[Violation] Hosmer & Lemeshow - Binary Logistics Regression

#1
I want to analyze some factors which contribute to smoking behavior in teenager and young adult. These are my variables:

y = smoking status (yes/no)

x1 = age (years)
x2 = duration of formal education years
x3 = media score (ratio)
x4 = working status (yes/no)
x5 = wealth index (1/2/3/4/5)
x6 = sex (male/female)
x7 = geography (urban/rural)

bivariate analysis of x1, x2, x3 (based on smoking status) giving significance result (p<0.05).
chi-square test of x4, x5, x6, x7 also giving significance result (p<0.05).

When i'm analyzing with binary logistics (with SPSS), in "Hosmer & Lemeshow Test" the significance value is 0,000 (then the model didn't fit with the data).
The significance didn't change even i'm using forward or backward method.

Then i'm trying to analysing one by one to search variable that pass the Hosmer & Lemeshow test, the result are x3 and x5 (from these 2 variable, only x5 give significance result and pass the Hosmer & Lemeshow test with backward method).

my question is: Is it any certain method to still use Binary Logistics Regression when there is violation in Hosmer & Lemeshow test assumption?
 
#3
Hosmer and Lemeshow themselves write about the limitations of this test (see I think Hosmer DW, Hosmer T, Lecessie S, Lemeshow S. A comparison of goodness-of-fit tests for the logistic regression model. Statistics in Medicine. 1997;16(9):965-980.)

Its worth considering this when you use it. I would by no means suggest that you only use a HL test to look at model fit.
 
#4
is there any alternative method to check the fit model?

As far as i know, we can check the fit model with its change on log likelihood or with its LR test (log likelihood ratio).
is it "enough" to said the model is fit based on likelihood?