Dealing with heteroskedasticity; regression with robust standard errors using R
Forecasting my weight with R
Getting data from pdfs using the pdftools package
Imputing missing values in parallel using {furrr}
Missing data imputation and instrumental variables regression: the tidy approach
{pmice}, an experimental package for missing data imputation in parallel using {mice} and {furrr}
Building formulae
Functional peace of mind
Get basic summary statistics for all the variables in a data frame
Getting {sparklyr}, {h2o}, {rsparkling} to work together and some fun with bash
Importing 30GB of data into R with sparklyr
Introducing brotools
It's lists all the way down
It's lists all the way down, part 2: We need to go deeper
Keep trying that api call with purrr::possibly()
Lesser known dplyr 0.7* tricks
Lesser known dplyr tricks
Lesser known purrr tricks
Make ggplot2 purrr
Mapping a list of functions to a list of datasets with a list of columns as arguments
Predicting job search by training a random forest on an unbalanced dataset
Teaching the tidyverse to beginners
Why I find tidyeval useful
tidyr::spread() and dplyr::rename_at() in action
Easy peasy STATA-like marginal effects with R
Functional programming and unit testing for data munging with R available on Leanpub
How to use jailbreakr
My free book has a cover!
Work on lists of datasets instead of individual datasets by using functional programming
Method of Simulated Moments with R
New website!
Nonlinear Gmm with R - Example with a logistic regression
Simulated Maximum Likelihood with R
Bootstrapping standard errors for difference-in-differences estimation with R
Careful with tryCatch
Data frame columns as arguments to dplyr functions
Export R output to a file
I've started writing a 'book': Functional programming and unit testing for data munging with R
Introduction to programming econometrics with R
Merge a list of datasets together
Object Oriented Programming with R: An example with a Cournot duopoly
R, R with Atlas, R with OpenBLAS and Revolution R Open: which is fastest?
Read a lot of datasets at once with R
Unit testing with R
Update to Introduction to programming econometrics with R
Using R as a Computer Algebra System with Ryacas

This document details section *12.4.5. Unobserved Heterogeneity
Example* from Cameron and Trivedi's book - MICROECONOMETRICS: Methods and
Applications. The original source code giving the results from table 12.2 are
available from the authors' site here and
written for Stata. This is an attempt to translate the code to R. I'd like to
thank Reddit user anonemouse2010 for his
advice which helped me write the function.

Consult the original source code if you want to read the authors' comments. If you want the R source code without all the commentaries, grab it here. This is not guaranteed to work, nor to be correct. It could set your pet on fire and/or eat your first born. Use at your own risk. I may, or may not, expand this example. Corrections, constructive criticism are welcome.

The model is \( y=\theta+u+\varepsilon \) where \( \theta \) is a scalar parameter equal to 1. \( u \) is extreme value type 1 (Gumbel distribution), \( \varepsilon \leadsto \mathbb{N}(0,1) \). For more details, consult the book.

You can consult the original source code to see how the authors simulated the data. To get the same results, and verify that I didn't make mistakes I prefer importing their data directly from their website.

```
data <- read.table("http://cameron.econ.ucdavis.edu/mmabook/mma12p2mslmsm.asc")
u <- data[, 1]
e <- data[, 2]
y <- data[, 3]
numobs <- length(u)
simreps <- 10000
```

In the code below, the following likelihood function:
$$\log{\hat{L}_N(\theta)} = \dfrac{1}{N} \sum_{i=1}^N\log{\big( \dfrac{1}{S}\sum_{s=1}^S \dfrac{1}{\sqrt{2\pi}} \exp \{ -(-y_i-\theta-u_i^s)^2/2 \}\big)}$$
which can be found on page 397 is programmed using the function `sapply`

.

```
denssim <- function(theta) {
loglik <- mean(sapply(y, function(y) log(mean((1/sqrt(2 * pi)) * exp(-(y - theta + log(-log(runif(simreps))))^2/2)))))
return(-loglik)
}
```

This likelihood is then maximized:

```
system.time(res <- optim(0.1, denssim, method = "BFGS", control = list(maxit = simreps)))
```

```
## user system elapsed
## 21.98 0.08 22.09
```

Convergence is achieved pretty rapidly, to

```
## [1] 1.101
```

which is close to the true value of the parameter 1 (which was used to generate the data).

Let's try again with another parameter value, for example \( \theta=2.5 \). We have to generate y again:

```
y2 <- 2.5 + u + e
```

and slightly modify the likelihood:

```
denssim2 <- function(theta) {
loglik <- mean(sapply(y2, function(y2) log(mean((1/sqrt(2 * pi)) * exp(-(y2 -
theta + log(-log(runif(simreps))))^2/2)))))
return(-loglik)
}
```

which can then be maximized:

```
system.time(res2 <- optim(0.1, denssim2, method = "BFGS", control = list(maxit = simreps)))
```

```
## user system elapsed
## 12.56 0.00 12.57
```

The value that maximizes the likelihood is:

```
## [1] 2.713
```

which is close to the true value of the parameter 2.5 (which was used to generate the data).