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Table of Contents

C++ Laplace Approximation of Mixed Effects Models

1 The cppad_mixed Maximum Likelihood Problem
2 Installing cppad_mixed in Unix
2.1 An Example Installation
2.1.1 Undo example_install.sh
2.2 bin/run_cmake.sh: User Configuration Options
2.3 Example and Test Using the Installed Version of cppad_mixed
3 Laplace Approximation for Mixed Effects Models
4 cppad_mixed: Public Declarations
4.1 User Defined Class Derived From cppad_mixed
4.1.1 mixed_cppad Derived Class: Example and Test
4.2 User Defined Random Likelihood Function
4.2.1 Random Likelihood: Example and Test
4.3 User Defined Fixed Likelihood Function
4.3.1 Random Likelihood: Example and Test
4.4 User Defined Fixed Effects Constraint Function
4.4.1 Using Constraints: Example and Test
4.5 Initialization After Constructor
4.6 Optimize Random Effects
4.6.1 Optimize Random Effects: Example and Test
4.7 Optimize Fixed Effects
4.7.1 Optimize Fixed Effects: Example and Test
4.7.2 An Ipopt Options Argument
4.7.3 Description of Ipopt Tracing Output
4.8 Compute the Hessian of The Fixed Effects Objective
4.8.1 Hessian of Fixed Effects Objective: Example and Test
4.9 Compute the Hessian of The Random Effects Objective
4.9.1 Hessian of Random Effects Objective: Example and Test
4.10 Sample Posterior for Fixed Effects
4.10.1 Sample From Fixed Effects Posterior: Example and Test
4.10.1.1 Testing the LDLT Reciprocal Condition Number Approximation
4.10.2 Sample Posterior for Fixed Effects Using Conditional Covariance
4.11 Simulation the Posterior Distribution for Random Effects
4.11.1 Sample From Fixed Effects Posterior: Example and Test
4.12 Compute the Observed Information For Fixed Effects
4.12.1 Observed Information Matrix: Example and Test
5 The CppAD::mixed Namespace Public Declarations
5.1 Types Defined in the CppAD Mixed Namespace
5.2 Set, Get, And Free A GSL Random Number Generator
5.2.1 Manage GSL Random Number Generator: Example and Test
5.3 Sparse Matrix Information
5.4 Optimal Solution Returned by optimize_fixed
5.4.1 Ipopt Warm Start Information
5.4.2 Ipopt Trace Information
5.5 CppAD Mixed Exceptions
6 User API Examples
6.1 Example Programs That are Also Speed and Memory Tests
6.1.1 A First Order Auto-Regressive Example and Speed Test
6.1.1.1 Example Using ar1_xam
6.1.2 A Capture Example and Speed Test
6.1.2.1 Example Using capture_xam
6.2 Absolute Value In Log-Density: Example and Test
6.3 No Random Effects: Example and Test
6.4 Constraints On Random Effects: Example and Test
6.5 Lasso on Fixed Effects: Example and Test
6.6 Random Effects Variance May Cause Data Mismatch
6.7 Nan’s During Optimization of Random Effects: Example and Test
6.8 Warm Starting Optimization: Example and Test
7 Changes and Additions to cppad_mixed
7.1 Release Notes for 2026
7.2 Release Notes for 2025
7.3 Release Notes for 2024
7.4 Release Notes for 2023
7.5 Release Notes for 2022
7.6 Release Notes for 2021
7.7 Release Notes for 2020
7.8 Release Notes for 2019
7.9 Release Notes for 2018
7.10 Release Notes for 2017
7.11 Release Notes for 2016
7.12 Release Notes for 2015
8 CppAD Mixed Wish List
9 Mathematical Notation