Questions tagged [likelihood-ratio]
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 sometimes called a generalized likelihood ratio.
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Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio
I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows:
Two URLs are compared for their ability to ...
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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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What are some of the robustness checks for the likelihood ratio test?
In the application of statistical methods in social science, one usually does a lot of robustness checks. If I got some publishable findings using LRT test by discrimination two theoretical models, ...
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What is the difference between the F-test and the Wald / Likelihood Ratio / Score tests of linear models?
In statistical inference, it's common that investigators will report the results from Wald tests for simple univariate inference or likelihood ratio tests for nested models. However, in regression ...
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When to use likelihood ratio test vs. incremental F-test in nested nonlinear model selection?
I have two nested nonlinear models and I want to know which provides a better fit to some data. I see descriptions of both the likelihood ratio test and of the incremental F-test (also called the ...
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Reference for implementing generalized likelihood ratio test to determine online whether time-series mean has shifted
What is a reference that describes the "generalized likelihood ratio" test to determine online (i.e., meaning that we add an observation, then check, then add an observation, then check) whether the ...
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P-value of LR test
I've been studying more about GLRT (Generalized Likelihood Ratio Tests) and I came up with the following problem.
Let $X\sim N(\theta,1)$ and consider the hypothesis $H_0:\theta\in[a,b]$ against $H_1:\...
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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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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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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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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 $H_0: \...
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Application of likelihood ratio test to test the Markov property
Do you know a reference (freely available on the web) where the likelihood ratio test is applied in order to test for the Markov property?
The setting is a directly observable discrete Markov-chain ...
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Likelihood ratio test versus AIC for model comparison
When performing model comparison, why does the likelihood ratio test require two nested models while this is not required when using the AIC?
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Likelihood ratio test: $f(x)=2x$ vs $f(x)=3x^2$: $2n$ degrees of freedom?
Suppose $X_1, . . . , X_n$ are i.i.d. with pdf $f(·)$.
We want to test the hypotheses
\begin{align}
H_0 &: f(x) = 2x , \;\, \text{ for } 0 \le x \le 1, \text{ against}, \\
H_1 &: f(x) = 3x^2 , ...
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