How do you implement hierarchical and multilevel models in Stan and what are the benefits and challenges?

1 What is Stan?

Stan is a free and open-source software that allows you to specify, fit, and evaluate Bayesian models using a probabilistic programming language. Stan can handle a wide range of models, from simple linear regression to complex hierarchical and multilevel models, and can perform full Bayesian inference using Markov chain Monte Carlo (MCMC) methods. Stan also provides tools for model checking, diagnostics, and comparison, as well as interfaces with various programming languages and platforms, such as R, Python, and Julia.

2 How to specify hierarchical and multilevel models in Stan?

To specify a hierarchical or multilevel model in Stan, you need to define the data, parameters, and model blocks in the Stan code. The data block declares the variables and dimensions of the data, such as the number of observations, groups, and predictors. The parameters block declares the unknown parameters and their prior distributions, such as the coefficients, variances, and correlations of the model. The model block defines the likelihood function and the prior distributions for the parameters, using the data and parameters declared in the previous blocks. You can use loops, vectorization, and indexing to express the hierarchical and multilevel structure of the model, as well as functions and custom distributions to capture nonlinear or complex relationships.

3 How to fit hierarchical and multilevel models in Stan?

To fit a hierarchical or multilevel model in Stan, you need to compile the Stan code, provide the data, and run the MCMC algorithm. You can use the Stan interface of your choice, such as RStan, PyStan, or CmdStan, to compile the Stan code into an executable file that can be used for sampling. You can also provide the data as a list or a dictionary of values that match the data block in the Stan code. Then, you can run the MCMC algorithm, which generates a sequence of samples from the posterior distribution of the parameters, given the data and the model. You can specify various options for the MCMC algorithm, such as the number of iterations, chains, warm-up, and thinning, as well as the algorithm type, such as NUTS or HMC.

4 How to evaluate hierarchical and multilevel models in Stan?

To evaluate a hierarchical or multilevel model in Stan, you need to analyze the output of the MCMC algorithm, such as the summary statistics, plots, and diagnostics. You can use the Stan interface of your choice, such as RStan, PyStan, or CmdStan, to access and manipulate the output of the MCMC algorithm, which is usually stored as a list or a dataframe of samples. You can use various functions and packages to compute and visualize the summary statistics, such as the mean, median, standard deviation, credible intervals, and posterior predictive checks, of the parameters and the model fit. You can also use various tools and methods to check the diagnostics, such as the convergence, mixing, efficiency, and autocorrelation, of the MCMC algorithm, and to identify and resolve any potential issues or problems.

5 What are the benefits of using Stan for hierarchical and multilevel models?

One of the main benefits of using Stan for hierarchical and multilevel models is that it allows you to specify and fit complex models with high flexibility and efficiency. Stan can handle models with nonlinear, non-normal, or non-Gaussian outcomes, as well as models with varying coefficients, random effects, or latent variables. Stan can also perform full Bayesian inference, which provides a coherent and principled framework for incorporating prior knowledge, quantifying uncertainty, and making predictions. Moreover, Stan can leverage the power of MCMC methods, which can explore the posterior distribution of the parameters without making restrictive assumptions or approximations.

6 What are the challenges of using Stan for hierarchical and multilevel models?

One of the main challenges of using Stan for hierarchical and multilevel models is that it requires a good understanding of Bayesian statistics, probabilistic programming, and MCMC methods. Stan can be difficult to learn and use for beginners or non-experts, as it requires writing code in a specific syntax, choosing appropriate prior distributions and likelihood functions, and tuning and monitoring the MCMC algorithm. Stan can also be computationally intensive and time-consuming, especially for large or complex models, as it requires generating and storing a large number of samples from the posterior distribution. Furthermore, Stan can encounter issues or errors, such as divergences, low effective sample size, or high R-hat, that can affect the validity and reliability of the inference.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?