What Are Linear Mixed Effects Models? A Beginner’s Guide

Key takeaways

Linear mixed effects models combine fixed effects (overall trends) with random effects (group variation) to analyze clustered data. Here are some important facts to know:

• The global data analytics market size is projected to grow from $82.23 billion in 2025 to $402.70 billion by 2032 [1].

• Linear mixed effects models allow you to more accurately model correlated, hierarchical, longitudinal, and repeated-measured data.

• You can use linear mixed effects models to capture variability in baseline measures (random intercepts) and variability in the relationship between predictor and outcome variables (random slopes) across groups.

Learn how to use and interpret linear mixed effects models to strengthen your ability to interpret data accurately and generate data-driven insights for informed decision-making. If you’re ready to start building your data analytics skills right away, consider preparing for a career in data analytics with the IBM Data Analyst Professional Certificate. 

What is a linear mixed effects model?

A linear mixed effects model (often written as LMM) is a type of regression model that combines a fixed effect and a random effect. When you have data that is grouped, clustered, or hierarchical in nature, using a linear mixed effects model can help you appropriately model insights, including correlated, hierarchical, longitudinal, and repeated-measured data, to gain a clearer picture of the story your data is telling. 

Fixed effects are parameters that describe the relationship between your predictor and outcome variables, applying equally across your population. For example, a fixed effect might be how much a test score improves with every additional hour of studying.

A random effect captures variation across groups or clusters. For example, some classes might have higher overall scores than others due to differences in teaching style, even after you take studying hours into account. When you include both fixed and random effects, you can look at the overall pattern in the data while accounting for variability across groups. 

Types of linear mixed effects models

From random intercept to multilevel, the type of model depends on the structure of your data. To begin, consider the following:

Random intercept model 

With this specification, you allow the baseline (intercept) to vary across your groups. The intercept represents the expected outcome when all predictors are set to zero, and by making it random, you acknowledge that different groups may start from different baselines. 

For example, classrooms may have different average starting scores due to resources, cities may have different average housing prices based on the cost of living, and age groups may have different average incomes. In each case, you can account for these baseline differences across groups using a random intercept, allowing you to find the “population-level effect” of your predictors on the outcome variable.

Random slope model

While random intercept models let the starting point vary across groups, adding a random slope enables the effect of the predictor variable to differ across groups. This means that the rate your outcome variable changes for each unit change in the predictor variable varies by group. 

For example, imagine you are studying how each additional unit of weight lifted corresponds to increased muscle mass. The female population may gain muscle mass at a different rate than men, meaning the relationship between the predictor and the outcome varies by group. By including random slopes, you can capture these differences and create a more flexible model.

Variance component model (multiple random effects)

As you become more comfortable with random effects, you can include multiple sources of variation in your model, known as a variance component model. Instead of allowing only one grouping factor to vary, variance component models let you estimate the contribution of several random effects at once. This can help you identify where differences are most pronounced.

For example, continuing the previous example with muscle mass growth, you might want to include random effects for age group, gender, and dosage of certain supplements simultaneously. By modeling them together in a variance component model, you can see how much variation in muscle growth is attributable to each factor, giving a clearer picture of your data and the relationships within it. 

Multilevel model

Multilevel models are an extension of mixed effects models that handle nested data structures with more than two levels. For example, you might want to nest learners within classrooms, then classrooms within schools. Or you might nest patients within hospitals, and hospitals within health care systems. 

Each level can contribute to variability in the outcome, and modeling them together can help you disentangle effects and understand how variation distributes across levels. 

Can you compare mixed effects models and linear models?

Yes, mixed effects models and linear models are comparable in their structure, but mixed effects models extend linear models by including both fixed and random effects. While linear models assume all observations are independent, mixed effects models extend linear models by adding random effects that account for grouped data. When you use a linear model, you’ll generate an estimate for the fixed relationship between predictor and outcome variables, while a mixed effects model will produce the overall trend alongside group-specific variation.

When to use a linear mixed effects model

You can use a linear mixed effects model whenever your data has grouping, clustering, or repeated measures that violate the assumption of independence required by a standard linear model. In many real-world settings, observations in your data will not be completely independent. 

For example, if you were collecting data on learner test scores, you would need to take into account learners who were “clustered” in different classrooms or with different instructors. The same applies for patients grouped within certain hospitals, repeated measures for the same individual, and so on. Combining fixed and random effects helps you model dependencies in your data, providing more accurate and meaningful insights.

How to interpret linear mixed effects model results

Building your model is only one step. From there, you need to be able to translate the findings to your audience effectively.

Your interpretation will depend on the type of model you built and what research question you’re looking at. In general, you can start with the big picture: What is the average relationship you found? Say it plainly (e.g., “People on the medication had blood pressure about five points lower”). Next, you can note how results differ across groups. Do some classes, clinics, or age groups start higher or lower, or improve faster or slower? Relay your point estimates along with how confident you are (think p-value or confidence interval). The goal here is to provide an accurate representation of your data and findings in a clear and interpretable manner.

Pros and cons of linear mixed effects models

While able to model complex data relationships, linear mixed effects models are more complex than standard linear models. Using them is a decision that you can make based on your priorities, available resources, and the type of data you have. Some benefits and potential limitations to consider when deciding whether this model is right for you include:

Pros:

• Handles hierarchical and repeated-measured data effectively

• Allows for modeling both fixed and random effects

• Able to show both population-wide trends and group-specific variation

• Flexible enough to handle complex data with multiple levels of variability

• Captures variability in random intercepts and random slopes across groups

Cons: 

• May be more complex than needed, depending on alternative options (e.g., aggregation)

• Required larger sample sizes to estimate higher-level random effects accurately

• Results may be sensitive to model assumptions

Linear mixed effects model example

Imagine you are studying the changes in blood pressure that occur in response to a new medication. Your data set includes 200 patients who have their blood pressure read three times (baseline, six months, and one year). If you used a standard linear model, you would treat all 600 blood pressure readings as independent, ignoring the fact that measurements from the same patients are likely correlated and patients at the same hospital may share influential treatment factors. 

Instead, you can use a linear mixed effects model. Within this model, the fixed effect estimates the average impact of medication use on blood pressure across the entire sample. A random intercept accounts for differences in baseline blood pressure between patients and hospitals. Random slopes capture the variability in how blood pressure changes over time, allowing some patients or hospitals to show greater reductions than others. 

By modeling both the overall treatment effect and the variability across patients and hospitals, you can use your linear mixed effects model to find more accurate insights into the medication’s efficacy in reducing blood pressure.

How to build a linear mixed effects model

To build a linear mixed effects model, the first step is to determine if using a linear mixed effects model is appropriate. In general, you will want to use this model when:

• You have hierarchical or clustered data.

• You have repeated measures within the same subjects.

• You expect baseline or predictor effect variability across groups.

• You want to know how much variability each level explains.

Once you have identified that your data is appropriate for this model design, one of the best ways to start building and exploring your model options is with R, a popular statistical programming language. With the global data analytics market projected to grow from $82.23 billion in 2025 to $402.70 billion by 2032, learning mixed models in R can help you build in-demand data skills that can open new career opportunities [1].

In R, you can load your data, fit a basic model with the lme4 package (e.g., start with a random intercept model), then add complexity (random slopes) as needed. You can check your model fit, explore diagnostics, examine variance components, and try out different model styles to determine what works best for your data. For guided practice, consider checking out beginner-friendly R courses on learning platforms like Coursera.

Explore our free resources for data analytics professionals

To explore more types of modeling techniques to make sense of your data, you can tune in for expert insights on the Coursera YouTube channel. Or check out the following data analytics resources to keep learning:

• Watch on YouTube: Why Data Analysts Need to Understand AI 

• Hear from an expert: 6 Questions with a Microsoft Data Analytics Leader 

• Build your vocabulary: Data Analysis Terms & Definitions 

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