The most basic panel estimation is the Pooled OLS model, this model combines all data across indices and performs a regular Ordinary Least Squares Estimation. {% highlight r %} load the PLM library for panel estimation library(plm) load the Crime data set data(Crime) {% endhighlight %} {% highlight r %} define the model m1 <- formula(crmrte ~ prbarr + prbconv + polpc) create a panel data.frame (pdata.frame) object PanelCrime <- pdata.frame(Crime, index=c(“county”, “year”) )

Some simulated data, borrowed from this post. {% highlight r %} library for generation multivariate distributions library(MASS) always use the same random numbers set.seed(123) the means and errors for the multivariate distribution MUs <- c(10,15) SIGMAs <- matrix(c(1, 0.5, 0.5, 2 ), nrow=2, ncol=2 ) the multivariate distribution mdist <- mvrnorm(n = 1000, mu = MUs, Sigma = SIGMAs) create unobserved covariate c <- mdist[ , 2]

A simple example {% highlight r %} library(AER) data(“CigarettesSW”) rprice <- with(CigarettesSW, price/cpi) tdiff <- with(CigarettesSW, (taxs - tax)/cpi) packs <- CigarettesSW$packs {% endhighlight %} Estimate using OLS. {% highlight r %} lm(packs ~ rprice) {% endhighlight %} {% highlight text %} Call: lm(formula = packs ~ rprice) Coefficients: (Intercept) rprice 222.209 -1.044 {% endhighlight %}

In a previous post we discussed the linear model and how to write a function that performs a linear regression. In this post we will use that linear model function to perform a [Two-Stage Least Squares estimation]. This estimation allows us to […] Recall that we built the follow linear model function. {% highlight r %} ols <- function (y, X, intercept=TRUE) { if (intercept) X <- cbind(1, X) solve(t(X)%%X) %% t(X)%*%y # solve for beta } {% endhighlight %}

The learNN package makes it easy to become familiar with the way neural networks work by demonstrating the key concepts using straightforward code examples. The package is based on previous post on this blog. Andrew Trask wrote an amazing post at I am Trask called: A Neural Network in 11 lines of Python In the post Hand Coding a Neural Network I’ve translated the Python code into R. In a follow up post called: