Hello Abderrahime,

The two tests evaluate altogether different hypotheses; as well, the Hosmer-Lemeshow only operates on continuous IVs, whereas the overall model test is evaluating the full set of IVs (15).

Hosmer-Lemeshow evaluates whether model performance is homogeneous throughout the range of the continuous IV. ("Internally congruent," if you will.)

The overall model test evaluates whether the reduction in log likelihood (vs. the null model), relative to model df (for you, 15) is statistically significant.

So, your main take-away here is that the model fails to perform at a level that is statistically distinguishable from the null model.

Good luck with your work.

David Morse thank you for your answer. From what I understood, if the model fails to perform at higher level of the null, then the results from the predictors (odds ratio) will not be valid. If you dont mind me asking, how do you recommend i preceed since it is my first time using regression models.

Thank you again Dr David Morse.

Hello again Abderrahime,

Models may fail to show statistical significance for a number of reasons. Among these are:

1. A genuine absence of effect in the population;

2. Poor measures (e.g., reliability or validity) for IVs and/or DV;

3. Mis-specified model (omitting important IVs; including unimportant/irrelevant IVs);

4. Sample not being representative of the target population (this can yield all sorts of issues, such as restriction of range for one or more variables);

5. Insufficient statistical power to detect the presence of an effect.

Your inclination, to ignore significance tests of individual regression coefficients when the overall model is non-significant, is generally on target. Should it turn out that one or more of the IVs shows a non-zero regression coefficient (and, therefore, the exponentiated value is different from 1), I'd settle for suggesting that those variables might be worth further exploration with new/additional data.

Consider the extreme case of running 15 models, each including one of your candidate IVs. Unless you impose some sort of adjustment for aggregate risk of Type I error, the chances are far higher that at least one will show up as significant, compared to the omnibus test of the 15-IV model, even if the null hypothesis is true in the population.

Good luck with your work.

Thank you very much Dr David Morse your answer is very helpful