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 ...

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How to test independence of two markov switching processes using likelihood ratio test

I would like to test for independence of two first order markov switching processes with two states each. I have read this can be done using the LR test (I know that this will be simulation based ...
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54 views

Likelihood Ratio Test statistic for the exponential distribution

I need to test null hypothesis $\lambda = \frac12$ against the alternative hypothesis $\lambda \neq \frac12$ based on data $x_1, x_2, ..., x_n$ that follow the exponential distribution with parameter ...
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64 views

Null-hypothesis testing and likelihood-ratio testing

In this book Wickens, T. D. (2002). Elementary signal detection theory. Oxford: Oxford University Press. You can read: and this confuses me as I thought that likelihood-ratio testing was a ...
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69 views

Likelihood Ratio vs Wald test

From what I've been reading, amongst others on the site of the UCLA statistics consulting group likelihood ratio tests and wald tests are pretty similar in testing whether two glm models show a ...
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25 views

G test with small observed counts (~zero)

I have an experiments that counts how many events happened during a certain period of time. The experiments is repeated many times in different "runs" (I have 65 runs). Here for example the list of ...
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1answer
15 views

Likelihood Ratio Criterion in EFA

This is in ref to pp. 54-55 in McDonald,R.P[1] in the context of exploratory factor analysis (EFA) ML estimation. The likelihood ratio criteria, to me, seems to be performing dual roles: I. Providing ...
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54 views

Likelihood Ratio Test for the variance of a normal distribution

I've found that the asymptotic LR test is used in simple vs bilateral hypothesis test in which it is impossible to actually compute the rejection region, or better, in which we would need to find a ...
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1answer
23 views

Why is the noncentral chi-squared approximate of the deviance bad?

The statistical model under consideration is given by the independent realizations of two independent binomial distributions: $$ x_1 \sim \mathrm{Bin}(n_1, p_1), \quad x_2 \sim \mathrm{Bin}(n_2,p_2), ...
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59 views

Why is there an intrinsic trade off between the probability of detection and probability of a false alarm in the operating characteristic?

I was reading some notes for fun on Binary Hypothesis testing and it claimed that there happens to be a tradeoff between the probability of detection (also known as the "power"): $$P_D = P(f(y) = H_1 ...
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35 views

Can the Operating Characteristic for the LRT be derived from minimizing Bayes Risk $ \varphi(f) = \alpha P_F - \beta P_D + \gamma$?

For fun I was reading some notes on Operating Characteristics and it said (paraphrased with notation definition): As Fig. 1 suggests (omitted from question), good detection probability $P_D = ...
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Is it possible to combine likelihood ratios if independence cannot be assumed?

Given a dataset with multiple likelihood ratios (LRs) for predicting Heart Failure: Previous Heart Failure = LR 2 Classical Exam Findings = LR 4 Previous Hypertension = LR 6 Assuming LR(Previous ...
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15 views

Likelihood ratio test in R for Generalized Pareto Distribution (GPD)

I am trying to use a likelihood-ratio test to compare between two Generalized Pareto Distribution (GPD) models. All the functions and packages I found are for Linear Models (LM) or Generalized Linear ...
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28 views

likelihood ratio test 0 degrees of freedom?

Would the results from a likelihood ratio test with 0 degrees of freedom not be interpretable? From what I understand, by definition when the degrees of freedom = 0, chi-squared = 0 thus making the ...
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1answer
36 views

Hypothesis testing using likelihood ratio test for a given value of $\alpha$, data from uniform

If $Y_1,Y_2,...,Y_n$ ~ $U[0, \theta]$, and we want to test $$H_0: \theta=\theta_0$$ $$H_1: \theta < \theta_0$$ what would be the likelihood ratio test for a given $\alpha$. What I know so far: ...
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26 views

Likelihood ratio test when multicollinearity is present

I want to compare two nested regression models using a likelihood ratio test to examine whether there is a statistically significant difference between the two models. However, there is ...
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25 views

likelihood-ratio test - models were not all fitted to the same size of dataset

I would like to test different predictors in a series of multi-level models for a dichotomous dependent variable. I use the glmer funtion from R's lme4 package to estimate my models. First step was a ...
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16 views

Likelihood ratio test: multiple observations

I have 32 samples and I can go through and calculate the likelihood of my observed data under different models and do a LRT for a given point under multiple models. However, is there a way that I ...
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38 views

Difference between pointwise mutual information and log likelihood ratio

I know this is a very silly question. But i came across some papers on statistical methods in natural language processing, particularly Ted Dunning's paper, and there i found the formula that he has ...
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32 views

Likelihood ratio tests and multiple testing

I'm running various likelihood ratio tests, and assessing the significance of each as a chi-sq test, using the difference in number of parameters as the degrees of freedom. There are quite a lot of ...
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31 views

Generalized likelihood ratio test - discrete data

Let $X_1, \dots , X_n$ be a random sample from an exponential distribution with the density function $f(x \mid \theta) = \theta \exp(-\theta x)$. Also $H_0 : \theta = 1$ versus $H_a : \theta \neq 1$, ...
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37 views

Likelihood-ratio test for three models?

The likelihood-ratio test is the optimal test for comparing the goodness-of-fit of two models. Is there some similar test that would allow me to test three models, or should I just compare models (A, ...
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103 views

Determining critical value of likelihood ratio test for two Poisson distributions

Let $X_1,X_2$ be two independent Poisson random variables with $X_1 \sim \text{Pois}(\lambda_1)$ and $X_2 \sim \text{Pois}(\lambda_2)$. Find the likelihood ratio test for $H_0:\, \lambda_1 = ...
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22 views

How to use the likelihood ratio test when I use dummy variable in lme model

I have a question about how to use the likelihood ratio test with dummy variables in lme model. I have six levels of nutrient treatment in my experiment, one is low, five are high. For the five high ...
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202 views

What are the ''desirable'' statistical properties of the likelihood ratio test?

I am reading an article whose method is fully based on the likelihood ratio test. The author says that the LR test against one sided alternatives is UMP. He proceeds by claiming that "...even when ...
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27 views

how to use the likelihood ratio test for model selection in the study with several subjects

In my study, I have 30 subjects, for each subject, I use likelihood ratio test to compare two models (nested logistic regression), and I get a chi-squared value and a p value like the result shown ...
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49 views

Likelihood ratio test for two independent poisson distributions

Suppose that $X_1, X_2, ..., X_n \sim Pois(\mu)$ and $Y_1, Y_2, ..., Y_n \sim Pois(\theta)$. $X$ and $Y$ are independent. Derive the likelihood ratio test of $H_0: \theta = \mu$ versus $H_a: \theta ...
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48 views

LMM: Model-comparison and evaluation

My problem is that the residuals of two models (that differ significantly) are not different, which confuses me. If two models are different, then surely we can expect the residuals from one of the ...
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90 views

Testing Fixed and Random Effect of Mixed Model

This pdf illustrates nicely how is to test the random effect of multilevel model . But I am simulating data from a two-level model and estimating the parameters of the model for various combination of ...
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22 views

Comparing influence of coefficents in cox regression (conditional logit)

I am estimating a discrete choice model (conditional logit) with the help of cox regression in SPSS. I would like to asses which of my coefficients has a greater impact on the model. So I ran a ...
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59 views

Comparing likelihoods from non-nested models

Short: I have a series of joint probabilities (likelihoods) for how likely sample $Q$ belongs to group $K$. I need to compute a p-value describing how "significant" the "top" group is compared to ...
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16 views

Given an transition matrix what is the likelihood an observed markov chain was derived from this matrix

To give a bit of background, I'm creating a MLE of a transition matrix from a set of empirical data. I'm then creating a simulation of the system that also produces a markov chain. I am looking for a ...
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2answers
158 views

BIC selection yields much smaller model than AIC - can I use the likelihood ratio test to compare?

I'm trying to model the data (not make predictions) and am NOT using lasso for this, just want to know if my plan is somewhat reasonable here: I'm modelling for a "yes/no" response variable, so I ...
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163 views

Ways to find a UMP test

I'm studying for my final exams and the subject of proof will basically test hypotheses, I will try to summarize here my doubts. For found the UMP test the ways are 1) Use Neyman–Pearson lemma ...
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1answer
31 views

Simple Cox-related question regarding the LR test

I'm writing the Results section of a paper: If the LR-test for a Cox proportional hazards model is not significant, but one of the predictors is significant, does one (usually) report the covariate's ...
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1answer
81 views

Likelihood ratio for normal distribution with known variance

Let $X_1,...,X_n$ random sample of $X$~$N(\mu,\sigma^2)$ with known $\sigma^2$.Take $a=.05$ find the expression for power function of the likelihood-ratio test $$H_0:\mu\leq 0\space vs\space ...
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1answer
94 views

Likelihood-ratio test

I was studying on this subject and I got some questions. Lets take the test $$H_0:\theta\in\Theta_0 \space vs\space H_1:\theta\in\Theta_0^c$$ where $\Theta$ is the parametric space and ...
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34 views

What does this terminology mean in this introduction to likelihood ratios?

I am currently reading In All Likelihood by Yudi Pawitan (2013 edition) and I am making my way through the second chapter on the likelihood function. In part 2.4 which is where likelihood functions ...
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177 views

Likelihood ratio test in Poisson distribution

I have a dataset that describe the number of passengers that fly with an airline per day. The airline guesses that on average 1300 passengers fly per day and I want to test this hypothesis using a ...
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1answer
67 views

LRT for one-sided Bernoulli parameter

Suppose $X_1,X_2,...,X_n$ are i.i.d. $\mathrm{Bernoulli}(\theta)$. We are interested in testing the hypotheses $$H_0:\theta\leq\theta_0$$vs. $$H_1:\theta>\theta_0$$ Show that if we use the ...
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2answers
250 views

R - Why does lrtest() not match anova(test=“LRT”)

I was looking for ways to do a likelihood ratio test in R to compare model fits. I first coded it myself, then found both the default anova() function and also lrtest() in the lmtest package. When I ...
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1answer
129 views

Likelihood-based hypothesis testing

$N_A$ and $N_B$ are variables of the counts of the number of events 'A' and events 'B' respectively. Those variables follow Poisson distributions with parameters $\lambda_A$ and $\lambda_B$. In ...
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1answer
112 views

likelihood ratio test with constrained null hypothesis

I am trying to understand a fundamental property of the Likelihood Ratio Test (LRT). For simplicity, the following example is framed as binomial data, which of course could be solved using a simple ...
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28 views

likelihood ratio testing

Let $Y_{1}, Y_{2}, \ldots, Y_{n}$ denote a random sample from a $N(\theta,\ \sigma^{2})$ population. Consider testing $H_{o}: \theta\geq\theta_{o}$ versus $H_{a}: \theta<\theta_{o}.$ If ...
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1answer
163 views

False Coverage Rate for confidence intervals of positive likelihood ratios of multiple dependent tests

I want to calculate confidence intervals of positive likelihood ratios of multiple dependent tests. To adjust the confidence level for the 'problem of multiple comparisons', I believe I should ...
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1answer
99 views

Eliminating a nuisance parameter in likelihood ratio test

I am having an argument with a co-author about how to eliminate a nuisance parameter in a simple likelihood ratio test and am hoping that the community helps us settle it. Our data $\mathbf{x}$ can ...
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58 views

Likelihood ratio test to choose between components of gaussian mixture model?

I have a Gaussian Mixture Model with 2 components. Is it possible to use a likelihood ratio test to determine the point at which the probability of being in component A is the same as being in ...
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1answer
110 views

I don't understand Chi squared

I think of the contingency table test. In all textbooks I've seen, the test statistic is calculated as the sum of $(O-E)^2/E$ over all cells. But the degree of freedom is not the number of all cells. ...
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185 views

fitdistr among Cauchy / Student-T / Normal distributions in R

I am posting this, hoping that it will also be useful to others. see also Fitting t-distribution in R: scaling parameter . my data series x is fat-tailed, 1063 obs. it seems straightforward to ...
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1answer
320 views

Neyman-Pearson lemma

I have read the Neyman-Pearson lemma from the book Introduction to the Theory of Statistics . But I have not understood the lemma . Can anyone please explain me the lemma in plain words ? What ...
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70 views

Likelihood Ratio approximation for Gaussian mixture models

I’ve been wondering about this question for few weeks now and hoped you might be able to help me with an answer: Following Wilk’s theorem, we know that the log likelihood ratio test is asymptotically ...