Analysis Plan — GPU-Enabled Differentiable Mixed Logit Estimation
1. Background and Motivation
Mixed logit models are widely used to capture preference heterogeneity in choice modelling. However, their empirical application is often constrained by computational cost, especially when large numbers of simulation draws, complex mixing distributions, or extensive robustness analyses are required.
This paper studies a GPU-enabled, differentiable estimation framework for mixed logit models, with a focus not only on raw acceleration, but on how such acceleration reshapes the feasibility frontier of empirical practice.
2. Research Questions
The analysis addresses four central questions:
Feasibility:
How does GPU-enabled automatic differentiation affect the computational feasibility of mixed logit estimation?Scalability:
How does estimation time scale with data size, model complexity, and simulation draws?Inference:
Does GPU acceleration make computationally intensive inference procedures, such as bootstrap, practically feasible?Predictability:
Can estimation time be anticipated ex ante based on model-induced computational demand and available hardware resources?
3. Computational Framework: Demand and Supply
3.1 Computational Demand Induced by the Model
For simulated maximum likelihood estimation of mixed logit models, the dominant computational workload arises from repeated evaluation of choice probabilities across individuals and simulation draws.
Abstracting from constant factors, the computational demand scales approximately as:
[ W ;\propto; N \times T \times J \times R, ]
where:
- (N) is the number of individuals,
- (T) is the number of choice tasks per individual,
- (J) is the number of alternatives,
- (R) is the number of simulation draws.
This demand is fully determined by the empirical design and modelling choices and is invariant to hardware architecture.
3.2 Computational Supply from Hardware
Hardware determines how much of this workload can be processed per unit time. Modern GPUs provide massive parallelism through thousands of compute units and are particularly effective when computations can be vectorised over independent dimensions.
In mixed logit estimation, both individuals and simulation draws naturally admit such parallelisation. We summarise hardware capability through effective computational throughput, which depends on:
- the number of available compute units,
- memory bandwidth,
- and the degree of parallel execution achieved by the algorithm.
3.3 Expected Wall-Clock Time
Combining computational demand and supply yields a simple but informative approximation:
[ \text{Wall-clock time} ;\approx; \frac{ N \times T \times J \times R }{ \text{Effective throughput of the hardware} }. ]
GPU acceleration does not alter the statistical model or its computational demand; instead, it increases effective throughput, thereby reducing wall-clock time and expanding the set of feasible empirical analyses.
This perspective highlights that computational speed becomes a predictable resource rather than an opaque constraint.
4. Experimental Design
4.1 Draw Scaling Experiment
Objective:
Evaluate how simulation draws affect estimation accuracy and runtime.
Design:
- Draw counts: (R \in {100, 300, 1000, 3000, 5000})
- Fixed model specification
- CPU vs GPU comparison
Outputs:
- Wall-clock time vs draws
- Parameter stability across draws
- Standard error behaviour
4.2 Demand–Supply Scaling Experiment
Objective:
Empirically validate the demand–supply framework by examining how runtime scales with computational workload and hardware capacity.
Design:
- Fix model structure
- Vary workload components:
- Number of individuals (N)
- Number of simulation draws (R)
- Compare runtime across:
- CPU execution
- GPU execution (when available)
Evaluation:
- Near-linear scaling of runtime with (N \times R)
- Differences in effective throughput between CPU and GPU
- Identification of saturation or memory-bound regimes
Expected Contribution:
- Demonstrate that runtime can be anticipated ex ante from known quantities
- Provide practical guidance for researchers to assess feasibility before estimation
4.3 Model Variant Experiment
Objective:
Assess feasibility of routine estimation of multiple model variants.
Design:
- Multiple starting values
- Alternative mixing specifications
- Different random-coefficient sets
Outputs:
- Total runtime for variant grids
- Parameter dispersion across specifications
- Convergence diagnostics
4.4 Bootstrap Inference Experiment
Objective:
Evaluate the practicality and benefits of bootstrap inference under GPU acceleration.
Design:
- Bootstrap replications (B \in {200, 500})
- Fixed and random simulation draws
- Comparison with asymptotic (Hessian-based) standard errors
Outputs:
- Bootstrap distributions
- Standard error comparisons
- Confidence interval coverage
- Computational cost per bootstrap replication
5. Evaluation Metrics
5.1 Computational Metrics
- Wall-clock time
- Effective throughput (relative)
- Scaling behaviour with workload
- GPU vs CPU speed ratios
5.2 Statistical Metrics
- Parameter stability
- Bias and variance
- Standard error consistency
- Confidence interval behaviour
6. Interpretation and Implications
The analysis will demonstrate that GPU-enabled differentiable estimation:
- Transforms computation from a binding constraint into a predictable resource;
- Enables systematic robustness checks previously deemed infeasible;
- Allows researchers to anticipate runtime based on data, model, and hardware;
- Improves transparency and planning in empirical mixed logit studies.
7. Reproducibility and Interactive Demonstration
An interactive notebook (e.g., Google Colab) will accompany the paper, allowing users to:
- Specify model dimensions and simulation draws;
- Automatically detect available hardware (CPU/GPU);
- Observe runtime scaling;
- Perform robustness and bootstrap analyses.
The notebook serves as both a reproducibility tool and a practical guide for empirical users.
8. Limitations and Extensions
Limitations include:
- GPU availability and memory constraints;
- Sensitivity to optimiser hyperparameters;
- Finite-sample behaviour under weak identification.
Future extensions may explore:
- Bayesian inference with GPU-accelerated MCMC or variational methods;
- Alternative optimisation algorithms;
- Extensions to other discrete choice models.
9. Timeline
| Stage | Milestone |
|---|---|
| 1 | Core estimation framework |
| 2 | Draw scaling experiments |
| 3 | Demand–supply scaling analysis |
| 4 | Bootstrap inference |
| 5 | Interactive notebook |
| 6 | Manuscript drafting and submission |