mypoisson3.ado adds options for a robust or a cluster–robust estimator of the variance–covariance of the estimator (VCE) to mypoisson2.ado, which I discussed in Programming an estimation command in Stata: Handling factor variables in a poisson command using Mata. mypoisson3.ado parses the vce() option using the techniques I discussed in Programming an estimation command in Stata: Adding robust and cluster–robust VCEs to our Mata based OLS command. Below, I show how to use optimize() to compute the robust or cluster–robust VCE.
I only discuss what is new in the code for mypoisson3.ado, assuming that you are familiar with mypoisson2.ado.
This is the twenty-second post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
A poisson command with options for a robust or a cluster–robust VCE
mypoisson3 computes Poisson-regression results in Mata. The syntax of the mypoisson3 command is
mypoisson3 depvar indepvars [if] [in] [, vce(robust | cluster clustervar) noconstant]
where indepvars can contain factor variables or time-series variables.
In the remainder of this post, I discuss Read more…
mypoisson2.ado handles factor variables and computes its Poisson regression results in Mata. I discuss the code for mypoisson2.ado, which I obtained by adding the method for handling factor variables discussed in Programming an estimation command in Stata: Handling factor variables in optimize() to mypoisson1.ado, discussed in Programming an estimation command in Stata: A poisson command using Mata.
This is the twenty-first post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
A Poisson command with Mata computations
mypoisson2 computes Poisson regression results in Mata. The syntax of the mypoisson2 command is
mypoisson2 depvar indepvars [if] [in] [, noconstant]
where indepvars can contain factor variables or time-series variables.
In the remainder of this post, I discuss Read more…
\(
\newcommand{\xb}{{\bf x}}
\newcommand{\betab}{\boldsymbol{\beta}}\)I discuss a method for handling factor variables when performing nonlinear optimization using optimize(). After illustrating the issue caused by factor variables, I present a method and apply it to an example using optimize().
This is the twenty post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
How poisson handles factor variables
Consider the Poisson regression in which I include a full set of indicator variables created from Read more…
\(
\newcommand{\xb}{{\bf x}}
\newcommand{\betab}{\boldsymbol{\beta}}\)I discuss mypoisson1, which computes Poisson-regression results in Mata. The code in mypoisson1.ado is remarkably similar to the code in myregress11.ado, which computes ordinary least-squares (OLS) results in Mata, as I discussed in Programming an estimation command in Stata: An OLS command using Mata.
I build on previous posts. I use the structure of Stata programs that use Mata work functions that I discussed previously in Programming an estimation command in Stata: A first ado-command using Mata and Programming an estimation command in Stata: An OLS command using Mata. You should be familiar with Read more…
\(
\newcommand{\xb}{{\bf x}}
\newcommand{\betab}{\boldsymbol{\beta}}\)I show how to use optimize() in Mata to maximize a Poisson log-likelihood function and to obtain estimators of the variance–covariance of the estimator (VCE) based on independent and identically distributed (IID) observations or on robust methods.
This is the eighteenth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
Using optimize()
There are many optional choices that one may make when solving a nonlinear optimization problem, but there are very few that one must make. The optimize*() functions in Mata handle this problem by making a set of default choices for you, requiring that you specify a few things, and allowing you to change any of the default choices.
When I use optimize() to solve a Read more…
\(\newcommand{\betab}{\boldsymbol{\beta}}
\newcommand{\xb}{{\bf x}}
\newcommand{\yb}{{\bf y}}
\newcommand{\gb}{{\bf g}}
\newcommand{\Hb}{{\bf H}}
\newcommand{\thetab}{\boldsymbol{\theta}}
\newcommand{\Xb}{{\bf X}}
\)I review the theory behind nonlinear optimization and get more practice in Mata programming by implementing an optimizer in Mata. In real problems, I recommend using the optimize() function or moptimize() function instead of the one I describe here. In subsequent posts, I will discuss optimize() and moptimize(). This post will help you develop your Mata programming skills and will improve your understanding of how optimize() and moptimize() work.
This is the seventeenth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
A quick review of nonlinear optimization
We want to maximize a real-valued function \(Q(\thetab)\), where \(\thetab\) is a \(p\times 1\) vector of parameters. Minimization is done by maximizing \(-Q(\thetab)\). We require that \(Q(\thetab)\) is twice, continuously differentiable, so that we can use a second-order Taylor series to approximate \(Q(\thetab)\) in a neighborhood of the point \(\thetab_s\),
\[
Q(\thetab) \approx Q(\thetab_s) + \gb_s'(\thetab -\thetab_s)
+ \frac{1}{2} (\thetab -\thetab_s)’\Hb_s (\thetab -\thetab_s)
\tag{1}
\]
where \(\gb_s\) is the \(p\times 1\) vector of first derivatives of \(Q(\thetab)\) evaluated at \(\thetab_s\) and \(\Hb_s\) is the \(p\times p\) matrix of second derivatives of \(Q(\thetab)\) evaluated at \(\thetab_s\), known as the Hessian matrix.
Nonlinear maximization algorithms start with Read more…
I show how to use the undocumented command _vce_parse to parse the options for robust or cluster-robust estimators of the variance-covariance of the estimator (VCE). I then discuss myregress12.ado, which performs its computations in Mata and computes VCE estimators based on independently and identically distributed (IID) observations, robust methods, or cluster-robust methods.
myregress12.ado performs ordinary least-squares (OLS) regression, and it extends myregress11.ado, which I discussed in Programming an estimation command in Stata: An OLS command using Mata. To get the most out of this post, you should be familiar with Programming an estimation command in Stata: Using a subroutine to parse a complex option and Programming an estimation command in Stata: Computing OLS objects in Mata.
This is the sixteenth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
Parsing the vce() option
I used ado-subroutines to simplify the parsing of the options vce(robust) and vce(cluster cvarname) in myregress10.ado; see Programming an estimation command in Stata: Using a subroutine to parse a complex option. Part of the point was to Read more…
I have posted a series of entries about programming an estimation command in Stata. They are best read in order. The comprehensive list below allows you to read them from first to last at your own pace.
- Programming estimators in Stata: Why you should
To help you write Stata commands that people want to use, I illustrate how Stata syntax is predictable and give an overview of the estimation-postestimation structure that you will want to emulate in your programs.
- Programming an estimation command in Stata: Where to store your stuff
I discuss the difference between scripts and commands, and I introduce some essential programming concepts and constructions that I use to write the scripts and commands.
- Programming an estimation command in Stata: Global macros versus local macros
I discuss a pair of examples that illustrate the differences between global macros and local macros.
- Programming an estimation command in Stata: A first ado-command
I discuss the code for a simple estimation command to focus on the details of how to implement an estimation command. The command that I discuss estimates the mean by the sample average. I begin by reviewing the formulas and a do-file that implements them. I subsequently introduce Read more…
I discuss a command that computes ordinary least-squares (OLS) results in Mata, paying special attention to the structure of Stata programs that use Mata work functions.
This command builds on several previous posts; at a minimum, you should be familiar with Programming an estimation command in Stata: A first ado-command using Mata and Programming an estimation command in Stata: Computing OLS objects in Mata.
This is the fifteenth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
An OLS command with Mata computations
The Stata command myregress11 computes the results in Mata. The syntax of the myregress11 command is
myregress11 depvar [indepvars] [if] [in] [, noconstant]
where indepvars can contain factor variables or time-series variables.
In the remainder of this post, I discuss the code for myregress11.ado. I recommend that you click on the file name to download the code. To avoid scrolling, view the code in the do-file editor, or your favorite text editor, to see the line numbers.
I do not discuss Read more…
\(\newcommand{\epsilonb}{\boldsymbol{\epsilon}}
\newcommand{\ebi}{\boldsymbol{\epsilon}_i}
\newcommand{\Sigmab}{\boldsymbol{\Sigma}}
\newcommand{\betab}{\boldsymbol{\beta}}
\newcommand{\eb}{{\bf e}}
\newcommand{\xb}{{\bf x}}
\newcommand{\xbit}{{\bf x}_{it}}
\newcommand{\xbi}{{\bf x}_{i}}
\newcommand{\zb}{{\bf z}}
\newcommand{\zbi}{{\bf z}_i}
\newcommand{\wb}{{\bf w}}
\newcommand{\yb}{{\bf y}}
\newcommand{\ub}{{\bf u}}
\newcommand{\Xb}{{\bf X}}
\newcommand{\Mb}{{\bf M}}
\newcommand{\Xtb}{\tilde{\bf X}}
\newcommand{\Wb}{{\bf W}}
\newcommand{\Vb}{{\bf V}}\)I present the formulas for computing the ordinary least-squares (OLS) estimator and show how to compute them in Mata. This post is a Mata version of Programming an estimation command in Stata: Using Stata matrix commands and functions to compute OLS objects. I discuss the formulas and the computation of independence-based standard errors, robust standard errors, and cluster-robust standard errors.
This is the fourteenth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.
OLS formulas
Recall that the OLS point estimates are given by
\[
\widehat{\betab} =
\left( \sum_{i=1}^N \xb_i’\xb_i \right)^{-1}
\left(
\sum_{i=1}^N \xb_i’y_i
\right)
\]
where \(\xb_i\) is the \(1\times k\) vector of independent variables, \(y_i\) is the dependent variable for each of the \(N\) sample observations, and the model for \(y_i\) is
\[
y_i = \xb_i\betab’ + \epsilon_i
\]
If the \(\epsilon_i\) are independently and identically distributed (IID), we estimate Read more…