Statistical Modeling of Latent Variables

Statistical modelling of latent variables refers to the suite of methods used to infer unobserved constructs from observed data. By representing underlying factors, traits or processes that cannot be measured directly, these approaches enable researchers to capture complex phenomena across disciplines such as psychology, ecology, economics and social science. Central to this field are measurement models, which link manifest indicators to latent factors, and structural models, which describe interdependencies among latent constructs. Common frameworks include factor analysis, structural equation modelling, latent class analysis and mixture models for discrete and continuous outcomes. Recent advances have addressed key challenges: ensuring model identifiability in high-dimensional settings, selecting relevant variables without overfitting through regularisation, and accommodating non-normal or discrete responses via generalised linear latent variable models. Improved computational techniques—ranging from expectation–maximisation algorithms to optimisation-based approximations—have broadened the applicability of latent variable models to large datasets, enabling applications from joint species distribution in ecology to the identification of psychological determinants in behavioural science.

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Statistical Modeling of Latent Variables publication trend

The graph below shows the total number of articles in statistical modeling of latent variables across all publications each year (not limited to Nature Index journals).

Technical terms

Latent variable: a construct not directly observed but inferred from measured indicators.

Structural equation model (SEM): a framework that combines measurement and structural components to represent relationships between observed and latent variables.

Generalised linear latent variable model (GLLVM): an extension of latent variable models for non-normal responses using link functions and exponential family distributions.

Regularisation: a penalty-based technique that controls model complexity to prevent overfitting and facilitate variable selection.

Variational approximation: a computational approach that approximates complex probability distributions by optimising simpler surrogate distributions.

References

1. A Practical Guide to Variable Selection in Structural Equation Modeling by Using Regularized Multiple-Indicators, Multiple-Causes Models. Advances in Methods and Practices in Psychological Science (2019).
2. Efficient estimation of generalized linear latent variable models. PLOS ONE (2019).
3. The Poisson-Lognormal Model as a Versatile Framework for the Joint Analysis of Species Abundances. Frontiers in Ecology and Evolution (2021).
4. Factor copula models for mixed data. British Journal of Mathematical and Statistical Psychology (2021).