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Exact matching on discrete covariates is the same as regression adjustment

I illustrate that exact matching on discrete covariates and regression adjustment (RA) with fully interacted discrete covariates perform the same nonparametric estimation. Read more…

Probability differences and odds ratios measure conditional-on-covariate effects and population-parameter effects

\(\newcommand{\Eb}{{\bf E}}
\newcommand{\xb}{{\bf x}}
\newcommand{\betab}{\boldsymbol{\beta}}\)Differences in conditional probabilities and ratios of odds are two common measures of the effect of a covariate in binary-outcome models. I show how these measures differ in terms of conditional-on-covariate effects versus population-parameter effects. Read more…

Doctors versus policy analysts: Estimating the effect of interest

\(\newcommand{\Eb}{{\bf E}}\)The change in a regression function that results from an everything-else-held-equal change in a covariate defines an effect of a covariate. I am interested in estimating and interpreting effects that are conditional on the covariates and averages of effects that vary over the individuals. I illustrate that these two types of effects answer different questions. Doctors, parents, and consultants frequently ask individuals for their covariate values to make individual-specific recommendations. Policy analysts use a population-averaged effect that accounts for the variation of the effects over the individuals. Read more…

Programming an estimation command in Stata: Consolidating your code

\(
\newcommand{\xb}{{\bf x}}
\newcommand{\gb}{{\bf g}}
\newcommand{\Hb}{{\bf H}}
\newcommand{\Gb}{{\bf G}}
\newcommand{\Eb}{{\bf E}}
\newcommand{\betab}{\boldsymbol{\beta}}
\)I write ado-commands that estimate the parameters of an exponential conditional mean (ECM) model and a probit conditional mean (PCM) model by nonlinear least squares, using the methods that I discussed in the post Programming an estimation command in Stata: Nonlinear least-squares estimators. These commands will either share lots of code or repeat lots of code, because they are so similar. It is almost always better to share code than to repeat code. Shared code only needs to be changed in one place to add a feature or to fix a problem; repeated code must be changed everywhere. I introduce Mata libraries to share Mata functions across ado-commands, and I introduce wrapper commands to share ado-code.

This is the 27th 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.

Ado-commands for ECM and PCM models

I now convert the examples of Read more…

Programming an estimation command in Stata: Nonlinear least-squares estimators

\(\newcommand{\xb}{{\bf x}}
\newcommand{\gb}{{\bf g}}
\newcommand{\Hb}{{\bf H}}
\newcommand{\Gb}{{\bf G}}
\newcommand{\Eb}{{\bf E}}
\newcommand{\betab}{\boldsymbol{\beta}}\)I want to write ado-commands to estimate the parameters of an exponential conditional mean (ECM) model and probit conditional mean (PCM) model by nonlinear least squares (NLS). Before I can write these commands, I need to show how to trick optimize() into performing the Gauss–Newton algorithm and apply this trick to these two problems.

This is the 26th 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.

Gauss–Newton algorithm

Gauss–Newton algorithms frequently perform better than Read more…

A simulation-based explanation of consistency and asymptotic normality

Overview

In the frequentist approach to statistics, estimators are random variables because they are functions of random data. The finite-sample distributions of most of the estimators used in applied work are not known, because the estimators are complicated nonlinear functions of random data. These estimators have large-sample convergence properties that we use to approximate their behavior in finite samples.

Two key convergence properties are consistency and asymptotic normality. A consistent estimator gets arbitrarily close in probability to the true value. The distribution of an asymptotically normal estimator gets arbitrarily close to a normal distribution as the sample size increases. We use a recentered and rescaled version of this normal distribution to approximate the finite-sample distribution of our estimators.

I illustrate the meaning of consistency and asymptotic normality by Monte Carlo simulation (MCS). I use some of the Stata mechanics I discussed in Monte Carlo simulations using Stata.

Consistent estimator

A consistent estimator gets arbitrarily close in Read more…

Programming an estimation command in Stata: Certifying your command

\(\newcommand{\xb}{{\bf x}}
\newcommand{\betab}{\boldsymbol{\beta}}\)Before you use or distribute your estimation command, you should verify that it produces correct results and write a do-file that certifies that it does so. I discuss the processes of verifying and certifying an estimation command, and I present some techniques for writing a do-file that certifies mypoisson5, which I discussed in previous posts.

This is the twenty-fifth 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.

Verification versus certification

Verification is the process of establishing Read more…

Programming an estimation command in Stata: Making predict work

I make predict work after mypoisson5 by writing an ado-command that computes the predictions and by having mypoisson5 store the name of this new ado-command in e(predict). The ado-command that computes predictions using the parameter estimates computed by ado-command mytest should be named mytest_p, by convention. In the next section, I discuss mypoisson5_p, which computes predictions after mypoisson5. In section Storing the name of the prediction command in e(predict), I show that storing the name mypoisson5_p in e(predict) requires only a one-line change to mypoisson4.ado, which I discussed in Programming an estimation command in Stata: Adding analytical derivatives to a poisson command using Mata.

This is the twenty-fourth post in the Read more…

Programming an estimation command in Stata: Adding analytical derivatives to a poisson command using Mata

\(\newcommand{\xb}{{\bf x}}
\newcommand{\betab}{\boldsymbol{\beta}}\)Using analytically computed derivatives can greatly reduce the time required to solve a nonlinear estimation problem. I show how to use analytically computed derivatives with optimize(), and I discuss mypoisson4.ado, which uses these analytically computed derivatives. Only a few lines of mypoisson4.ado differ from the code for mypoisson3.ado, which I discussed in Programming an estimation command in Stata: Allowing for robust or cluster–robust standard errors in a poisson command using Mata.

This is the twenty-third 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.

Analytically computed derivatives for Poisson

The contribution of the i(th) observation to the log-likelihood function for the Poisson maximum-likelihood estimator is Read more…

Programming an estimation command in Stata: Allowing for robust or cluster–robust standard errors in a poisson command using Mata

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…