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The Stata Journal
Volume 7 Number 3: pp. 376-387

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Profile likelihood for estimation and confidence intervals

Patrick Royston
Cancer and Statistical Methodology Groups
MRC Clinical Trials Unit
London, UK
Abstract.   Normal-based confidence intervals for a parameter of interest are inaccurate when the sampling distribution of the estimate is nonnormal. The technique known as profile likelihood can produce confidence intervals with better coverage. It may be used when the model includes only the variable of interest or several other variables in addition. Profile-likelihood confidence intervals are particularly useful in nonlinear models. The command pllf computes and plots the maximum likelihood estimate and profile likelihood–based confidence interval for one parameter in a wide variety of regression models.
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