# How do you interpret the likelihood ratio?

Contents

## How do you interpret the likelihood ratio?

Likelihood ratios (LR) in medical testing are used to interpret diagnostic tests. Basically, the LR tells you how likely a patient has a disease or condition. The higher the ratio, the more likely they have the disease or condition. Conversely, a low ratio means that they very likely do not.

### What does Wald mean in logistic regression?

It is similar to a standard deviation to a mean. Wald χ2– This is the test statistic for the individual predictor variable. A multiple linear regression will have a t test, while a logistic regression will have a χ2 test. This is used to determine the p value.

#### What does a significant LRT mean?

If (and only if) this pertains to a Likelihood Ratio test between two models (fitted by likelihood maximization techniques), a significant test would mean the ‘alternative’ model has a better fit (read: higher likelihood) on your data than the ‘null hypothesis’ model (see Michael Chernick’s comment).

What does a Wald test do?

The Wald test (also called the Wald Chi-Squared Test) is a way to find out if explanatory variables in a model are significant. If the Wald test shows that the parameters for certain explanatory variables are zero, you can remove the variables from the model.

What does a positive likelihood ratio mean?

 A positive likelihood ratio, or LR+, is the “probability that a positive test would be expected in a patient divided by the probability that a positive test would be expected in a patient without a disease.”.

## What is positive likelihood ratio?

Likelihood ratios (LR) are used to express a change in odds. They are used most often in the realm of diagnosis. The positive likelihood ratio (+LR) gives the change in the odds of having a diagnosis in patients with a positive test. The change is in the form of a ratio, usually greater than 1.

### What is the null hypothesis for likelihood ratio test?

The likelihood ratio test is a test of the sufficiency of a smaller model versus a more complex model. The null hypothesis of the test states that the smaller model provides as good a fit for the data as the larger model.

#### What is the null hypothesis for Wald test?

The Wald test works by testing the null hypothesis that a set of parameters is equal to some value. In the model being tested here, the null hypothesis is that the two coefficients of interest are simultaneously equal to zero.

How is the likelihood ratio test statistic calculated?

Now that we have both log likelihoods, calculating the test statistic is simple: So our likelihood ratio test statistic is 36.05 (distributed chi-squared), with two degrees of freedom.

How can I perform the likelihood ratio and Wald test in?

In general, both tests should come to the same conclusion (because the Wald test, at least in theory, approximate the LR test). As an example, we will test for a statistically significant difference between two models, using both tests.

## Where can I get a copy of likelihood ratios?

Address correspondence and requests for reprints to Dr. McGee: University of Washington Seattle-Puget Sound VA Health Care System (S-111 GIMC), 1660 S. Columbian Wy., Seattle, WA 98108 (e-mail: [email protected]). Copyright2002 by the Society of General Internal Medicine

### Which is the likelihood ratio of the χ2 distribution?

The likelihood ratio test statistic is also compared to the χ2 distribution with (r − 1)(c − 1) degrees of freedom. This statistic is also given at the bottom of Table 12.10, and is seen to be almost exactly equal to the “usual” χ2 statistic.