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Maximum Likelihood Estimation With Stata Fourth Edition: A Comprehensive Guide

Allan James

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$$L(\theta | x) = P(x | \theta)$$

where:

$L(\theta | x)$ is the likelihood function
$\theta$ is the vector of parameters to be estimated
$x$ is the observed data

The MLE estimator is the value of $\theta$ that maximizes the likelihood function:

Maximum Likelihood Estimation with Stata, Fourth Edition

by William Gould

4.9 out of 5

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$$\hat{\theta}= \arg\max_{\theta}L(\theta | x)$$

The MLE estimator is asymptotically consistent, efficient, and normally distributed under certain regularity conditions.

Stata provides several commands for performing maximum likelihood estimation. The most commonly used command is mlogit, which can be used to fit a variety of models, including linear regression models, logistic regression models, and probit regression models.

To fit a maximum likelihood model in Stata, you can use the following syntax:

stata mlogit depvar indepvars [if] [in] [weight] [, options]

where:

depvar is the dependent variable
indepvars are the independent variables
if and in are optional clauses that can be used to select observations and variables, respectively
weight is an optional variable that can be used to weight observations
options are a variety of options that can be used to control the estimation process

For example, the following command fits a linear regression model with maximum likelihood estimation:

stata mlogit y x1 x2 x3

The output from the <code>mlogit</code> command includes the estimated coefficients, standard errors, and t-statistics for the independent variables, as well as the log-likelihood value and other goodness-of-fit statistics. <h2>Practical Examples of Maximum Likelihood Estimation</h2> Maximum likelihood estimation is a powerful tool that can be used to fit a variety of statistical models. Here are a few practical examples of how MLE can be used: * **Estimating the parameters of a linear regression model.** MLE can be used to estimate the slope and intercept of a linear regression model. This information can be used to predict the value of the dependent variable for a given value of the independent variable. * **Estimating the parameters of a logistic regression model.** MLE can be used to estimate the coefficients of a logistic regression model. This information can be used to predict the probability of an event occurring for a given set of values of the independent variables. * **Estimating the parameters of a probit regression model.** MLE can be used to estimate the coefficients of a probit regression model. This information can be used to predict the probability of an event occurring for a given set of values of the independent variables. * **Estimating the parameters of a generalized linear model.** MLE can be used to estimate the parameters of a generalized linear model. This type of model is a generalization of the linear regression model that allows for a variety of different response distributions. Maximum likelihood estimation is a powerful statistical technique that can be used to fit a variety of statistical models. It is asymptotically consistent, efficient, and normally distributed under certain regularity conditions. Stata provides several commands for performing maximum likelihood estimation, making it a convenient and accessible tool for statistical analysis.</body></html>

Maximum Likelihood Estimation with Stata, Fourth Edition

by William Gould

4.9 out of 5