innovate

A Python library for simplifying innovation and policy diffusion modeling.

This library provides a flexible and robust framework for modeling the complex dynamics of how innovations, technologies, and policies spread over time. It is designed for researchers and practitioners in economics, marketing, public policy, and technology forecasting.

Core Philosophy

innovate is built on a modular architecture, allowing users to combine different models and components to simulate real-world scenarios. The library supports everything from classic S-curve models to advanced agent-based simulations.

Key Features

• Modular Design: A suite of focused modules for specific modeling tasks:
  • innovate.diffuse: For foundational single-innovation adoption curves (Bass, Gompertz, Logistic).
  • innovate.substitute: For modeling technology replacement and generational products (Fisher-Pry, Norton-Bass).
  • innovate.compete: For analyzing market share dynamics between competing innovations.
  • innovate.hype: For simulating the Gartner Hype Cycle and the impact of public sentiment.
  • innovate.fail: For understanding the mechanisms of failed adoption.
  • innovate.adopt: For classifying adopter types based on their adoption timing.
• Efficient Data Handling: Uses pandas with an Apache Arrow backend for high-performance data manipulation.
• Advanced Parameterization:
  • Covariate-Driven Parameters: Allow model parameters (like p, q, and m in the Bass model) to be functions of external variables (e.g., price, advertising).
  • Time-Varying Parameters: Model structural breaks and policy impacts by allowing parameters to change at a specified time.
  • Mixture Models: Automatically identify and model distinct adopter segments from your data using the Expectation-Maximization algorithm.
• Extensible: Designed with clear base classes to make it easy to add new custom models.
• Computationally Aware: Leverages vectorized NumPy operations for efficiency, with a backend abstraction that will support future acceleration (e.g., with JAX).

Model Feature Matrix

Feature	Bass	Gompertz	Logistic	Lotka-Volterra	Fisher-Pry	Norton-Bass
Core Diffusion	✅	✅	✅	✅	✅	✅
Covariates	✅	✅	✅	❌	❌	❌
Time-Varying Params	✅	✅	✅	❌	❌	❌
Mixture Model	✅	✅	✅	❌	❌	❌

Innovate in the Ecosystem

innovate is designed to fill a unique gap in the Python ecosystem. While some libraries offer diffusion models and others provide generic agent-based modeling (ABM) frameworks, innovate is the first to integrate both under a unified, domain-specific toolkit for innovation dynamics.

Feature	innovate	PyDiM / bassmodeldiffusion	Mesa / AgentPy / BPTK-Py
Core Diffusion Models	✅ (Bass, Gompertz, Logistic)	✅ (Primarily Bass)	❌ (Not its focus)
Competition Models	✅ (Lotka-Volterra)	❌	✅ (Via custom ABM)
Substitution Models	✅ (Fisher-Pry)	❌	✅ (Via custom ABM)
Hype Cycle Modeling	✅ (Composite & DDE models)	❌	✅ (Via custom ABM)
Advanced Parameterization	✅ (Covariates, Time-Varying, Mixtures)	❌	❌ (Requires manual implementation)
Agent-Based Modeling	✅ (Integrated with mesa)	❌	✅ (Core functionality)
Pre-configured ABM Scenarios	✅ (Competition, Hype, Disruption)	❌	❌ (Requires manual implementation)
System Dynamics	❌	❌	✅ (BPTK-Py only)
Unified Framework	✅ (Diffusion + Competition + ABM)	❌ (Focused on diffusion)	❌ (Focused on ABM/SD)
Parameter Fitting	✅	✅	❌ (Not a primary feature)
Visualization	✅	✅	✅ (Network/Grid plots)

This integrated approach means you can start with high-level diffusion models and seamlessly transition to complex, bottom-up agent-based simulations without changing frameworks.

Roadmap

The innovate library is under active development. For detailed plans on upcoming features, including the Agent-Based Modeling (ABM) framework and advanced policy analysis tools, please see our Roadmap.

Installation

pip install innovate

(Note: The package is not yet available on PyPI under this name, but will be in the future).

You will also need to install pyarrow:

pip install pyarrow

Usage

Examples and tutorials will be provided in the examples/ directory to demonstrate how to use the library for various modeling scenarios.

Example Plots

Here is a sample of the kinds of visualizations you can generate with innovate.

Bass Diffusion	Lotka-Volterra Competition

Hype Cycle	Reduction Analysis

Gompertz Diffusion	Logistic Diffusion

Fisher-Pry Substitution	Norton-Bass Substitution

Multi-Product Diffusion	Adoption Curve

Backend Performance

The innovate library supports both NumPy and JAX backends. The JAX backend can provide a significant performance benefit for fitting complex models, especially those with a large number of parameters. However, the performance benefit is less significant for simple models.

The following table shows the results of a benchmarking script that compares the performance of the NumPy and JAX backends for a variety of tasks:

Model	Backend	Task	Time (s)
BassModel	numpy	fit	1.53
BassModel	jax	fit	1.39
GompertzModel	numpy	fit	0.03
GompertzModel	jax	fit	0.03
LogisticModel	numpy	fit	0.05
LogisticModel	jax	fit	0.05
BassModel	numpy	predict	0.06
BassModel	jax	predict	0.06
GompertzModel	numpy	predict	0.06
GompertzModel	jax	predict	0.06
LogisticModel	numpy	predict	0.10
LogisticModel	jax	predict	0.10
BassModel	numpy	simulate_1000	0.64
BassModel	jax	simulate_1000	0.62
GompertzModel	numpy	simulate_1000	0.61
GompertzModel	jax	simulate_1000	0.61
LogisticModel	numpy	simulate_1000	1.06
LogisticModel	jax	simulate_1000	1.08

As you can see, the JAX backend is slightly faster than the NumPy backend for fitting the BassModel. However, the performance is about the same for the other models and tasks.

We are continuing to investigate opportunities for optimization, including the use of pyarrow and other high-performance libraries.

License

This project is licensed under the Apache 2.0 License.

Testing

See the Testing Strategy document for details on how to run the test suite and how different tests are categorized.

Setup

Install the project dependencies before running the tests:

pip install -r requirements.txt

After installing the requirements, you can run pytest. The full recommended command is documented in docs/testing_strategy.rst.

Branching Strategy

This repository now uses work as the primary development branch. Existing branches can be rebased or merged onto work.