I have performed a hierarchical logistic regression with four steps, with various health risk variables including cigarette smoking. How do I interpret a change in odds ratio in step 1 for cigarette smoking OR 5.75 to that in step 2 OR 3.98 while adding in other risk behaviors like use of alcohol and drugs. All odds are significant throughout the models.
OR=5.75 in step 1 means that smokres have 5.75 as large risk (or 4.75 times larger risk) as non-smokers. Can we say that smoking increases risk 4.75 times? Not necessarily. Smoking can be related to other risk factors. Smokers use peppermint chewing gum a lot, what if chewing peppermint gum is also a risk factor? If we do not include it in model we can not separate risk due to smoking from risk due to chewing gum. These two risks combine to give OR=5.75.
Adding "chewing gum" variable to model allows for separation of those two risks. After doing this OR for smoking will probably drop. We can say that this new OR is free from chewing gum risk (more elegantly: it is "adjusted to chewing gum")
OR=3.98 in step 2 means that risk behaviors, that you added, were "included" in smoking's OR. So, 4.75 times increase found in step 1 was not only due to smoking. Some part of it was related to risk behaviors added in step 2. And, after removing them, risk increase due to smoking is 2.98 times.