not indicate the proportion of the variance explained by the fixed effects.

The variance explained by the fixed effects is the reduction in the residual variance when the fixed effects are added to the model.

Quality Controls and Reproducibility

The quality of the mixed model analysis depends on the quality of the data and the model specification. The quality controls should be in place to ensure the validity of the results.

Data Quality

The data should be checked for the missing values, the outliers, and the errors. The data should be checked for the consistency of the variables.

Model Quality

The model should be checked for the convergence and the fit. The model should be checked for the assumptions of the residuals and the random effects.

Reproducibility

The analysis should be reproducible. The data and the code should be shared. The software and the version should be documented.

The Committee on Publication Ethics core practices require that the data and the analysis be reported transparently. The reporting should include the details of the model specification and the fitting.

Reporting the Results of a Mixed Model

The reporting of the mixed model results should follow the reporting guidelines. The EQUATOR Network provides the reporting guidelines for the research studies.

The Reporting of the Fixed Effects

The fixed effects should be reported with the estimates, the standard errors, and the confidence intervals. The p-values should be reported for the tests of the fixed effects.

The Reporting of the Random Effects

The random effects should be reported with the variance components and the ICC. The variance components should be reported with the uncertainty.

The Reporting of the Model

The model should be reported with the specification, the fitting algorithm, and the diagnostics. The model should be reported with the software and the version.

Limitations of Mixed Models

The mixed models have the limitations that should be considered in the interpretation.

The Assumption of the Normality

The mixed model assumes the normality of the random effects and the residuals. The normality assumption can be violated in the data. The violation can be addressed by the transformation of the response.

The Assumption of the Linearity

The mixed model assumes the linearity of the relationship between the predictors and the response. The linearity can be violated in the data. The violation can be addressed by the inclusion of the nonlinear terms.

The Assumption of the Independence

The mixed model assumes the independence of the observations within the groups. The independence can be violated in the data. The violation can be addressed by the inclusion of the autocorrelation structure.

The Sample Size

The mixed model requires the sufficient sample size for the estimation of the variance components. The small sample size can lead to the unstable estimates.

Safety and Regulatory Context

The use of the mixed models in the research is the subject to the regulatory requirements. The research should be conducted in the accordance with the ethical and the regulatory standards.

The National Institutes of Health provides the funding for the research. The research should be conducted in the accordance with the NIH policies.

The ORCID provides the researcher identity. The researcher should be identified with the ORCID.

A Decision Framework for Choosing Between Fixed and Random Effects

The distinction between fixed and random effects is not always clear from statistical theory alone. In practice, biologists must make this choice for every predictor in their model, and the decision has direct consequences for the scope of inference, the standard errors, and the conclusions that can be drawn. This section provides a structured decision framework that can be applied before fitting a model, along with a record system for documenting the decisions and a troubleshooting method for when the model output contradicts the intended interpretation.

The Four-Question Screening Test

Before assigning any predictor to a fixed or random effect category, work through four questions. The answers determine the appropriate classification and prevent the common error of treating a random effect as fixed or vice versa.

Question 1: Are the levels of the predictor the complete set of interest?

If the levels in the study are the only levels you want to make inferences about, the predictor is fixed. For example, a study comparing three specific fertilizer formulations has a fixed effect for fertilizer because the conclusions apply only to those three formulations. If the levels are a sample from a larger population, the predictor is random. For example, a study using 20 field sites selected from a region has a random effect for site because the conclusions should generalize to the region, beyond the 20 sites.

Question 2: Would the study be repeated with the same levels?

If you would use the same levels in a replication of the study, the predictor is fixed. If you would draw a new sample of levels, the predictor is random. A study of four specific temperatures would use the same four temperatures in a replication, so temperature is fixed. A study of 15 patients would draw a new sample of patients in a replication, so patient is random.

Question 3: Is the predictor a nuisance factor or a factor of scientific interest?

If the predictor is a source of variation that must be accounted for but is not the focus of the research question, it is a candidate for a random effect. If the predictor is the focus of the research question, it is fixed. For example, in a study of a drug effect, the drug is fixed and the subject is random. The subject is a nuisance factor because the interest is in the drug effect, not in the specific subjects.

Question 4: How many levels does the predictor have?

The number of levels affects the reliability of the variance component estimate. A random effect with fewer than five levels produces an unstable variance estimate. The National Library of Medicine hosts research-method references that discuss the minimum number of levels for reliable variance estimation. In practice, a random effect with fewer than five levels should be treated as fixed or the variance estimate should be interpreted with caution.

Applying the Framework

The framework produces one of three classifications for each predictor.

Fixed classification. The predictor is fixed when the levels are exhaustive, the study would be repeated with the same levels, the predictor is of scientific interest, and the number of levels is small and complete. The model estimates a coefficient for each level.

Random classification. The predictor is random when the levels are a sample, the study would be repeated with new levels, the predictor is a nuisance factor, and the number of levels is sufficient for variance estimation. The model estimates a variance component.

Borderline classification. The predictor is borderline when the levels are a sample but the number of levels is small, or when the predictor is of scientific interest but the levels are a sample. In the borderline case, the decision depends on the research question. If the interest is in the average effect across a population of levels, the predictor is random. If the interest is in the specific levels, the predictor is fixed.

A Record System for Model Decisions

The decisions made in the framework should be recorded before the model is fit. The record provides a reference for the interpretation of the results and for the reproducibility of the analysis. The record should include the following fields for each predictor.

Predictor name. The name of the predictor as it appears in the data.

Classification. The classification as fixed, random, or borderline.

Rationale. The answers to the four questions and the reason for the classification.

Number of levels. The number of levels in the data.

Levels complete or sample. Whether the levels are the complete set of interest or a sample from a larger population.

Scientific interest. Whether the predictor is of scientific interest or a nuisance factor.

Date of decision. The date the decision was made.

The record is stored with the data and the model code. The record is used when the model is reviewed or when the results are reported. The record is also used when the model is revised, because the revision should be based on the record and not on the results of the model.

The Troubleshooting Method

The troubleshooting method is used when the model produces a result that is inconsistent with the intended structure. The method is a sequence of checks that identify the source of the problem.

Check 1: The variance component is zero.

A zero variance component for a random effect indicates that the groups do not differ in the response. The random effect is not needed in the model. The predictor should be removed from the random structure and included as a fixed effect if it is of scientific interest, or removed from the model if it is a nuisance factor.

Check 2: The variance component is negative.

A negative variance component is not possible in a valid model. The negative estimate indicates a problem with the model specification or the data. The model should be checked for the correct specification of the random effects and for the presence of outliers.

Check 3: The ICC is zero.

An ICC of zero indicates that the grouping factor does not contribute to the total variance. The observations are independent with respect to the grouping factor. The random effect is not needed in the model.

Check 4: The ICC is one.

An ICC of one indicates that all observations within a group are identical. The residual variance is zero. This is a sign of a problem in the data, such as a single observation per group or a constant response within each group.

Check 5: The random slope variance is zero.

A zero variance of the random slope indicates that the effect of the predictor does not vary across groups. The random slope is removed from the model and the predictor is included as a fixed effect only.

Check 6: The random intercept and random slope are perfectly correlated.

A correlation of one between the random intercept and the random slope indicates that the model is overparameterized. The correlation is removed from the model and the random intercept and the random slope are estimated independently.

The Decision Log

The decision log is a record of the troubleshooting process. The log is used to document the problems that were identified and the actions that were taken. The log is stored with the model records and is used in the reporting of the results.

The log has the following fields.

Date. The date of the check.

Model version. The version of the model that was checked.

Check performed. The check that was performed.

Result. The result of the check.

Action taken. The action that was taken in response to the result.

Model version after action. The version of the model after the action was taken.

The log is a record of the model development. The log is used to demonstrate the transparency of the analysis and to support the reproducibility of the results.

The Reporting of the Decisions

The decisions made in the framework and the troubleshooting method are reported in the methods section of the paper. The report includes the classification of each predictor, the rationale for the classification, and the checks that were performed. The report is written in the following format.

The predictor was classified as a fixed effect because the levels were the complete set of interest and the study would be repeated with the same levels. The predictor was classified as a random effect because the levels were a sample from a larger population and the interest was in the variation across the levels.

The report also includes the results of the checks. The report states that the model converged, that the variance components were positive, and that the ICC was within the expected range.

The EQUATOR Network provides the reporting guidelines for the research studies. The guidelines require the transparent reporting of the model specification and the decisions. The report of the decisions is part of the transparent reporting.

The Limitations of the Framework

The framework is a decision aid, not a rule. The classification of a predictor as fixed or random depends on the research question and the design of the study. The framework does not replace the judgment of the researcher.

The framework is limited by the information that is available at the time of the decision. The researcher may not know whether the levels are a sample from a larger population or whether the study would be repeated with the same levels. The researcher should document the uncertainty in the record.

The framework is also limited by the statistical properties of the model. The variance components are estimated with uncertainty, and the uncertainty is larger for the small number of groups. The researcher should report the uncertainty in the variance components.

The National Institutes of Health provides the funding for the research. The research should be conducted in the accordance with the NIH policies. The policies require the transparent reporting of the methods and the results.

The Practical Use of the Framework

The framework is used in the following steps.

Step 1. List all predictors in the model.

Step 2. Apply the four questions to each predictor.

Step 3. Record the classification and the rationale in the record.

Step 4. Fit the model with the specified structure.

Step 5. Check the model for the convergence and the variance components.

Step 6. If the model is not valid, use the troubleshooting method to identify the problem.

Step 7. Record the problem and the action in the log.

Step 8. Report the decisions and the results in the paper.

The framework is applied before the model is fit. The framework prevents the common error of the treating a random effect as a fixed effect and the treating a fixed effect as a random effect. The framework also prevents the common error of the including a random effect with the insufficient number of groups.

The framework is a practical tool for the biologist. The framework is used in the design of the study and in the analysis of the data. The framework is used in the reporting of the results and in the review of the model.

The ORCID provides the researcher identity. The researcher is identified with the ORCID in the publication. The ORCID is used to link the researcher to the data and the code.

The Comparison of the Framework to the Alternative Approaches

The framework is compared to the alternative approaches for the classification of the predictors. The alternative approaches include the use of the design of the study, the use of the number of levels, and the use of the statistical tests.

The design of the study is the primary basis for the classification. The framework uses the design of the study in the four questions. The framework is a formalization of the design-based approach.

The number of levels is a secondary basis for the classification. The framework uses the number of levels in the fourth question. The framework does not use the number of levels as the sole basis for the classification.

The statistical test is not a basis for the classification. The statistical test is used after the model is fit to test the significance of the variance components. The framework does not use the statistical test for the classification.

The framework is a structured approach that is based on the design of the study. The framework is a practical tool for the biologist. The framework is used in the design of the study and in the analysis of the data.

The framework is a decision aid that is used in the context of the research question. The framework is not a substitute for the judgment of the researcher. The framework is a tool that is used to make the decision explicit and to document the decision for the reproducibility of the analysis.

The National Library of Medicine hosts the research methods references that describe the design-based approach to the classification of the effects. The references are used for the further reading on the topic.

The framework is a practical tool for the biologist. The framework is used in the design of the study and in the analysis of the data. The framework is used in the reporting of the results and in the reproducibility of the research.

Frequently Asked Questions

What is the difference between a fixed effect and a random effect?

A fixed effect is a predictor whose levels are of direct interest and are assumed to be reproducible. A random effect is a predictor whose levels are a sample from a larger population. The fixed effect is estimated with the coefficient, and the random effect is estimated with the variance.

How do I decide whether a predictor should be fixed or random?

The decision is based on the research question. If the interest is in the specific levels of the predictor, the predictor is fixed. If the interest is in the variation across the levels, the predictor is random.

What is the intraclass correlation coefficient?

The intraclass correlation coefficient (ICC) is the proportion of the total variance that is due to the between-group differences. The ICC is the correlation between the two observations from the same group.

How do I interpret the variance of the random intercept?

The variance of the random intercept is the between-group variance. A large variance means that the groups differ substantially in the intercept.

How do I interpret the variance of the random slope?

The variance of the random slope is the variance in the effect of the predictor across the groups. A large variance means that the effect of the predictor varies substantially across the groups.

What is a singular fit?

A singular fit is a model with the zero variance of the random effect or the perfect correlation between the random effects. The singular fit means the random effect structure is too complex for the data.

How do I report the results of a mixed model?

The results should be reported with the fixed effects, the random effects, and the model. The fixed effects should be reported with the estimates, the standard errors, and the confidence intervals. The random effects should be reported with the variance components and the ICC.

What are the limitations of a mixed model?

The limitations include the assumption of the normality, the linearity, and the independence. The limitations also include the sample size requirements. The limitations should be considered in the interpretation.

Using the Evidence

Related Bioinformatics Guides

• Foundation Models in Genetics: Opportunities and Challenges
• How to Interpret Gene Set Enrichment Analysis Results
• Benchmarking Machine Learning Models in Bioinformatics: Best Practices and Pitfalls
• Foundation Models for Genomics: From Single Cells to Health Trajectories
• Medical Image Segmentation Models: A Comparative Guide for Clinical Deployment

Related Clinical & Scientific Guides

• A Practical Guide to Detecting Antimicrobial Resistance Genes in Shotgun Metagenomic Data
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References and Further Reading

• Research Methods Resources. National Library of Medicine.
• EQUATOR Network. EQUATOR Network.
• Core Practices. Committee on Publication Ethics.
• NIH Grants and Funding. National Institutes of Health.
• ORCID for Researchers. ORCID.
• Data Management and Sharing Policy. National Institutes of Health.
• NCBI Data Resources. National Center for Biotechnology Information.
• EMBL-EBI Training. European Bioinformatics Institute.
• Endovascular thrombectomy after large-vessel ischaemic stroke: a meta-analysis of individual patient data from five randomised trials.. Lancet (London, England), 2016.
• Telerehabilitation services for stroke.. The Cochrane database of systematic reviews, 2020.
• Mixed model analysis of censored longitudinal data with flexible random-effects density.. Biostatistics (Oxford, England), 2012.

This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.