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".
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One sided likelihood ratio test for a logistic regression model?
I need to run a one-sided test on one parameter of a logistic regression model:
$H_0$: $\beta = 0$
$H_1$: $\beta \geq 0$
I want to avoid Wald-equivalent methods as these are known to have problems ...
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How to make the profile likelihood model for estimation?
I tried to make the age estimation model using the chemical compound results from The soil. Initially, I used the multivariable regression model. However, the reviewer highly recommend using the ...
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Grid search for estimation of degrees of freedom parameters in likelihood function
In the script below I attempt to estimate parameters for Apple and Amazon using a Gaussian Copula with t-Student marginals for the purpose of this exercice.
When executing the script, I notice at each ...
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Profile (quasi-)likelihood score tests
Suppose I have a log-likelihood or quasi-log-likelihood for my data in terms of the parameter vectors $\theta$ and $\psi$:
$$L(\theta;\psi)=\frac{1}{T}\sum_{t=1}^T{\log{f(y_t|\theta;\psi)}}.$$
(I am ...
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Profile likelihood vs quadratic log-likelihood approximation
I want to compare two alternative approaches for evaluating the uncertainty of the multi-dimensional MLE $\widehat \theta$ based on a log-likelihood function $l$:
Compute a Fisher-information-based ...
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Approximating profile likelihood confidence intervals when I only have a score function and not a likelihood
I'm working on a modeling problem where I can define a score function that looks a lot like a binomial likelihood, but the model isn't really binomial. I'd like to use profile likelihood to estimate ...
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Maximum Likelihood with a sign restriction
Suppose that we have a log-likelihood function of five parameters and an observed data sample $y=[y_1,\ldots,y_N]$:
$$\mathcal{l}(\beta_1, \beta_2, \beta_3, \beta_4, \beta_5;\;y) =\log f_Y(y;\;\beta_1,...
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Tweedie Dispersion Parameter Estimation Methods
In the book Generalized Linear Models with Examples in R - Dunn and Smyth, in Chapter 6.8, it is recommended to use the Pearson estimator of the dispersion - "This makes the Pearson estimator the ...
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Confidence Interval for factor loadings of 2PL model
I estimated a 2PL model obtained for some dichotomous data presenting answers of 12 "yes/no" questions from about 200 individuals. Now I want to calculate the confidence intervals for the ...
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justification for 'population prediction intervals'?
Suppose we are living in a frequentist world and want to compute confidence intervals on some quantity that is a complicated function of the parameters $q_1 = f(\Theta)$ (i.e., there's no closed-form ...
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Relationship Between "Profile Likelihood" and "EM Algorithm"?
I was reading Rao (2017) (Ch3) on profile likelihood. An example is provided which shows how the parameters of a Weibull Distribution can be estimated using the "profile likelihood approach"...
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How to correct Chi-square's p-value when working with very unbalanced contingency tables?
I'm studying the association between a rare disease and smoking. Because the disease is rare, my contingency table is highly unbalanced with way more Non-Diseased than Diseased individuals, ...
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How to get the $95\%$ Wald test confidence interval for $\theta$? [closed]
Suppose that iid random samples $X_i$ from a discrete CDF $F(x)$ on $\{x_1,\dots, x_n\}$ with mean $EX=\theta$. We want to estimate $F(x)$. We consider empirical likelihood for $F(x)=\sum_{i=1}^n p_i ...
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Pooling Profile Penalised LTRs in multiple imputation
I am analysizing data from a clinical trial.
I used multiple imputation to impute the (binary) outcome variable, which is the only variable with missing data.
All of the covariates are categorical and ...
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Calculation of p-values in logistf package
I'm trying to understand profile likelihood used in the logistf package. In the code, it seems the p-values are calculated by:
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