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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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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17 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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38 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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19 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 ...
4
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0answers
68 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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15 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 ...
2
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0answers
42 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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10 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 ...
2
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2answers
41 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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25 views

How to numerically compute Likelihood Ratio Test for a Logistic Regression?

Suppose I am simulating a data set from a binary logistic regression with $k=5$ predictors out of which $k_2=3$ are inactive i.e., $\beta_3=\beta_4=\beta_5=0,$ and remaining $k_1=2$ are active having ...
3
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1answer
89 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 ...
0
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1answer
26 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 ...
2
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1answer
42 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 ...
2
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1answer
57 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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24 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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1answer
45 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 ...
2
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1answer
41 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
72 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 ...
3
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1answer
95 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 ...
2
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1answer
61 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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21 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
112 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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44 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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36 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 ...
2
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1answer
84 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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81 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 ...
4
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1answer
175 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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39 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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1answer
247 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) ...
2
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2answers
272 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 ...
0
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0answers
93 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, ...
5
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1answer
324 views

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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42 views

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 ...
4
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2answers
219 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 ...
0
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0answers
18 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 ...
4
votes
1answer
121 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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56 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 ...
0
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1answer
233 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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20 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 ...
11
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2answers
1k views

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

Consider the following data from a two-way within subjects design: ...
3
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1answer
246 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 ...
0
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1answer
62 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
50 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 ...
2
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1answer
516 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 ...
5
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1answer
455 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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28 views

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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71 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
406 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 ...
2
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2answers
277 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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22 views

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 ...