Questions tagged [likelihood-ratio]
The likelihood ratio is the ratio of the likelihoods of two models (or a null and alternative parameter value within a single model), which may be used to compare or test the models. If either model is not fully specified then its maximum likelihood over all free parameters is used - this is sometimes called a generalized likelihood ratio.
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Comparison of multilevel models via deviance test
I have a question regarding the comparison of the following two multilevel models:
Null model: outcome.nullmodel <- lmer(outcome ~ 1 + (1 | ID), data=multileveldata)
Random slopes model: outcome....
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Likelihood ratio tests vs. ANOVA for interactions in linear mixed model
I am analyzing a longitudinal study where patients received either treatment 1, treatment 2 or no treatment (placebo) using linear mixed models (LMM) in R. I have a baseline measure that is related to ...
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When using a likelihood ratio test to test for significance of a main effect, should I use the most maximal or minimal model as a base model?
Lets suppose I have a set of n covariates, and I want to test for the significance of the main effect of covariate i. I want to do this using a likelihood ratio test; fitting a model with covariate i ...
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Generalized likelihood ratio test for a left-truncated exponential distribution [duplicate]
I am doing self study in statistical inference and am rather confused about how to approach generalized likelihood ratio test (GLRT) problems. I am trying the traditional approach by definition and ...
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How to perform likelihood ratio test for bayesian neural network?
I am building a Bayesian neural network with Poisson likelihood and 50 features for time series prediction. Parameters of the model are learned using variational inference. I am trying to see whether ...
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p-value ratio for Likelihood Ratio Test with multicollinear data
I have two datasets where my independent variables (of which I have 6) are highly correlated. In one dataset I know for certain that the dependent variable should only depend on 1 independent variable ...
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Likelihood ratio test vs p value for Poisson regression
I have a Poisson regression model, from its summary table, I could see the p-value for a certain variable, e.g. gender. Since the p-value is testing the hypothesis whether the coefficient of gender ...
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Exact Likelihood ratio statistic for discrete distribution
Suppose that the random variables in a sample $Y_1, Y_2, \ldots, Y_n$ are iid with values in $[0,1]$, and that an investigator knows that the underlying probability density $f_Y(y)$ has the form
$f_Y(...
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Using likelihood ratios instead of p-values
I am analysing data from an experiment consisting of 4 treatments, and I am interested in treatment differences of DNA damage caused by a toxicant. I have consulted a statistician to discuss some of ...
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Is it valid to compare nested models even if proportional hazards assumption is violated in Cox models
I am trying to understand when are Cox models still informative and useful even when the proportional hazards (HR) assumption is violated and came across this interesting answer. It includes a link to ...
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Why can a likelihood ratio not give evidence for the null since it is a model comparison?
I am curious as to why a likelihood ratio cannot give positive evidence for the null, since it is a model comparison.
Indeed, this is more confusing given the fact that Bayes Factors are similar ...
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Comparison of variances: symmetric F-test is likelihood ratio test?
Suppose $X_i\stackrel{IID}\sim N(\mu,\sigma^2)$ for $i=1,...,n$, where $\mu$ is known. We want to apply the likelihood ratio test to decide between the hypotheses
$$
H_0: \sigma=\sigma_0 \\
H_1: \...
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Why doesn't the G-test's Chi-squared "threshold" scale with sample size?
In the popular likelihood ratio test of goodness-of-fit (also known as the G-test: see, e.g., here), the test statistic is calculated as
$$G(\mathbf{O},\mathbf{E})=2\sum_{i=1}^{M}O_{i}\log\frac{O_{i}}{...
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Likelihood Ratio vs Modified Frequentist Approach (CLs)
I'm a physicist trying to finally get a hold on practical statistics for particle physics and am having problem with the following -- I apologize for the lack of formality below.
Suppose the number of ...
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Generalized Likelihood Ratio Test - Why is the denominator a union
For GLRT, the ratio is:
$$
\Lambda^* = \frac{\max_{\theta \in \omega_0} L(\theta)}{\max_{\theta \in \omega_1}L(\theta)}
$$
but we instead use:
$$
\Lambda = \frac{\max_{\theta \in \omega_0}L(\theta)}{\...
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