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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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Comparing Models with Unequal Sample Sizes

I have performed an association analysis where I have associatiated several different perdictor variables to a dependent variable. For each predictor, I run two models and compare them via the ...
CAM_etal's user avatar
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is the likelihood ratio test "best" for finite samples?

Wikipedia says The Neyman–Pearson lemma states that this likelihood-ratio (lr) test is the most powerful among all level α alpha tests for this case. Is this only true for infinite sample sizes? Is ...
A Friendly Fish's user avatar
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Rejection region in LRT test

Let's say I have $X_i \sim Bi(1, \theta$) and want to test $H_0: \theta \geq \theta_0$ vs $H_1: \theta < \theta_0$. I've found that $\lambda = \frac{\sup_{\theta \in \Theta_0}L(\theta)}{\sup_{\...
Peter Sampodiras's user avatar
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Comparison of two test metrics

I'm trying to compare two test metrics (Metric A and Metric B) to determine which one better predicts a delta value, which represents a Euclidean difference. I am unsure how to determining which ...
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Hypothesis Test Finite Sample Spatial Gaussian Mixture Model

I have $n$ observations of pairs $(x, y)$ and three different models I would like to compare. Model0 is nested within Model1. Model0 is also nested within Model2. I would like to do hypothesis ...
A Friendly Fish's user avatar
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Likelihood ratios not distributed as a chi2 distribution with the correct dof (Wilks' theorem)

I perform Bayesian inference on a mixture model such that $\mu$ is the mixture weight for a feature in the mixture $p(x | \mu, \theta) = \mu p_{f}(x|\theta) + (1-\mu)p_{nf}(x|\theta)$ I have prior $p(\...
malavika v vasist's user avatar
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1 answer
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Likelihood-ratio and score tests of a (non)linear combination of coefficients

The likelihood-ratio and score test are typically used for simple scalar hypotheses such as $\beta_1 = 0$ or $\beta_1 = \beta_2 = 0$. How can we test a linear combination of coefficients using the ...
DrJerryTAO's user avatar
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3 votes
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likelihood ratio tests on bounded parameters

I am confused by the likelihood ratio test's boundary condition limitation. A commonly stated is that it causes problem for variance parameter because it is bounded below by 0. Can these models ...
quibble's user avatar
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1 vote
1 answer
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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 ...
Mohan's user avatar
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Lower threshold for Sequential Probability Ratio Test on Contingency Table testing

For testing whether a die is fair, we have the log likelihood ratio: $$ \Lambda = \frac{1}{2} \sum_{i} \mathrm{observed}_i \log\left(\frac{\mathrm{observed}_i}{\mathrm{expected}_i}\right). $$ Suppose ...
shabbychef's user avatar
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LR statistics add up for nested models. What about the Wald test?

Consider models M0, M1, M2. Let M0 $\subset$ M1 $\subset$ M2, i.e. let the models nest each other. I test the following pairs of models using the likelihood-ratio (LR) test: M0 vs. M2, M0 vs. M1, M1 ...
Richard Hardy's user avatar
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Am I using the correct test statistic for a binomial glm using the type III Anova function in the package car?

I am trying to look at how the likelihood of event Y is influenced by two factors A (5 levels) and B (2 levels) and my model is as follows: ...
Insect_biologist's user avatar
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2 answers
166 views

Why do I get a negative chi-squared value in my type III ANOVA output for my binomial GLM?

I am trying to look at how the likelihood of event X occurring is affected by three factors A (5 levels), B (2 levels) and C (3 levels). To do this I have run a binomial glm followed by a type 3 ANOVA ...
Insect_biologist's user avatar
2 votes
1 answer
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equivalence between the likelihood ratio test and t-tests

The linked sites (link1, link2) demonstrate that the likelihood ratio tests and the corresponding one- and two-sample t-tests are equivalent. However, based on my understanding, the null distribution ...
quibble's user avatar
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How to translate the set of contrasts over model coefficients into definitions of two nested models for Likelihood Ratio testing?

With the data as below: Categorical predictor: "Group" with 2 levels: Group 1 and Group 2 Categorical predictor: "Treatment" with 3 levels: A, B, C Categorical binary response: &...
AshanaShiiii's user avatar
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How to test specific contrasts about levels of categorical variables through nested models? [closed]

This is not about obtaining any dataset. I HAVE the dataset. This is not about debugging code, this is about EXPLAINING the way to obtain statistical relationship between the nested models (LRT ANOVA) ...
AshanaShiiii's user avatar
2 votes
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57 views

SUR estimated by OLS: restricted model has higher likelihood

I have three versions of a system of linear regression models: M, M0 and M00. I think each ...
Richard Hardy's user avatar
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1 answer
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How do I quantify the effect of a factor with many levels?

I want to look at the effect of brood ID on fledging success (a binary variable) in a sample of wild birds. Brood ID has ~150 levels. I have performed a likelihood ratio test comparing two logistic ...
Emadeel's user avatar
3 votes
2 answers
122 views

Replicate t or F test from regression using regression likelihoods

I've heard that the t-test and F-test we use to get the significance of our regression results are derived from the likelihood ratio test, but I'm having trouble replicating the p-value of the t/F ...
A Friendly Fish's user avatar
5 votes
4 answers
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Distribution of $Z^2 \cdot I(Z > 0)$ where $Z \sim \text{N}(0,1)$

When using the Likelihood Ratio test for testing particular hypotheses and attempting to obtain an size-$\alpha$ test, I run into the expression $$ \mathbb{P}\left( Z^2 \cdot I(Z > 0) > c \right)...
YessuhYessuhYessuh's user avatar
3 votes
1 answer
55 views

Why is it preferable to test the effect of a predictor using a likelihood ratio test?

In their fantastic book Applied Longitudinal Data Analysis: Modeling Change and event Occurrence Singer and Willett advocate a iterative model comparison technique for testing the effect of predictors:...
llewmills's user avatar
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How to report results from the likelihood ratio test of two lme models?

I am trying to find an appropriate way to report the results of the likelihood ratio test in a paper. I wrote: The likelihood ratio tests reported a significant main effect of FE (χ²(1)=6.06, p < 0....
Patlane's user avatar
2 votes
2 answers
43 views

How to compare 2 multiply imputed nested Cox proportional hazards models?

I've got 2 nested Cox models, which I fit to 10 imputed datasets. Pooling the regression coefficient estimates and associated p-values I've done already. I'm trying to work out if adding one extra ...
Isaac Allen's user avatar
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1 answer
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Constructing a one-sided hypothesis test for joint probabilties of negative binomial distributions

I am conducting research on Codling moth population/trap capture models. The end goal is to have a hypothesis testing model that will provide whether or not (at some significance level $\alpha$) the ...
Pacific Bird's user avatar
4 votes
2 answers
102 views

How do I work out the significance of main effects in negative binomial models with more than two factors?

I am trying to look at how the number of events X is affected by the three factors A (4 levels), B (2 levels) and C (2 levels) using a negative binomial model as follows: ...
Insect_biologist's user avatar
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30 views

Equivalent to likelihood ratio test for null and fitted generalized linear model (Gamma) in R?

I have a dataset of ellipses and I am trying to perform regressions with different categorical variables to see what influences different ellipse parameters the most. As was suggested in the answer to ...
ElizaBeso000's user avatar
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1 answer
57 views

Can I use the ratio of two p-values under two hypotheses as a likelihood ratio?

I am designing a simple study where I ask participants a problem. Then I code the answers as either correct or incorrect. I have a prediction from the literature that the percentage of correct answers ...
Denis's user avatar
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5 votes
1 answer
109 views

Does performing Likelihood Ratio Test to compare two nested LASSO models make statistical sense?

From what I've studied, the LRT is used to compare two nested models, i.e. 2 models having different sets of nested features, in my case e.g. Model1: binary_outcome ~ X1 + X2 Model2: binary_outcome ~ ...
Argh__1's user avatar
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3 votes
1 answer
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Karlin-Rubin theorem: relationship between test statistic having the MLR property vs being sufficient

Let's suppose we are trying to compare two hypotheses for a single parameter $\theta$. The null hypothesis $H_0$ is that $\theta = \theta_0$, and the alternative is that $\theta ≥ \theta_0$. The ...
Mike Battaglia's user avatar
1 vote
1 answer
89 views

Local Linearity vs Regularity Conditions for the asymptotic distribution of the Likelihood Ratio

In his book 'Asymptotic Statistics,' Aad van der Vaart when discussing the asymptotic distribution of the log-likelihood-ratio says: "The most important conclusion of this chapter is that, under ...
PMTokai's user avatar
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6 votes
1 answer
205 views

Permutation test for exponential null hypothesis: really bad?

Having found nice formulas for testing the null hypothesis under exponentially-distributed samples, I wanted to see how well permutation tests could do the job. And the answer, assuming no mistakes, ...
feetwet's user avatar
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1 vote
1 answer
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When and why is a likelihood ratio preferable to a difference as a test statistic?

We want to know whether two sample sets {x} and {y} were drawn from the same distribution. The null hypothesis $H_0$ is that they are. As statisticians we test the hypothesis by calculating the p-...
feetwet's user avatar
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8 votes
1 answer
861 views

What is a *likelihood ratio test* for a specific distribution, and how does it relate to hypothesis tests?

I'm just now being introduced to likelihood-ratio tests (LRT), and I am having trouble following the concept and terminology. For example, I posed a question about determining whether two samples {x} ...
feetwet's user avatar
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Likelihood ratio exponential family under permutation of parameters

I'm reading "ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD AND ITS VARIATIONAL APPROXIMATION FOR STOCHASTIC BLOCKMODELS" Bickel et al. 2013. In their proof of Lemma 3, they claim a result and I ...
Josh Willcox's user avatar
1 vote
1 answer
289 views

How to interpret DESeq results with LRT vs. with Wald's test

I am new to the field of RNA-Seq and wanted to ask for advice concerning the proper use of the two DESeq() test options (LRT vs. Wald test). Briefly, my ...
Luise Charlotte's user avatar
1 vote
0 answers
52 views

UMP two sided tests for exponential families

Consider a random variable $X$ with density $$f(x : θ) = C(θ)e^{η(θ)T(x)}h(x), θ ∈ Θ$$. Assume that $η(θ)$ is strictly increasing in $θ$ and that the family is full rank. Show that there will not be ...
user671269's user avatar
4 votes
1 answer
100 views

What are the degrees of freedom to consider for a G-test when some cells have expected values of 0?

Let's say I conduct a survey where people can mention their favorite color among four options (red, green, blue, yellow). After collecting the data, I create a contingency table crossing gender with ...
Daniela's user avatar
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1 vote
0 answers
69 views

Likelihood ratio as minimal sufficient statistics in infinite parameter space

I just read a question from here (Likelihood ratio minimal sufficient) and have some thoughts. Let me restate the question first: Consider a family of density functions $f(x|\theta)$ where the ...
Cyno Benette's user avatar
3 votes
1 answer
341 views

How to use the likelihood ratio test (LRT) to test whether a three-way interaction is significant?

Our hypothesis is that there is a 3-way interaction between A, B, and C. I have defined a model as follows: Y=A+B+C+AB+AC+BC+ABC+error I aim to use the likelihood ratio test (LRT) to determine if the ...
zjppdozen's user avatar
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3 votes
1 answer
180 views

Likelihood Ratio Testing for Binomial Distributions

I have a feeling this is a silly question. I am working on a research paper, at some point in it we perform a likelihood ratio test. The first guess would be to apply Wilks's theorem. However, if we ...
Al-Fahad Mohammed Al-Qadhi's user avatar
3 votes
1 answer
178 views

Residual likelihood ratio test for fixed effects in a linear mixed model

I know (but now I have doubts) that "Comparing models that are fitted with REML and differ in their fixed effects never makes sense," just as @BenBolker explains in this answer. I've been ...
dipetkov's user avatar
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4 votes
1 answer
87 views

Does the "log-likelihood" measure cover all details about model fit, like covariance structure, adjustments, robust variance estimator, etc?

Just a general statistical question: when any statistical software returns log-likelihood of some model, does it account for all details in it? For example, when we employ generalized least square ...
NadirCamzani's user avatar
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0 answers
129 views

Can be any example of testing contrasts using Wald's approach reproduced with Likelihood Ratio testing?

For illustration I will use R, but the question is general statistical question, totally not R related. Assume I have a numerical variable and categorical variable with 3 levels, like A, B and C, for ...
NadirCamzani's user avatar
4 votes
1 answer
291 views

Understanding residuals vs. fitted plot for a linear mixed model

I am modeling body mass (y var) according to indices of dysregulation for different physiologic systems (x vars). I did a likelihood ratio test, which supported using a linear mixed model, with a ...
burphound's user avatar
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1 vote
1 answer
36 views

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....
statquest's user avatar
1 vote
1 answer
186 views

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 ...
BulkySplash's user avatar
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0 answers
28 views

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 ...
snickerdoodles777's user avatar
1 vote
0 answers
35 views

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 ...
392781's user avatar
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0 answers
33 views

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 ...
newbie's user avatar
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1 answer
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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 ...
Tom Waits's user avatar
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