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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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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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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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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77 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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19 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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104 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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10 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 ...
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76 views

Likelihood ratio tests using ML vs. REML

I am using Mixed effects models (nlme package in R) to choose the model with the best random and fixed effects. I am following the procedure of Zurr et al. (2009) ...
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2answers
150 views

Likelihood Ratio for the Bivariate Normal distribution

For a random sample from a Bivariate Normal distribution with $\rho=\frac{1}{2}$ and equal variances, i.e. $\sigma^2_x=\sigma^2_y=\sigma^2$, I would like to derive the Likelihood Ratio Test for the ...
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54 views

lm and nls F test in R

I am trying to compare a linear model and other non linear models(Asymptotic, Logistic and Ricker) by means of an F test or a likelihood ratio test. I have tried anova(Linear, Logistic,Ricker, ...
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R lmerTest and Tests of Multiple Random Effects

I'm curious about how lmerTest package in R, specifically the "rand" function, handles tests of random effects. Consider the example from the lmerTest pdf on CRAN that uses the built in "carrots" ...
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Fit statistics and imputed data

I have a general question about pooling fit statistics when using multiple imputations. I am trying to pool the AIC, BIC, G-squared, or log likelihood across 10 imputed data sets. Is it possible to ...
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113 views

Can I use likelihood-ratio test to compare two samples drawn from power-law distributions?

I have to compare two large samples ($N = 10^{6}$) of discrete data drawn from power-law distributions to assess whether they are significantly different. I can't do that by means of a two-sample ...
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11 views

Heterogeneity test for risk factor association (hazard ratio/coefficient) in two or more different survival outcomes

Suppose I'm interested in comparing smoking category (current, ex, non-smoker) as a risk factor in two or more different but similar (considerably exclusive) outcomes, say lung cancer of different ...
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90 views

Likelihood ratio test disagrees with cross-validation results

I have computed two logistic models of the same data (for different formulas) in R, and compared them using likelihood ratio test: ...
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42 views

Likelihood Ratio and Expected Value Relationship

I am to prove that: 1) The expected value of (Λ^n|H_1) = E(Λ^(n+1)|H_0) 2)The expected value of (Λ|H_0) = 1 where Λ is the likelihood ratio. I know that the likelihood ratio is equal to ...
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84 views

Should I include this fixed effect? lme4 likelihood ratio test and lmerTest anova disagree

I have a mixed-effects model with two fixed effects and one random effect (group membership) estimated using lme4. log_dv ~ iv1 + iv2 + (1 | group) I want to ...
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15 views

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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382 views

Random- and fixed-effects structure in linear-mixed models

Consider the following data from a two-way within subjects design: ...
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136 views

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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49 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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1answer
46 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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1answer
188 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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251 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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47 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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210 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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184 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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14 views

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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39 views

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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188 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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1answer
50 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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68 views

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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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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90 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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135 views

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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277 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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421 views

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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132 views

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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194 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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296 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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50 views

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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1answer
521 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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445 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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39 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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59 views

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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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 ...