rmdcev

Implement MDCEV model in R using Stan

https://github.com/plloydsmith/rmdcev

Repository

Implement MDCEV model in R using Stan

README.Rmd

---
output: github_document
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# Kuhn-Tucker and Multiple Discrete-Continuous Extreme Value (MDCEV) Model Estimation and Simulation in R: The rmdcev Package


[![R build status](https://github.com/plloydsmith/rmdcev/workflows/R-CMD-check/badge.svg)](https://github.com/plloydsmith/rmdcev/actions)
[![R-CMD-check](https://github.com/plloydsmith/rmdcev/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/plloydsmith/rmdcev/actions/workflows/R-CMD-check.yaml)


The **rmdcev** R package estimate and simulates Kuhn-Tucker demand models with individual heterogeneity. The models supported by **rmdcev** are the multiple-discrete continuous extreme value (MDCEV) model and Kuhn-Tucker specification common in the environmental economics literature on recreation demand. Latent class and random parameters specifications can be implemented and the models are fit using maximum likelihood estimation or Bayesian estimation. All models are implemented in Stan, which is a C++ package for performing full Bayesian inference (see https://mc-stan.org/). The **rmdcev** package also implements demand forecasting and welfare calculation for policy simulation.

## Current Status

Development is in progress. Currently users can estimate the following models:

1. Bhat (2008) MDCEV model specifications
2. Kuhn-Tucker model specification in environmental economics (von Haefen and Phaneuf, 2005)

Models can be estimated using

1. Fixed parameter models (maximum likelihood or Bayesian estimation)
2. Latent class models (maximum likelihood estimation)
3. Random parameters models (Bayesian estimation)

## Installation

I recommend you first install **rstan** by following these steps:

https://github.com/stan-dev/rstan/wiki/RStan-Getting-Started

Once **rstan** is installed, you can install **rmdcev** from CRAN using

``` r
install.packages("rmdcev")
```

Or install the latest version of **rmdcev** from GitHub using devtools

``` r
if (!require(devtools)) {
  install.packages("devtools")
  library(devtools)
}
install_github("plloydsmith/rmdcev", dependencies = TRUE, INSTALL_opts="--no-multiarch")
```

If you have any issues with installation or use of the package, please let me know by [filing an issue](https://github.com/plloydsmith/rmdcev/issues).

## References

Background on the models, estimation, and simulation as well as a walk through of the package is provided in

Lloyd-Smith, P (2021). ["Kuhn-Tucker and Multiple Discrete-Continuous Extreme Value Model Estimation and Simulation in R: The rmdcev Package"](https://doi.org/10.32614/RJ-2021-015) The R Journal, 12(2): 251-265.

For more details on the model specification and estimation:

Bhat, C.R. (2008) ["The Multiple Discrete-Continuous Extreme Value (MDCEV) Model: Role of Utility Function Parameters, Identification Considerations, and Model Extensions"](https://www.sciencedirect.com/science/article/pii/S0191261507000677) Transportation Research Part B, 42(3): 274-303.

von Haefen, R. and Phaneuf D. (2005) ["Kuhn-Tucker Demand System Approaches to Non-Market Valuation"](https://link.springer.com/chapter/10.1007/1-4020-3684-1_8) In: Scarpa R., Alberini A. (eds) Applications of Simulation Methods in Environmental and Resource Economics. The Economics of Non-Market Goods and Resources, vol 6. Springer, Dordrecht.

For more details on the demand and welfare simulation:

Pinjari, A.R. and Bhat , C.R. (2011) ["Computationally Efficient Forecasting Procedures for Kuhn-Tucker Consumer Demand Model Systems: Application to Residential Energy Consumption Analysis."](https://www.caee.utexas.edu/prof/bhat/MDCEV_Forecasting.html) Technical paper, Department of Civil & Environmental Engineering, University of South Florida.

Lloyd-Smith, P (2018). ["A New Approach to Calculating Welfare Measures in Kuhn-Tucker Demand Models."](https://www.sciencedirect.com/science/article/pii/S1755534517300994) Journal of Choice Modeling, 26: 19-27

## Estimation

As an example, we can simulate some data using Bhat (2008)'s 'Gamma' specification. In this example, we are simulating data for 2,000 individuals and 10 non-numeraire alternatives. We will randomly generate the parameter values to simulate the data and then check these values to our estimation results.

```{r} 
library(pacman)
p_load(tidyverse, rmdcev)
set.seed(12345)
model <- "gamma"
nobs <- 2000
nalts <- 10
sim.data <- GenerateMDCEVData(model = model, nobs = nobs, nalts = nalts)
```

Estimate model using MLE (note that we set "psi_ascs = 0" to omit any alternative-specific constants)
``` {r}
mdcev_est <- mdcev(~ b1 + b2 + b3 + b4 + b5 + b6,
				   data = sim.data$data,
				   psi_ascs = 0,
				   model = model,
				   algorithm = "MLE")
```

Summarize results
``` {r}
summary(mdcev_est)
```


Compare estimates to true values
``` {r}
coefs <- as_tibble(sim.data$parms_true) %>%
	mutate(true = as.numeric(true)) %>%
 cbind(summary(mdcev_est)[["CoefTable"]]) %>%
	mutate(cl_lo = Estimate - 1.96 * Std.err,
		   cl_hi = Estimate + 1.96 * Std.err)

head(coefs, 200)
```

Compare outputs using a figure
```{r, warning = FALSE}
coefs %>%
	ggplot(aes(y = Estimate, x = true))  +
	geom_point(size=2) +
	geom_text(label=coefs$parms,position=position_jitter(width=.5,height=1)) +
	geom_abline(slope = 1) +
	geom_errorbar(aes(ymin=cl_lo,ymax=cl_hi,width=0.2))
```


## Welfare simulation

Create policy simulations (these are 'no change' policies with no effects)
```{r}
npols <- 2 # Choose number of policies

policies <-	CreateBlankPolicies(npols, mdcev_est)

df_sim <- PrepareSimulationData(mdcev_est, policies, nsims = 1) 
```

Simulate welfare changes
```{r}
wtp <- mdcev.sim(df_sim$df_indiv, 
				 df_common = df_sim$df_common, 
				 sim_options = df_sim$sim_options,
				 cond_err = 1, 
				 nerrs = 15, 
				 sim_type = "welfare")
summary(wtp)
```

## Thanks

This package was not developed in isolation and I gratefully acknowledge Joshua Abbott, Allen Klaiber, Lusi Xie, the [apollo team](http://www.apollochoicemodelling.com/), and the Stan team, whose codes or suggestions were helpful in putting this package together.

Owner

GitHub Events

Committers

Last synced: over 3 years ago

Issues and Pull Requests

Last synced: over 2 years ago

Packages