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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compute likelihood statistic with permutation test

This question is about hypothesis testing, where we want to use the likelihood ratio statistic with permutations test. Suppose we sample $n$ observations from the distribution $F_{XY}$, which is the ...
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Should you still report or interpret odds ratios on levels of a factor if the likelihood ratio test is not significant?

I am running a logistic regression to study the association between a three-level factor and a binary outcome, after controlling for covariates. My sample is small to medium (~800). The likelihood ...
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Is it legitimate to compare likelihood ratios from different datasets?

I have two nonlinear models, $M_1$ and $M_2$, where $M_2$ has all parameters of $M_1$ and a few additional ones. Since $M_2$ is more expressive than $M_1$, it will always be at least as good as $M_1$ ...
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LR test for overlapping return data using bootstrap

I wish to test a null hypothesis as in Christoffersen (1998) to see whether a sequence of Value-at-Risk forecasts $Q_t(p) \in \mathcal{F}_t$ possesses correct conditional coverage. Here $p \in [0,1]$ ...
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What exactly is the difference between LMR-LRT, adjusted LMR-LRT, and VLMR-LRT?

I'm trying to understand the difference between these models and all of the citations I'm finding seem to interchange the names, or in some cases confuse which came first. I'm pretty sure it was LMR, ...
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Which statistical test to compare same model with different parameters?

I have two datasets on people buying apples based on weight and price. One dataset in 2019 the other in 2020. I estimate a logit model with Utility = betaWeight * weight + betaPrice * price. Training ...
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Converting Log-Likelihood to Chi-square

I'm using two different algorithms to get a periodogram. One outputs log-likelihood and the other outputs chi-squared test statistic, but I would like a way to convert from log-likelihood to $\chi^2$ ...
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Finding region of rejection with likelihood ratio test

Let $X_1,\ldots,X_n$ be i.i.d. from a Gamma distribution with p.d.f. $f(x;\theta) = \theta^{-2} x e^{-x/\theta}$ for $x>0$ where $\theta$ is an unknown parameter. I would like to test the ...
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Monotone Likelihood Ratio for simple null vs composite alternative

I was studying the monotone likelihood ratio property. I have a small query. We know that once a distribution has a MLR in $T(X)$ for $\theta$ then I can test one sided hypothesis of the form $H_0:\...
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Critical region for an uniform distribution

Let $X_1, X_2, ... , X_n$ be a random sample from the uniform distribution over $[0, \theta]$. Suppose we wish to test $H_0 : \theta = 5$ versus $H_A : \theta < 5$ at significance level $\alpha = 0....
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Non-centrality of likelihood ratio test statistic chi2 under alternate hypothesis

I am having trouble understanding how to determine the non-centrality parameter of the $\chi^2$ distribution symptotically followed by the likelihood ratio test statistic if the data follow the ...
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On the test of significance under penalized likelihood estimation

I start using brglm2 package to implement logistic regression under a perfect separation problem. Is there any way to test the significance of the parameters using ...
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Likelihood Ratio Test for Averaging Two Regressors

How would I go about in formulating a likelihood ratio test to compare the fit of two models, one of them containing an average of two columns? For example, I would like to compare these two models: $$...
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Why use the Wald test in logistic regression?

Some statistical software use the Wald statistic when reporting on the regression coefficients. As examples, R and Stata report Wald by default. The logistic regression article on Wikipedia says, ...
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Likelihood ratio test for a discrete random variable with constraints on probabilities

Let us have a discrete random variable on points $(y_0,y_1, ..., y_d)$ with probabilities $(p_0, p_1, ..., p_d)$. We would like to check hypotesis $H:$ $p_1 = p_2 + p_3 + p_4$ with Likelihood ratio ...
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Uniformly most powerful test does not exists

I am having tough time understanding this concept The book says: “We caution the reader that UMP tests for testing H0 : θ1 ≤ θ ≤ θ2 and H0′ : θ = θ0 for the one-parameter exponential family do not ...
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Generalized Likelihood Ratio Test with null hypothesis defined by union of sets

Suppose you have a model with likelihood $ \mathcal L(\theta;\boldsymbol X) $, where $\theta \in \Theta$ are parameters and $\boldsymbol X = (X_1, \ldots, X_n ) $ denotes i.i.d. data. Likelihood ratio ...
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On the P-value of the variance of random intercept in glmer model

I'm using a logistic mixed-effect model with random intercept through glmer function from lme4 package. I want to test the ...
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Likelihood Ratio test returns negative deviation

I've ran the likelihood ratio test (statistc in 3rd row and p-value in 4th row) between the APARCH and the GJR. For some of the time series in analysis it returned a negative value for the test ...
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How can we select the best GARCH model by carrying out likelihood ratio test?

I have carried out the likelihood ratios of different GARCH models. GARCH(1,1) and GARCH(1,0)- Rejected null hypothesis so I chose GARCH(1,1) to do more sophistication. GARCH(3,1) and GARCH(1,1)- ...
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How to calculate confidence intervals for logistic regression predictions? How does `statsmodels` do it in `summary_frame`?

I am fitting a logistic regression in Python's statsmodels and want a confidence interval for the predicted probabilities. This has been easy to get using ...
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How to calculate p-values in a glmer with multiple explanatory variables using likelihood ratio tests in R

I would like to ask a quite general question about how to use likelihood ratio tests to calculate p-values in a glmer. The goal is to report these in a paper to show whether each of the explanatory ...
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Nested Model Comparison via AIC

As you know, Log likelihood Ratio Test(LRT) for nested model is well orgarnized. Especially, we can test whether null model is rejected or not by using the fact that LRT test statistics follow chi-...
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Failing to obtain $\chi^2(1)$ asymptotic distribution under $H_0$ in a likelihood ratio test: example 2

I have a large sample (a vector) $\mathbf{x}$ from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test the null ...
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Failing to obtain $\chi^2(1)$ asymptotic distribution under $H_0$ in a likelihood ratio test: example 1

I have a large sample (a vector) $\mathbf{x}$ from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test the null ...
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Asymptotic null distribution of the LR statistic with point null and point alternative

I have a large sample (a vector) $\mathbf{x}$ from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test the null ...
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1answer
39 views

Testing a nonstandard hypothesis: constructing test statistic, finding rejection region and obtaining $p$-value

I have a sample of size $n=1$ (a single observation $x_1$) from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test ...
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Likelihood ratio test for Markov orders - What succession of tests?

I want to estimate the Markov order of a binary sequence. For that I calculated transition matrices and the log likelihoods for the orders of interest 0,1,2 and 3. Essentially the one with the highest ...
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The procedure of adding interaction terms in regression models

What is the more sensible way to add interaction terms in regression models? I have a basic model which includes only the main effects. To add interactions to the basic model, do I add all of them at ...
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Does the R anova() or car::Anova() care of the type 1 error being a series of LR tests over nested models?

As in the question. Isn't it that the output of anova(model, model_reduced) or car::Anova(model, type=3) makes the problem of multiple comparisons? What about the aov(), which is type 1 ANOVA, but ...
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KL-divergence log likelihood ratio negative value

I have been trying to understand and implement KL-divergence for two normal distributions. However, one thing that I seem to be missing is how can KL-divergence always be a non-negative value, if the ...
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Likelihood ratio test multiplying by 2

Regarding the likelihood ratio test. I can't seem to find an answer to why we multiply the log likelihood ratio's with 2. On wikipedia it says we multiply by 2, in order to mathematically, say they ...
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Determining the sample size for a counting experiment

In a simple hypothesis testing, the sample size N is fixed in advance of the experiment. However, in a counting experiment in particle physics, people often define the observation time within which ...
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Is there a G-test equivalent for continuous variables?

The G-test is similar to the chi-square test for goodness of fit. It is proportional to the kl-divergence. I am wondering if there is a similar test that is applicable to continuous variables. Since ...
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Likelihood Ratio Test for model selection

I have a dataset with 6 variables, a1, a2, a3, a4, a5, a6 the outcome is Y. This is the model fit statistics after including only first three variables , a1,a2, a3 ...
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Comparing model efficiency

I hope you all don't mind me asking this question. I have two models : general linear mixed effects model ...
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How to report the results of a Likelihood-Ratio-Test (LRT) from the anova() R function

My goal is to compare different regression models and to textually report the comparison. However, I'm not sure what and how to report based on the information provided by the following output: ...
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Assumptions of Likelihood Ratio and Chi-Square tests for a 2x2 table?

In testing independence in a 2x2 contingency table, are the assumptions of the Likelihood Ratio and Chi-Square tests the same or do they differ?
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Neyman-Pearson hypothesis testing and composite alternative hypothesis

I am in love with the idea of setting up a statistical test à la Neyman-Pearson when possible, because it is just so intuitive. Most of times, $H_0$ is some kind of point hypothesis, but $H_1$ is ...
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How to interpret significant likelihood ratio and insignificant Chi-square tests?

To analyze frequencies in a 2x2 table, I ran a statistical test procedure using SPSS. It returned a p less than .05 for the likelihood Ratio but greater than .05 for Chi-Square and Fisher Exact Test (...
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Degrees of freedom for asymptotic likelihood ratio test?

When testing: $H_{0}: p_{1}=p_{2}=p_{3}$ vs. $H_{1}$: at least one is different With the asymptotic likelihood ratio test, by Wilk's theorem, how many degrees of freedom would the Chi-square ...
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Likelihood ratio test for nested model

I'm having a question about a likelihood ratio test in favor of the simpler, nested model. Assume we have a complex model $M_1=(\alpha, \beta)$, that correctly describes the data, and another, nested ...
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Is there a different name for a non-asymptotic chi-square difference test or is it always a Likelihood Ratio Test?

I already know that $-2log(Likelihood Ratio)$ is asymptotically $\chi^2$ distributed according to Wilks' theorem. It seems that a comparison of nested models involving computing the difference of $\...
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Finding the likelihood ratio to test which distribution has the largest mean

The problem: Let $X_1, \ldots, X_n$ and $Y_1, \ldots, Y_m$ be two i.i.d. samples drawn from $\mathcal{N}(\mu_x, \sigma^2)$ and $\mathcal{N}(\mu_y, \sigma^2)$, respectively. I wanna test $H_0: \mu_x \...
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How to do liklihood ratio test comparing two models using pchisq [duplicate]

This questino doesn't answer my question since it is asking about lrtest and pchisq comparison I am simply asking that how to do likliehood test for 2 models using ...
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How to do liklihood ratio test comparing two models [duplicate]

This questino doesn't answer my question since it is asking about lrtest and pchisq comparison I am simply asking that how to do likliehood test for 2 models using ...
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23 views

What does the “e” stand for in the notation of generalized likelihood ratio testing?

From Larsen and Marx, I read the following: For notational simplicity, we denote $\max _{\omega} L(\theta)$ and $\max _{\Omega} L(\theta)$ by $L\left(\omega_{e}\right)$ and $L\left(\Omega_{e}\right),$...
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P-value of LR test

I've been studying more about GLRT (Generalized Likelihood Ratio Tests) and I came up with the following problem. Let $X\sim N(\theta,1)$ and consider the hypothesis $H_0:\theta\in[a,b]$ against $H_1:\...
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the interpretation of high likelihood ratio test statistic

In wikipedia, In wikipedia, the interpretation of high likelihood ratio test statistic is: High values of the statistic mean that the observed outcome was nearly as likely to occur under the null ...
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Likelihood Ratio Test Involving Two Separate (simple) Regressions?

I'm having some trouble conceptualizing the following in a paper I've come across: A remark is made on using a likelihood ratio test for the following hypothesis $$\begin{align} H_0: \beta_{1,1} = \...

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