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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Does likelihood ratio has any meaning in this case?

Let $Y$ be a real-valued random variable and $X$ a random variable with realizations in $L^2[0,1]:=L^2([0,1],\lambda)$, where $\lambda$ is a Lebesgue measure. Consider some functional ...
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Testing sequentially nested models

Assume I have a simple model with (at least) four parameters $\beta_1, \beta_2, \beta_3, \beta_4$. If I would want to test $H_o: \beta_1 = \beta_2 \& \beta_3 = \beta_4$ by using the likelihood ...
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Random- and fixed-effects structure in linear-mixed models

Consider the following data from a two-way within subjects design: ...
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Understanding confidence intervals in Firth penalized logistic regression

I recently discovered penalized likelihood ratio methods to cope with sparse and/or separated data. I'm having some problems though in understanding the results a logistic regression using Firth ...
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30 views

Finding maximum likelihood estimates of parameters of multiple normal populations

I've just started studying maximum likelihood and likelihood ratio tests. I've calculated the maximum likelihood of a normal population with unknown mean and variance. However, I've been given this ...
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40 views

Probability of a model given an image

I would like to write the likelihood function for an image with respect to theoretically predicted values. Assuming uniform Gaussian noise, the pixels are statistically independent, and we can write a ...
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53 views

Compare poisson and negative binomial regression with LR test

My question is related to the question Compare negative binomial models. I have some difficulties understanding UCLA guide in http://www.ats.ucla.edu/stat/r/dae/nbreg.htm (I am using ...
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188 views

Why do p values for test of likelihood ratio vs Fisher's Exact Test not agree

In a 2x2 analysis of categorical data, what causes the p value for the test of the likelihood ratio to differ from both the Fisher's Exact Test and the test of linear-by-linear Association? ...
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Joint significance testing w/ large samples

long time listener, first time caller. Unfortunately I can't show code as the computer the analysis is done on has rather tight security. I need to test for joint significance in a logit model that ...
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34 views

Generalized likelihood ratio test

Does anyone use the generalized likelihood ratio test for detecting a sudden change in time series forecasting (ARIMA Model)? A paper by Bonne Zhu uses this technique for anomaly detection, but I ...
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1answer
83 views

Likelihood ratio test for comparing two exponential distributions

I am trying to use a likelihood ratio test to compare the parameters of two exponential distributions. by this thread Likelihood Ratio for two-sample Exponential distribution I found that I can use ...
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133 views

Testing whether the coefficients of one model and another are statistically significantly different

I am currently testing two models which have the exact same specification except for one is when z=0 and when z=1, where z could be something like male and female. Essentially, the effect of X on Y if ...
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Degrees of freedom when splitting populations

I have a question relating to degrees of freedom when I have a number parameters in a model for a population, and then I want to split the population. Say for a certain population I have a the ...
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Help finding critical on a hypothesis contrast

I´ve tried finding the variance using the moment-generating function but apparently that is not the correct method for finding the critical. Can you help me with this?
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Compare linear mixed models with Likelihood ratio tests and significant fixed effects

I am comparing two models with likelihood ratio tests and I have found the -2LL increases with the more complex model (when a 3-way interaction between 3 fixed effects is included). However, the tests ...
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160 views

How to choose between exponential and gamma distributions

I have same data and I would like to choose a model for it. To start with I fit an exponential distribution and a gamma distribution. Now I wanted to do a simple likelihood ratio test . However, I ...
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44 views

Normalized likelihoods

AIC (BIC) model selection methods are widely used. These methods can select non-nested models unlike likelihood ratio type selection that requires model to be nested. The AIC has definition ...
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Likelihood Ratio as statistical test for Transfer Entropy with MatLab

I estimated a Transfer Entropy value TE(XY). Now I want to establish the statistical significance of the estimated value. Therefore I used the method of shuffled surrogates to estimate a shuffled ...
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57 views

Likelihood ratio test to determine if average number of accidents has dropped?

I can't find any worked (non-trivial) practical example for a likelihood ratio test, believe me I have spent hours looking. Here is a question I've been trying to complete but I can't get any further. ...
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Motivating likelihood ratio test vs Wald test for paper reviewer

I've got back reviews for a paper I've submitted, with the following problem. I have two logistic regression models, say y ~ A, and y ~ A + B, where B is a factor with several levels. I have ...
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54 views

Constrained Maximization and Likelihood Ratio Tests for Nested Linear Models

Suppose $\boldsymbol \beta \in \mathbb{R}^k$ is a vector of coefficients for a generalized linear model with $g \left[ E(Y|X) \right] = X\beta$ for a link function $g$ and I wish to test the composite ...
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Generalized log likelihood ratio test for non-nested models

I understand that if I have two models A and B and A is nested in B then, given some data, I can fit the parameters of A and B using MLE and apply the generalized log likelihood ratio test. In ...
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259 views

Question about Dynkin Lehmann Scheffe Theorem

I'm self-studying for an examination, and I would like to understand how to use the Dynkin Lehmann Scheffe theorem for an applied question. I am using Bickel and Doksum's "Mathematical Statistics" ...
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Clarification on interpreting Wald's test and Likelihood ratio tests

I am running multinomial logistic regression analysis on my data. The response variable is the number of calves produced each year (0,1, or 2). I am trying to evaluate the influence of the X ...
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Goodness of fit likelihood ratio test with zero values

I have a vector of observed frequencies that have zero values in some cells and a vector of expected frequencies generated by a model. I would like to do a likelihood ratio test rather than a chi ...
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129 views

Hypothesis Testing of endpoint of Uniform distribution

Let $c$ be a positive constant. Suppose I have $X$~$Unif(0,\theta)$ and I wish to test the null hypothesis $H_0: \theta \leq c$ against the alternative hypothesis $H_1:\theta > c$. Suppose I did a ...
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269 views

Why doesn't Wilks' 1938 proof work for misspecified models?

In the famous 1938 paper ("The large-sample distribution of the likelihood ratio for testing composite hypotheses", Annals of Mathematical Statistics, 9:60-62), Samuel Wilks derived the asymptotic ...
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fitting LMEMs for repeated measures with no correlation between intercept and slope

For a simulation study, I contrast the power of different LMEMs for repeated measures. To get p-values, I use likelihood ratio tests where I compare a model including a fixed treatment effect with one ...
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293 views

What are the regularity conditions for Likelihood Ratio test

Could anyone please tell me what the regularity conditions are for the asymptotic distribution of Likelihood Ratio test? Everywhere I look, it is written 'Under the regularity conditions' or 'under ...
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293 views

Wald test and Likelihood ratio test, where do the confidence intervals on the regression coefficients come from?

So I'm trying to build my own Wald test and likelihood ratio test code within a machine learning pipeline. I can get the final fitted logistic regression coefficients from liblinear. I'm coding in ...
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38 views

Likelihood ratio tests versus signed likelihood ratio tests

What is the difference between likelihood and signed likelihood ratio tests (SLRT)? What is the use of having the "sign" function in it? In short, what is the advantage of having SLRT over LRT? ...
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How to formulate a likelihood ratio test for an exponential distribution? [duplicate]

Find the form of the likelihood ratio test of $H_0 : \lambda = \lambda_0$ against $\lambda\neq\lambda_0$ when $X_1,X_2,...,X_n$ is a random sample from $Ex(\lambda)$. Simplify it as much as ...
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327 views

Neyman-Pearson lemma: critical region and hypothesis testing

Let $X_1,X_2,...,X_n$ be i.i.d r.v's with common p.d.f. $$ \mbox f(x)=\frac{x^5e^{-x/\theta}}{5!\theta^6} $$ where $\theta$ > 0. Show that the Neyman-Pearson lemma produces a test of ...
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Type I error in t tests and LRT

In situations where unequal variance t-test is appropriate, if we use equal variance t-test, type I error would be inflated. I created a likelihood ratio test (LRT) equivalent of unequal variance ...
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255 views

Likelihood Ratio Test and boundary parameters

The chi-square approximation of the distribution of the test statistic in Likelihood Ratio Test (LRT) may not be reliable if a parameter of a model is on the boundary of a parameter space --- is ...
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52 views

Likelihood ratio test statistic

Let $X_{1},..,X_{n}$ be a random sample from a normal distribution with mean ${\theta}$ and variance 1. Let $H_{0}:{\theta}=0$ and $H_{1}:{\theta}{\neq}0$. Using likelihood ratios, show the critical ...
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43 views

hypothesis test likelihood ratio

Let $X_{1},..,X_{36}$ be a random sample from a bernouilli distribution with parameter $p$. Suppose the sample probability is $1/3$. Using a norml approximation and likelihood ratios, we wish to test ...
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217 views

Log-Likelihood Ratio Test: Difference of Equations

I have noticed that the sign at the front of the log-likelihood ratio formula changes depending on what source I have been looking at. Below are the two formula I have seen, exactly as they were ...
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What is the relationship between the GINI score and the log-likelihood ratio

I am studying classification and regression trees, and one of the measures for the split location is the GINI score. Now I am used to determining best split location when the log of the likelihood ...
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203 views

One-Sample t Test and Likelihood Ratio Test

Concerning testing the hypotheses about the mean $\mu$ of a single population I know of things like the One-Sample $t$ test where there is a null hypothesis: $H_0: \mu = \mu_0$, and a test statistic ...
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Empty asymptotic confidence interval?

I have a sample $x=(4, 3, 1, 2, 2, 2, 2, 5, 7, 3, 1, 2, 3, 4, 3, 2, 3, 3, 3, 4)$ of size $n=20$. from a binomial distribution with 10 trials and probability of success $p$. I am asked to construct the ...
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195 views

What is it meant by the “rejection region” and “power” of a likelihood ratio test?

Suppose that $X_1,...,X_n$ are i.i.d. data from a $N(\mu, 100)$ distribution. I am trying to find the rejection region for the likelihood ratio test for level $\alpha= 0.10$ of the test: $H_0: \mu = ...
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Autoregressive Markov chain simulation and the likelihood ratio test for Markov property

I am trying to estimate a Markov chain of second order (Markov chain that fulfills $P[X_t|X_{t-1},X_{t-2}]=P[X_t|X_{t-1},X_{t-2},...,X_{t-p}]$) using an AR(2) process. Once I have simulated the ...
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262 views

Hypothesis testing with Neyman–Pearson (finding cutoff quantile of Poisson dist)

I am currently trying to solve a problem that should be very easy, yet I am stumped, and help would be GREATLY appreciated!! The background of the question is this: Q: The number of typing errors in ...
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28 views

Ways the likelihood ratio test may fail

I have a question related to: Why is a likelihood-ratio test distributed chi-squared? On point 2 of @StasK's answer, he states: The theorem assumes that all the relevant derivatives are ...
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516 views

Reporting from a likelihood ratio test

I don't know if this belongs here or in StackExchange, it is a mixed but probably pretty simple question. How do I normally report a Likelihood Ratio Test? I would love a good reference in your ...
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179 views

Non-significant p-values for factor levels with only 0s in negative binomial glm using glm.nb() in R

I am trying to fit a negative binomial GLM to fish catch data with month of the year (factor) as my explanatory variable. I have selected the month with the greatest number of catches as my reference ...
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Comparison between Log-likelihood ratios and beta coefficients

I was asked a question recently which I could not find an answer for and was hoping someone could enlighten me. The question was regarding the significance of a single variable in a linear model. ...
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Likelihood ratio test - lmer R - Non-nested models

I am currently reviewing some work and have come across the following, which seems wrong to me. Two mixed models are fitted (in R) using lmer. The models are non-nested and are compared by ...
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Maximum power test

Question: In a count that was held a year ago in a reserve , there were 15 tigers counted. 7 females and 8 males, which were marked with numbers from 1 to 15. a. By recent reports, there was fear ...