Indifference points | Families and boundaries | Priors | Trial-level choice | Reading Bayesian output | Random effects

Overview | 1. Decision tree: which RE structure? | 2. Factor-expanded REs | 3. Multi-block pdBlocked | 4. Reading subject-level results | Plot and amplitude/persistence guards | 5. Group metrics with conditioning | Marginalization order | 6. Diagnostics | Variance components per block | Multi-start | Convergence troubleshooting | 7. End-to-end workflow | 8. Continuous within-subject random slopes (dose-response) | Cross-references

Why TMB | Some data | Fitting a model | Inspecting the fit | Subject-level rates | Predictions | Diagnostics | Choosing an equation | Beyond one group and one random effect | Practical notes | Relationship to Young (2017) | See also | References

Simulate a two-group study | Fit with a factor design on log k | Estimated marginal means of k | Contrasts | Visualizing the contrasts | Trial-level choice models | The Bayesian analogs | Which backend when

Data format | Structural model | Descriptive model (Young, 2018) | S3 methods | From the 27-item MCQ to choices | Indifference points and choices agree | Where to go next | References

Indifference points | Screening for unsystematic data | Fitting a discounting model | Area under the curve | Working at scale | Where to go next | References

The questionnaire | Data format | Scoring | A magnitude effect | Summarizing a sample | A model-free look at the choice gradient | Converting between layouts | Handling missing responses | From choices to trial-level data | References

A one-minute discounting task | The raw data | Scoring delay discounting | Response times | Scoring probability discounting | References

Introduction | What Is Convergence? | Optimization in Nonlinear Models | TMB Convergence Codes (nlminb) | L-BFGS-B Convergence Codes | NLME Convergence Warnings | Understanding Severity | The apVar Issue | NLS Convergence (Fixed-Effect Models) | The Key Insight | Diagnostic Checklist | 1. Parameter Plausibility | TMB Models | NLME Models | Hurdle Models | 2. Standard Errors and Variance Estimates | 3. Gradient Norm (TMB-Specific) | 4. Hessian / apVar Status | 5. Comparison with Nested Converged Models | 6. Stability Across Starting Values | Decision Framework | TMB Decision Table | NLME Decision Table | Remedies by Model Tier | NLME Remedies | Increasing Iterations | Loosening Tolerance for False Convergence | Switching Covariance Structure | Simplifying Random Effects | TMB Remedies | Adjusting TMB Control | Switching Optimizer | Using Warm Starts | Hurdle Model Remedies | Fixed-Effect NLS Remedies | Using check_demand_model() | TMB Example | NLME Example | Live Example with Fixed-Effect Model | Accessing Fit Warnings Directly | Summary | Cross-References | References

Introduction | When to Use Hurdle Models vs. Standard Models | Model Specification | Part I: Binary Model (Probability of Zero Consumption) | Part II: Continuous Model (Consumption Given Positive) | Random Effects Structure | Getting Started | Data Requirements | Basic Model Fitting | Interpreting Output | Diagnostics | Understanding Results | Fixed Effects | Subject-Specific Parameters | Model Selection: 2-RE vs 3-RE | When to Use Each | Likelihood Ratio Test | Predicting and Scoring | Visualization | Simulation and Validation | Simulating Data | Monte Carlo Simulation Studies | Interpreting Monte Carlo Results | Integration with beezdemand Workflow | Combining with Other Analyses | Exporting Results | Technical Details | TMB Backend | Control Parameters | Custom Starting Values | References | See Also

Why indifference points need a bounded error distribution | What the SLT-beta density is | The boundary problem, in the example data | Fitting the mixed-effects model | Choosing a family | How much to trust it | References

Introduction | When to Use Demand Analysis | Quick Decision Guide | Data Quality First | Grouped Checks with by | Tier 1: Fixed-Effects NLS | When to Use | Complete Example | Tier 2: Mixed-Effects Models | The LL4 Transformation | Post-Hoc Analysis with emmeans | Tier 2b: TMB Mixed-Effects Models | Advantages Over NLME | Group Comparisons with TMB | Tier 3: Hurdle Models | Understanding the Two-Part Structure | Comparing Hurdle Models | Choosing an Equation | Choosing Parameters | The k Parameter | Interpreting Key Parameters | Troubleshooting FAQ | Model Convergence Issues | Zero Handling | Parameter Comparison Across Models | Summary | Next Steps | References

Introduction | Quick Start | Choosing an Equation | Mathematical Specifications | Random Effects Structure | Estimating vs. Fixing k | Examining Results | Summary and Coefficients | Subject-Specific Parameters | Amplitude–Persistence Decomposition | Confidence Intervals | Variance-Covariance and the Delta Method | Predictions | Population Metrics | Visualization | Diagnostics | Advanced Visualization | Expenditure and Elasticity | Loss Surface and Profile | Subject Heterogeneity | Multi-Model Comparison | Group Comparisons | Joint Tests | Estimated Marginal Means | Pairwise Comparisons | Model Comparison | Building Nested Models with update() | Convergence Tips | tmb_control Options | Choosing Between fit_demand_tmb() and fit_demand_mixed() | References | See Also

Rationale Behind beezdemand | Note About Use | Installing beezdemand | CRAN Release (recommended method) | GitHub Release | GitHub Development Version | Using the Package | Example Dataset | Converting from Wide to Long and Vice Versa | Quick conversion with pivot_demand_data() | Obtain Descriptive Data | Change Data | Identify Unsystematic Responses | Analyze Demand Data | Obtaining Empirical Measures | Obtaining Derived Measures | Normalized Alpha ($\alpha^*$) | Share k Globally; Fit Other Parameters Locally | Learn More About Functions | Next Steps | Free beezdemand Alternative with Graphical User Interface | Acknowledgments | Recommended Readings

Introduction | Model with Two Factors (Additive) | Model with Two Factors and Interaction | Using Different equation_form and y_var | Collapsing Factor Levels | Example: Same collapsing for both parameters | Example: Different collapsing for Q0 and alpha | EMMs and Comparisons with Collapsed Factors | Visualizing Multi-Factor Models | Plotting a Two-Factor Model with Faceting | Plotting a Model Fit with equation_form = "simplified" | Analyzing Estimated Marginal Means (get_demand_param_emms) | Performing Pairwise Comparisons (get_demand_comparisons) | Advanced Topics | More Complex Random Effects Structures | Continuous Covariates and fixed_rhs | A) Additive continuous covariate via continuous_covariates | B) fixed_rhs with a factor (drug) and a continuous covariate (dose) | Trends with emtrends | Model Comparison and Overlay | Comparing Nested Models | Overlaying Demand Curves | See Also

Introduction | Fitting with Different Equations | Hursh & Silberberg ("hs") | Koffarnus ("koff") | Simplified ("simplified") | The k Parameter | Inspecting Fits | tidy(): Per-Subject Parameter Estimates | glance(): Model-Level Summary | augment(): Fitted Values and Residuals | confint(): Confidence Intervals | summary(): Formatted Summary | Normalized Alpha ($\alpha^*$) | Plotting | Basic Demand Curves | Faceted by Subject | Axis Transformations | Diagnostics | Model Checks | Residual Plots | Predictions | Default Predictions | Custom Price Grid | Aggregated Models | Mean Aggregation | Pooled Aggregation | Grouped Analysis with by | Fitting by Group | Grouped Plotting | Grouped Systematicity and Descriptive Checks | Conclusion | See Also

Introduction | Data Preparation | Fitting Demand Models with fit_demand_mixed() | APT Fit and Plot | LL4 transformation with ZBEn | Simplified Exponential | Koffarnus (Exponentiated) Equation Form | Inspecting Fits (tidy / glance / augment) | Diagnostics | Loss Surface and Profile | Basic Model (No Factors) | Model with One Factor | Inspecting Model Fits | Making Predictions (predict()) | Visualizing Model Fits with plot() | Example 1: Plotting a Single-Factor Model | Example 2: Plotting Subject-Specific Lines | Example 3: Customizing Axes (e.g., Log Scale) | Conclusion | See Also

Introduction | Setting Up Groups | Running the Extra Sum-of-Squares F-Test | Visualizing Group Comparisons | See Also

Introduction | Data Structure | Complete Cross-Price Analysis Workflow | Loading the cp Dataset | Step 1: Fit Target Demand (Alone Condition) | Step 2: Fit Target Demand (Own Condition) | Step 3: Fit Cross-Price Model (Alt Condition) | Comparing Results Across Conditions | Combined Visualization | Checking Unsystematic Data | Demonstration from Rzeszutek et al. (2025) | Low Nicotine Study (Kaplan et al., 2018) | Unpublished Cannabis and Cigarette Data | In Progress Experimental Tobacco Marketplace Data | Nonlinear Model Fitting | Two Stage | Fit to Group (pooled by group) | Fit to Group (mean) | Linear Model Fitting | Linear Mixed-Effects Model | Extracting Model Coefficients | Post-hoc Estimated Marginal Means and Comparisons | See Also

Overview | Why Migrate? | Quick Migration Reference | Basic Migration | Before (FitCurves) | After (fit_demand_fixed) | Extracting Results | Getting Parameter Estimates | Getting Model-Level Statistics | Working with Predictions | Plotting | New in 0.2.0: Diagnostics + Residual Workflows | New in 0.2.0: Unified Systematicity Wrappers | Advanced Features | Aggregated Data (Mean/Pooled) | Parameter Space | Feature Comparison | Suppressing Deprecation Warnings | Need Help? | See Also | Session Information