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 deal with zero-valued probability?

I have a few models which I would like to combine later on; for each model I have the sensitivity and specificity. I then calculate for each model the likelihood ratio to get a feel of how well the ...
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Is it correct to compare likelihood ratio indices between logistic regression and multinomial logistic regression models?

In the paper "Including Transfer-Out Behavior in Retention Models: Using the NSLC Enrollment Search Data" (http://www.studentclearinghouse.org/colleges/files/ST_UofMD_casestudy.pdf) the author ...
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Should I use an Odds Ratio or a Likelihood Ratio to report prevalence of x in a Case-Control study?

I am trying to report the prevalence data for a case control study. I first ran a $\chi^2$ test on a 2x2 table of the prevalence data. I got a $\chi^2$ and Likelihood ratio result in SPSS. It ...
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12 views

Queries regarding 'logistftest' function of logistf package for model comparison

I am a user of r package ‘logistf’, I have 2 queries regarding the ‘logistftest’ function when doing model comparisons, I would appreciate if anyone can give helps. I am comparing two models (one ...
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22 views

How to deal with big data sets (big $n$) in R? (beginner question) [duplicate]

Say that data is assumed to be exponentially distributed with mean $\zeta$. The likelihood function then incldues the factor $\exp{- \sum x_i/\zeta}$. For a big data set, this is potentially a really ...
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Likelihood ratio test seems to show little difference between models with AICc difference of 3

I'm running a multinomial logistic regression analysis of the behavioural responses of deer to camera traps using no reaction, reaction and strong reaction as dependent variables and season, camera ...
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16 views

Statistical significance of highly correlated explanatory variables

Let's assume I am predicting a Y with 2 x-es: x1 and x2. Let's also assume that x1 and x2 are highly correlated. Let's also say fit 1 uses both x1 and x2 to predict Y while fit 2 only uses x2. ...
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56 views

Log-likelihood ratio test vs. information criteria for model selection

I am trying to select the model with the best fit among GARCH(1,1), ARMA(2,2) and GJR-GARCH(1,1) models for a time series of log returns. The results from IC (Akaike, Bayesian) and likelihood-ratio ...
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13 views

Implementing the Wald Test in PEST Procedure

I'm trying to code a PEST sequence in MATLAB but am unsure about how and when the Wald test is actually implemented. Having read the MATLAB help page for the test, I think my confusion lies with what ...
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27 views

How to infer the likelihood ratio between two examples shown to a Neural Network?

How can I construct a neural net enabling me to efficiently estimate the likelihood of some input relative to some other input? (i.e. a likelihood ratio) An example: Let's say we train this network ...
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25 views

Log likelihood is sufficient statistic

We have two hypotheses: \begin{align} \mathcal H_0&: X \sim P\\\mathcal H_1&: X \sim Q\end{align} Define $F = \log \frac{dP}{dQ}$ to be used for the likelihood ratio test with threshold ...
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Profile Likelihood Algorithm Assumptions

Given a statistical model $$\{p_\theta(y) : \theta \in \Theta \}$$ and same data $y$. The log likelihood function is then $l(\theta)=\log(p_\theta(y))$. For a one parameter hypothesis $\theta_j=\beta$ ...
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15 views

References for how to bound the approximation error of a likelihood ratio test?

In likelihood inference, if your log-likelihood is quadratic, then the key values of likelihood theory (Fisher Information, Wilks LR Statistic) have exact probabilistic interpretations. However, if ...
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42 views

Mean-variance spanning test

Is anyone familiar with a mean-variance spanning test? We would like to do a mean-variance spanning test of the diversification benefits of commodities in a portfolio. What you do is that you run a ...
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1answer
27 views

Generalized likelihood test question

This example appears in Rice's stats book. In the first rectangle, why do we have to maximize the denominator? and why do we use MLE as the denominator to maximize it? I know that MLE best reduces ...
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1answer
37 views

Compare two sets of probabilities to outcome data

Suppose there are two predictive models that both output the probability that the home team wins a given match. Then suppose there is data for thousands of matches, in the format: ...
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20 views

Trouble interpreting the likelihood ratio chi-squared test statistic

I have obtained a likelihood ratio chi-squared test statistic and I don't know if it is significant or not. Do I: Compare my likelihood ratio chi-squared test statistic with the critical value in ...
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1answer
109 views

AIC versus Likelihood Ratio Test in Model Variable Selection

The software that I am currently using to build a model compares a "current run" model to a "reference model" and reports (where applicable) both a chi-squared p-value based on likelihood ratio tests ...
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9 views

Likelihood Ratio Test for Exponential Distribution with a Limited Parameter Space [duplicate]

Suppose that we are given an exponential distribution model with a pdf $f(x,\theta) = \theta^{-1}\exp(-x/\theta)$ with an iid sample $X_1, ..., X_n$, and we would like to test hypothesis $H_0 : \theta ...
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1answer
56 views

Likelihood Ratio Test for Exponential Distribution with a Limited Parameter Space

Suppose that we are given an exponential distribution model with a pdf $f(x,\theta) = \theta^{-1}\exp(-x/\theta)$ with an iid sample $X_1, ..., X_n$, and we would like to test hypothesis $H_0 : \theta ...
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20 views

Does the deviance have a known sampling distribution or not?

In their book Generalized Linear Models, McCullagh & Nelder seem to imply that the sampling distribution of the deviance is generally not known: This is strange, because the deviance of a model ...
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53 views

Expectation of log likelihood ratio

Given that $X_{1},...,X_{n}$ are i.i.d random variables with joint distribution $f(x\mid \theta) $ with 1 dimensional parameter $\theta$, let $\hat\theta$ be the maximum likelihood estimator of ...
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1answer
89 views

Mysterious results from likelihood ratio confidence bounds on a Weibull reliability estimate

I'm trying to calculate a confidence interval on an estimate of the cumulative distribution of a two-parameter Weibull distribution. (Actually 1-cdf, the survival probability.) I want to do this using ...
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16 views

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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1answer
97 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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92 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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165 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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1answer
51 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
19 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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1answer
69 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
26 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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65 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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40 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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30 views

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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36 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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31 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
37 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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36 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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39 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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20 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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71 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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44 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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44 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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57 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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1answer
147 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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31 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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277 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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34 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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55 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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55 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 ...