Latent Variable Modeling Explained: Methods, Examples, and Applications

Key takeaways

Latent variable modeling allows you to combine measurable variables to represent an abstract, unobservable construct. Here are some important things to know:

• Latent variable modeling is increasingly used in big data analytics. Recently, researchers applied a latent variable model to a data set of 30,000 respondents, 300 items, and 30 latent dimensions, demonstrating scaling potential to very high-dimensional models [1].

• Professionals across various industries, including medicine, economics, psychology, politics, and bioinformatics, use latent variable modeling to uncover abstract concepts. 

• You can choose different latent variable models to examine the relationship between your variables based on whether you have continuous or categorical data.

Learning how to use latent variable models can help you uncover hidden patterns and abstract constructs in your data sets. If you’re ready to start applying these methods in practice, you can build a foundation through the IBM Data Science Professional Certificate. This 12-course series introduces modern data science and machine learning techniques that closely align with latent variable modeling.

What is latent variable modeling?

Latent, or “hidden,” variable modeling is a statistical method that studies hidden concepts by analyzing measurable indicators that reflect them. To estimate these hidden constructs, researchers begin with observable data, like test scores or behaviors, and use them to make inferences about underlying concepts, including academic ability, mental health, or customer satisfaction. 

For example, consider that you want to measure a customer’s satisfaction with a certain brand. You can’t assign a single number to satisfaction itself, but you can make an inference about this by using survey questions, repeat purchasing behavior, or rates of return. By looking at patterns in observable data, you can make an informed estimate of the customer’s satisfaction. 

Types of latent variable models

When it comes to latent variable models, you can use several types, depending on whether your observed and latent variables are continuous or discrete. Consider the following model recommendations.

Both your latent variable and observed variable are continuous

If both your latent variable and observed variable are continuous, you can use factor analysis or structural equation modeling. You can use factor analysis to identify underlying dimensions (factors) that explain patterns in continuous data, like how multiple test scores may reflect overall mathematical ability. 

Structural equation modeling (SEM), on the other hand, builds on factor analysis by not only identifying latent variables but also modeling the relationships between multiple latent and observed variables simultaneously. SEM could test how math self-efficacy (latent) and basic math competency (observed) influence math achievement (latent).

Your latent variable is continuous, and your observed variable is discrete

If your latent variable is continuous and your observed variable is discrete, you can use item response theory (IRT). You can use IRT to estimate how a certain trait (latent) influences the likelihood of answering a question a certain way (discrete: scales, right/wrong, yes/no). 

For example, you might find that survey responders with a certain personality trait are more likely to answer in one way, while those with another personality trait typically answer differently. 

Your latent variable is discrete, and your observed variable is continuous

If your latent variable is discrete and your observed variable is continuous, you can use latent profile analysis or mixture modeling to analyze the data. Latent subgroup analysis identifies hidden subgroups or “profiles” in a population. 

For example, you might use latent variables to identify vocational behavior profiles, such as “high work investment” or “low work investment,” based on work attitudes, office engagement, and other factors. Mixture modeling is a more flexible approach that allows for overlapping subgroups and estimates which subgroup each person is “most likely” to call into. 

Both your latent variable and observed variable are discrete

If both your latent variable and observed variable are discrete, you can use latent class analysis. This method categorizes people based on patterns of categorical responses. As a health care provider, you might classify patients into disease risk subpopulations based on the presence or absence of symptoms and characteristics. 

Learn more: What Is Latent Space?

Why do latent variable models matter? 

Latent variable models matter because they provide a way for you to study variables that are meaningful, yet hard to measure directly. Without latent variable models, you could only assess surface-level behaviors, not the deeper, more abstract concepts underlying them. 

What is latent variable modeling used in?

You can use latent variable models when you can’t directly measure the concept you want to study with a single number or observation. These models help capture abstract constructs, such as intelligence, self-esteem, or satisfaction, through patterns of several measurable indicators. 

The flexibility of latent variable models to work with different variable types and research questions makes it useful across several industries, and you can choose to apply the type of latent variable model that makes the most sense for your particular use case. Recent advances have also made these models increasingly scalable, making them a great choice when you are working with very high-dimensional data or using machine learning techniques. For example, new algorithms have successfully estimated models involving 30,000 respondents, 300 items, and 30 latent dimensions [1].

Who uses latent variable models? 

Professionals use latent variable models across a wide range of fields that study abstract constructs that can’t be measured directly, including psychology, medicine, physics, natural language processing, management, bioinformatics, and more. The way in which you use latent variable models, and the type of model you choose, will depend on your field and the type of variables you have. 

If you work in education, you might use structural equation modeling to uncover personality dimensions related to academic ability, while you might choose IRT to develop and refine tests. For example, when creating a math exam, IRT can help identify which questions best measure skill across the full range of student ability. 

If you work in health research, you might choose to use latent variable mixture models (LVMMs) to evaluate patient-reported outcomes (PROs). LVMMs combine the strengths of IRL and latent class analysis, allowing you to both measure hidden traits and uncover subgroups of patients who respond systematically in different ways.

If you work in psychology, you might use factor analysis to study underlying behaviors and characteristics tied to certain “unmeasurable” traits. For example, you might look at how sustainability, adaptability, social cohesion, gender, and age all tie together to represent resilience. 

Pros and cons of latent variable models

You can generate many types of powerful insights using latent variable models, but like any method, it’s important to be aware of their strengths and limitations. Knowing when and how to best apply these types of models can help you make the most of this tool

Strengths

• Measure abstract concepts: You can study abstract concepts like intelligence and customer satisfaction.

• Work with flexible models: You can work with individual or combined latent variable model types to most accurately reflect your data and generate insights.

• Reveal hidden patterns: You can identify subgroups in populations that otherwise may have remained hidden. 

Limitations

• May require a larger sample size: If you have non-normal data, certain types of latent variable models may not work well with small sample sizes.

• More complex than observed models: Constructing an accurate latent variable model is generally a more complex process than nonlatent variable models. 

• Must be interpreted under certain assumptions: If you don’t account for hidden differences within a population, such as unmeasured patient characteristics that affect responses, it can bias latent variable model estimates.

Bayesian latent variable model vs. Gaussian latent variable model​

In addition to assessing whether your data is continuous or discrete, understanding whether it’s normally distributed and whether you want to incorporate historical data can further help you choose the appropriate model. If your variables follow a normal (bell-curve) distribution, you can often use a Gaussian model. A Bayesian model, on the other hand, goes beyond distributional assumptions by allowing you to incorporate prior knowledge and update it as new data becomes available. 

How to estimate a latent variable model​: Best practices

Because you can’t directly measure your latent variables, designing your model requires careful planning and thoughtful design to ensure construct validity. To begin, identify the measurable variables that capture the construct of interest most effectively. Using multiple indicators often helps reduce error and provides a more reliable estimate.

Once you have specified your model, you should check fit using appropriate diagnostics. Common approaches include overall goodness-of-fit tests, such as chi-square statistics, which are particularly effective with large samples. When data are sparse or sample sizes are small, you may want to use resampling methods like parametric bootstrapping. Once you’ve estimated your model, it’s important to validate it to increase confidence that your findings are robust, reproducible, and accurately represent what you intended.

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