Query Regarding Hosmer and Lemeshow Test and its interpretation

[Mukesh Pal]

Respected Neeraj Sir and Group members,

I have a query regarding the significance of the Hosmer and Lemeshow tests in considering the goodness of the fit index and strength of the model. 

In attached screenshot of one of the published research paper,  Authors have explained the model summary as beloe:

"Nagelkerke R2 is observed equal to 0.667, and the Hosmer and Lemeshow test is also satisfactory; these are considered the goodness of the fit index and strength for an explanatory regression model (Field, 2009)." 

My queries are: 

1.if p-value is 0.012, which is below 0.05 (statistically significant). In such cases,. Shall we consider the goodness of model fit as mentioned in the paper? Is there any thumb rule to signifies the Hosmer and Lemeshow test validity?

2. In many papers, Hosmer and Lemeshow  test result in the range of 19.661, 66.126 as well. What is the significance of this value in binary logistic regression?

3. In addition to that, in many research papers, authors have just mentioned the Nagelkerke R2, Hosemen and Lemeshow test results in model summary without P-value. To what extent is it feasible and justify the model strength?

4. Can we only mentioned the Nagelkerke R2 value to justify the goodness of model fit ?

Thank You,