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The profile likelihood function is an inference function constructed from the likelihood function. If the likelihood function depends on many parameters and only some are of interest, then the other parameters are removed "by concentration", which means that they are "maxed out".

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Profile likelihood confidence intervals

Very good question. In this link it is explained that SAS uses a numerical approximation (which basically consists of a modification of the Newton-Raphson algorithm) Setting this option to both …
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