When applying logistic regression to identify predictors of an outcome, it is not clear whether the Wald test or likelihood ratio test is preferred for evaluating the significance of candidate variables or coefficients and whether this decision depends on the sample size, statistical power or widths of confidence intervals.
The Wald test is based on a rather crude assumption about the shape of the likelihood. The LRT takes the likeihood values as they are. Therefore LR-tests are usually superior to Wald-tests, given the underlying probability model is sensible or at least not too unreasonable.
Hi David,
It is not clear from your description exactly what you are trying to do. When running a logistic regression, p values are presented along with confidence intervals. So in terms of "significant" variables, it's all right there for you. I am not sure why you would need a LRT?
Now, if you are trying to build a parsimonious model and you have a large number of covariates to choose from, then you may need to ferret out those variables that do not contribute to the model in any meaningful way. If this is what you are after, then I would suggest a couple of things. First, use a more robust modeling approach than straight-up logistic regression. There are many classification algorithms available that outperform logistic regression by a wide margin (see for example boosted regression, random forests, etc.). Next, use a training set and holdout (test) set for your model building exercise. There are several different approaches to use here, but 10-fold cross-validation is the standard approach for most applications. Finally, review the classification statistcs and ROC curves for the various models to see which classifies individuals the most accurately.
Again, if you provide more specific information, I could provide a more specific response.
I hope this helps
Ariel
The Wald test is based on a rather crude assumption about the shape of the likelihood. The LRT takes the likeihood values as they are. Therefore LR-tests are usually superior to Wald-tests, given the underlying probability model is sensible or at least not too unreasonable.
I'm with Jochen. The difference is in the shape of the likelihood function. Wald-based assumes it's symmetric. LR-test doesn't. Often this doesn't matter much, but if you've got the choice, and it doesn't add hours to your analysis, then I prefer the answers from the LR-test.
Standard statistical software usually quote the Wald-based p-values alongside the estimates and confidence intervals, and you have to specifically ask for the LR-test based p-values. I guess that's because assuming symmetry is consistent with the method they use for the confidence intervals. But if you wanted to go the whole way, you could go for a profile-likelihood based confidence intervals or something like that too...
But given that focus on the p-values is often inappropriate in my area of application (health research), and I tend to round the p-value to just one or two significant figures, I don't particularly care that the Wald-based method is approximate, and I'm more interested in the estimate and confidence interval.
I think they give a different kind of information: Wald test tests the significance of the relation between the independent variable and the outcome within the logistic model, while LRT compares two nested models (i.e. a "null" model - or, more general, a model with less independent variables - and a "full" model with at least one more variable respect to the null model). If Wald test is not significant, the independent variable should be discarded; otherwise (p
Dear Colleague
If the sample size is large, I suggest Likelihood test and for the small samples Wald test is better and it can test the parameters with one or two sided tests.
If you expect the test to variable selection, there is other deterministic approach.
I developed the k-fold cross validation and model selection methods.
See my papers after 2014.
If we want to test the model, should LRT test insignificant while comparing full model and reduced model( nested model)?
I am now diagnosing cancer by the blood, and 2 group discrimination is done with logistic regression, Fisher's LDF, SVM, and Optimal LDF. There are many problems with Fisher's LDF, but AIC or BIC minimum model is chosen in all models in addition to the test of individual models. Moreover, we compare four LDFs.
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