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I am building regression models to evaluate the effect of several characteristics of genetic variants (my predictors) on a handful of phenotypic parameters (continuous and binary - hence I am building linear and binomial models).
In some cases I am observing that:

  • the p-value for the 'slope coefficient' of predictor Z within the model is not significant (p-value displayed in the output of the summary() function in R

but

  • when I compare nested models ([A~ X+Y] vs [A~ X+Y+Z]) with a likelihood ratio test, the model containing Z among predictors has a significantly lower residual deviance than one without Z. I do this with the R command:

    anova(lm(A~X+Y,data=vardata),lm(A~X+Y+Z,data=vardata),test="LRT")  
    

How should this type of results be interpreted?

In my understanding this means that, when taken into account, predictor Z significantly improves the model's performance. However, I would then also expect the coefficient of Z in the model to be significantly different from 0.

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