Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [profile-likelihood]

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".

Wikipedia has an article with further information and references.

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Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R?

Dear everyone - I've noticed something strange that I can't explain, can you? In summary: the manual approach to calculating a confidence interval in a logistic regression model, and the R function confint() give different results. I've been going…
Andrew
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Constructing confidence intervals based on profile likelihood

In my elementary statistics course, I learnt how to construct 95% confidence interval such as population mean, $\mu$, based on asymptotic normality for "large" sample sizes. Apart from resampling methods (such as bootstrap), there is another…
user2264
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What are the disadvantages of the profile likelihood?

Consider a vector of parameters $(\theta_1, \theta_2)$, with $\theta_1$ the parameter of interest, and $\theta_2$ a nuisance parameter. If $L(\theta_1, \theta_2 ; x)$ is the likelihood constructed from the data $x$, the profile likelihood for…
ocram
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What is the relationship between profile likelihood and confidence intervals?

To make this chart I generated random samples of different size from a normal distribution with mean=0 and sd=1. Confidence intervals were then calculated using alpha cutoffs ranging from .001 to .999 (red line) with the t.test() function, the…
Flask
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What is the exact definition of profile likelihood?

Does anyone here know the exact definition of Profile Likelihood? Or does it have one?
shijing SI
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Hessian of profile likelihood used for standard error estimation

This question is motivated by this one. I looked up two sources and this is what I found. A. van der Vaart, Assymptotic Statistics: It is rarely possible to compute a profile likelihood explicitly, but its numerical evaluation is often feasible.…
mpiktas
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How can I estimate 95% confidence intervals using profiling for parameters estimated by maximising a log-likelihood function using optim in R?

How can I estimate 95% confidence intervals using profiling for parameters estimated by maximising a log-likelihood function using optim in R? I know I can asymptotically estimate the covariance matrix by inverting the hessian, but I am concerned…
fmark
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Yet another "Bayesian vs Maximum Likelihood" question

In the fully Bayesian approach, the predictive distribution is: $$ P( Y|X ) = \int P(\theta | X ) P( Y | \theta ) d\theta $$ When the integral is difficult to compute, we might resort to the Maximum Likelihood approach, and approximate the…
usual me
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Profile likelihood confidence intervals

The theory behind profile likelihood (PL) confidence intervals (CIs) is clear to me. (See here, for example). SAS is surprisingly quick in calculating the PL CIs for all the covariates in a given model. Therefore I was wondering if there is another…
boscovich
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Inconsistency in Two stage Maximum Likelihood Estimation

I want to maximize a log-likelihood function (L) that is a function of parameters $\beta_i$ for $i=1,..,k$ and $\alpha_1, \alpha_2$. Ideally, I want to perform the estimation of all parameters in one step. Unfortunately, I cannot perform one step…
Stat
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Profile Likelihood: why optimize all other parameters while tracing a profile for a partitcular one?

Profile likelihood is sometimes used to get estimates for the confidence limits of parameters from an n-dimension parameter fit to a model. It can be used for example instead of Monte Carlo estimation. I don't understand the intuition of the…
rhody
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Determining if two profile likelihood curves are significantly different

I want to compare two profile likelihood curves and determine if they are significantly different from one another. For example are the following curves significantly different from one another: I realize I can find a 95% confidence interval for a…
Ben Haley
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Likelihood analysis for exponential distribution

Assume a collection of independent exponential random variables $y_{1}, \ldots, y_{n}$ with means $\mu_{1}, \ldots, \mu_{n}$; where $\mu_{i} = \beta_{0}+\beta_{1}x_{i}$. How can I find the profile likelihood of $\beta_{1}$? From what I gather, the…
user9171
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Confidence interval on the percentage difference of two binomial distributions

I have survey data for women and men following a binomial distribution. Their means are $p_1$ and $p_2$ respectively. I have calculated $(p_1-p_2)/p_2$ and would like to attach a confidence interval to this percentage. How can this be done? Given…
Big AL
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Is my explanation of profile likelihood plots correct?

Using the metafor package in R to conduct a mixed-effects meta-analysis and meta-regression, I checked the profile likelihood plots of the variance components, following Viechtbauer's (2017) approach described here. Since we are writing for an…
Johanna
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