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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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Likelihood ratio test, Wald test and LM test for variance of a normal distribution

Let y1, y2....yt follow a N(0,sigma^2) distribution. [Note that the mean is zero and you know that it is zero]. Derive the LR, LM and Wald test of hypothesis sigma^2 = 1. I have got the MLE, the ...
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ANOVA selects a model with autocorrelated residuals

I want to know which temperature dataset (Aa1, Bb, Cc, Dd) is/are the best predictor for laying date (medini). First, I used simple linear regression: median...
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Statistical test to compare the mean of two samples

There's a competition with 20 categories, and each category has 3 winners. I have an array of the winner's performance of the next year (60 values), and other array with the average of the competitors ...
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Select mixed model same degree of freedom

When I have a two mixed models (lme function) with different df then ANOVA summary shows the p-value of likelihood ratio test as following : ...
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How much bias am I risking by doing model goodness of fit comparison without accounting for clustering?

I am interested in testing whether an interaction term is statistically significant or not in a logistic regression. Data is large and observations are clustered by family and suffer from sparsity for ...
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Reproduce figure of “Computer Age Statistical Inference” from Efron and Hastie

The summarized version of my question (26th December 2018) I am trying to reproduce Figure 2.2 from Computer Age Statistical Inference by Efron and Hastie, but for some reason that I'm not able to ...
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confusing result from likelihood ratio test when covariate is factor

I got really confusing result from likelihood ratio test. I'm using mtcars data as an example. The following code works as expected. In ...
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Calculating the relative likelihood with AIC values

I'm using AIC for model selection, and would like to use a relative likelihood measure to quantify how many times a model with minimum AIC (AICmin) fits better than the alternative (with AICi). For ...
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Comparing nested models with orthogonal predictors using the t-statistic

Imagine we have a pair of nested models. Model A includes $n$ terms. Model B includes $n+m$ terms. To assess the "value add" of ...
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Calculating Log-Likelihood of Logistic Adaptive-Quadrature GLMM for Comparison with Fixed Model

Fitting a binary logistic GLMM here, with ungrouped data (all responses either 0 or 1). It says in this thread and in the documentation of anova.merMod that the ...
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Degrees of freedom of likelihood ratio test with equal dimension on the null and the parameter space?

Let $x_1,\dots,x_n$ be iid samples from a $N(\mu,\sigma^2)$ and consider the hypotesis $$H_0:\theta\in\Theta_0,\,\,\,\,\,\,vs\,\,\,\,\,\,H_1:\theta\in\Theta _{0}^c$$ where $\Theta _{0} = \{\mu>0,\...
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What should my critical region look like in this LR test for shifted exponential distribution with pdf $e^{-(x-\theta)}\mathbf1_{x>\theta}$?

I have a small confusion over describing the cutoff point for the critical region in a likelihood ratio test when the null hypothesis is composite. Take this exercise in particular: Let $(X_1,X_2,\...
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Basic likelihood ratio test

I should perform a likelihood ratio test on the following null hypothesis : α = Aψ where α and A (p * m) are known vectors. ψ (m*r) is a matrix of free parameters. The likelihood ratio test is ...
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LR test for VAR model selection: p value goes increases and then decreases

I have a question on VAR model using LR test to select the lag lengths. My result is shown below and you can see that LR test rejects lag 4, so seemingly I should use lag 3. But then lag 5 has p-value ...
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Likelihood Ratio Given Conditionals

For each person, I have at least one report indicating whether they have a disease or not. I have the actual disease status of a decent chunk of this population, and I'd like to be able to predict ...
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Why is the false acceptance probability not improving with increasing sample size?

We have a normal distribution with zero mean. We have two hypotheses for the variance $\sigma^2$: $$H_0: \sigma^2=\sigma_0^2$$ $$H_1: \sigma^2=\sigma_1^2$$ We make $n$ independent observations $X_1, ...
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Are EFA and/or ESEM models on the same data set with different factor solutions nested models?

Are EFA and/or ESEM models on the same data set with different factor solutions nested models? If yes, how are they nested? Are EFA and/or ESEM models and more restrictive CFA models on the same data ...
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Different p-values for coefficients and LRT in univariate cox regression (coxph R)

I have used Cox PH to test the relationship between one predictor and survival for 6 patients. Cox PH was used since the predictor is continuous. Using the "cox.zph" function, there was no significant ...
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difference between Wald and LR in Anova(car) and p-values

I am having difficulty understanding the p-values of a Anova(glm) in the car package in terms of Type II error. Are they testing ...
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Why always AIC and BIC are used in mixture model than Vuong test

I am working with mixture models. I fitted more than one model to the data and then try to select the most appropriate model using different selection criteria, for example, AIC. My supervisors asked ...
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Philosophy behind “hypothesis” in Bayes factor

The posterior odds is the ratio of the Bayes factor $\times$ prior odds of the hypotheses. $\frac{p(H_0 | D)}{p(H_1 | D)}$ = $\frac{p(D | H_0)}{p(D | H_1)} \frac{p(H_0)}{p(H_1)}$ It is considered a ...
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How to obtain a power curve from a likelihood ratio test for linear regression as a function of varying a coefficient of the more complex model?

I am currently doing a test of model complexities for two linear regression models: First Model: $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$ vs. Second Model: $Y = \beta_0 + \beta_1X_1 + \...
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Joint probability of multivariate normal distributions with missing dimensions

Suppose I conduct two experiments, each measuring a subset of possible parameters. From experiment #1 I measure two parameters and estimate the multivariate normal distribution $$ \mathbf{X}_1=\left [...
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Is there a special meaning behind a hypothesis test that consistently report 0.5 as the p-value? [closed]

I have been conducting Likelihood Ratio Tests on Full and Reduced form linear models and there is a specific scenario where I consistently obtain p-values of 0.5. I am wondering if there was a special ...
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Comparison of nested regression models vs predictor's significance within model

I am building regression models to evaluate the effect of several characteristics of genetic variants (my predictors) on a handful of phenotypic parameters (continuous and binary - hence I am building ...
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Is this model “nested” and fit for LR Test?

i want to see if different dummy variables are capturing significanly different effects from one another so i am running LR tests in which two (of the 4) dummies independent variables are merged in ...
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Likelihood ratio test normalization for performance evaluation

I'm performing a log-likelihood ratio test on simulated data and I want to derive a ROC (receiver operating characteristic). In order to do this I follow these steps: I create N false alarm dataset (...
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GLRT Inconclusive for Gaussian Detection

When constructing a detection test between two Gaussian vectors, I have $H_0: \mathcal{N}(0,\sigma_n^2)$ and $H_1: \mathcal{N}(0,\sigma_n^2+\sigma_s^2)$, and $\sigma_n^2$ is unknown while $\sigma_s^2$ ...
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Likelihood Ratio Testing For Model Selection

I have seen, in various places, the likelihood ratio test being used to compare models. From my understanding, the likelihood ratio statistic is very useful because Wilks Theorem shows that ...
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75 views

Reporting betareg outcome - how to compare non-nested models?

I am looking for advice how to gain and report results using beta regression for an ANCOVA-like model. My model is as follows: ...
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LRT and $\text{Uniform}(0, \theta)$

We have one observation of variable $X$ that is distributed uniformly on $[0, \theta]$. Null hypothesis is $H_0 \colon \theta = 1$ and alternative hypothesis is $H_1 \colon \theta = 2$. What is the ...
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Analysing Repeated Measures RCT study. emmeans / lsmeans estimate and back-transform problems. Approach doubts

Background I am writing a project on a big multicenter RCT study, where subjects are following different dietary patterns for 2 years. I have access to their dietary intakes and I am grouping them in ...
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When to use Neyman Pearson or Likelihood ratio

question about Neyman-Pearson lemma vs the likelyhood ratio. From my textbook it says that if you want to test: $H_0: \theta \in \Theta_0$ vs $H_1: \theta \in \Theta_0 ^ c$, then you can use a LRT $...
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LR test of merged dummy coefficients in a Heckman

i'm running a Heckman test and want to demonstrate if different dummy variables have a statistically similar effect. im performing an LR test by first running the full Heckman, storing the log-...
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testing the null hypothesis that two coefficients are equivalent (LR)

I'm running a replication study on Livingston's (2005) examination of reputational effect on online auctions. sellers are divided into dummy quartiles based on their feedback scores. I have run a ...
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LRT of normal distribution - explanation of numerator

Let $X_1,...,X_n$ be random sample of $X$~$N(\mu,\sigma^2)$ with known $\sigma^2$. I am trying to derive test statistic for that distribution I know that $\hat{\mu}=\overline{X}$ $$\lambda(x)=\...
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R or Stata shortcut to significance test interaction term including restricted cubic splines?

I fit the following model in R using the lme4 package, which is a linear mixed effects regression of outcome "WT_abs_change" (absolute weight change) on various factors, including "ns(WT_dtime, df=3)*...
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How to use bootstrap to do a hypothesis test in mixed models

I have a mixed model with multiple covariates. I want to test if some of the covariates are insignificant. Since I have mixed model the LR-test will result in a p-value which is too low, hence I want ...
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Probability of sample point given a Linear Regression

This question may be ill-posed, but hopefully you all can help talk me through it. Given a probability density function $f(\cdot)$ parameterized by one or more parameters $\theta$, we can compute the ...
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LRT for PRT both unknown

I have a random sample of ${X_1,...,X_n}$ from the following pdf: $${\theta \beta^ \theta \over {x^{\theta+1}}}$$ where $\theta>0$, $\beta>0$, $x\ge\beta$ I want to find the LRT to test $H_o:\...
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How to adjust for the number of nested model tests?

How should I adjust for the number of tests I do when using the likelihood ratio difference test in a model estimated using maximum likelihood (or some flavor of), where the null hypothesis of the ...
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Deriving LRT for comparing two sample proportions

I have two sample proportions, and want to test: $$ H_0: p_1 = p_2 \quad \text{vs.} \quad H_a: p_1 \neq p_2 $$ i.e., that they really come from distributions with the same common probability $p$. My ...
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Optimal Neyman Pearson Test and Decision Region

I am working on a problem but i stacked. Suppose that $x_1$ and $x_2$ are jointly distributed Gaussian random variables. There are two hypotheses for their joint distribution. Under either ...
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Likelihood ratio test between two hypothesis [closed]

I have two hypothesis as below: Under $H_1$, $f_x(x) = 3/2 * x^2$ where $x \epsilon (-1,1)$ Under $H_0$, $f_x(x) = 1/2 $ where $x \epsilon (-1,1)$ What is the maximum likelihood decision rule to ...
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Likelihood ratio test for finite parameter space

Suppose $X_1 \ldots X_n$ are iid generated by $Norm(\mu, \sigma^2)$. We usually use likelihood ratio test on a parameter with a continuous parameter space, like $H_0: \mu = 0$ vs $H_1: \mu \neq 0$. ...
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What are the degrees of freedom for the chisquared distribution for comparing values within a likelihood function?

Let's say I have a likelihood function for a vector X. I get this as dnorm(X, mean(X), sd(X) Obviously the MLE will be the mean here. But let's say I want to ...
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Reason for making hypotheses and hypotheses tests?

I'm currently studying hypothesis testing and this question has been appearing in my thoughts quite frequently. It seems to me that the hypothesis tests (at least at an introductory level) concern ...
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Why do we use $\chi^2_{1-\alpha}$ as test statistic when conducting likelihood ration test?

I understand that when given significance level $\alpha$ and have obtained $-2ln(\Lambda)$ , we have to compare it with $\chi^2_{1-\alpha}$. Can anyone explain to me why we compare with $\chi^2_{1-\...
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Should p-values for chi-square and likelihood ratio chi-square tests be identical when estimated by Monte Carlo simulation?

The question and answer here suggest that the answer is “yes,” but my own analysis in SPSS suggests otherwise: Note: I understand that the likelihood ratio chi-square and chi-square test are expected ...
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Performance of likelihood ratio chi-square and chi-square test when table contains both relatively large and small expected counts

Agresti (1990) writes the following about the likelihood-ratio chi-square [1]: The χ2 approximation is often poor for G2 when n/c < 5. When c is large, it can be decent for χ2 for n/c as small ...