Interaction terms
- Thread starter DrFurbs
- Start date
hi,
no, but it is only giving the ORs for the simple cases like the OR between no symptoms and anxiety. The combined case w =1 and x6 = 1 is not given, wich is imho ok. I suspect that the value in the OR column at the interaction term is simply the exponential of the corresponding coefficient , which for the simple terms is really the OR but I guess it has no straight interpretation for the interaction term.
no, but it is only giving the ORs for the simple cases like the OR between no symptoms and anxiety. The combined case w =1 and x6 = 1 is not given, wich is imho ok. I suspect that the value in the OR column at the interaction term is simply the exponential of the corresponding coefficient , which for the simple terms is really the OR but I guess it has no straight interpretation for the interaction term.
Are the binary variables coded 0/1, or some other way? Would be best to have them coded 0/1. I'll assume that you do.
Ok I think you mentioned the OR for psychotic symptoms was 5, and the OR for anx/dep was 6? So you might think that a person with both would have an OR of 30, but there is an interaction effect of psychotic symptoms with anx/dep so the OR for a person with both is actually 0.52 * 30 = 15.6.
Ok I think you mentioned the OR for psychotic symptoms was 5, and the OR for anx/dep was 6? So you might think that a person with both would have an OR of 30, but there is an interaction effect of psychotic symptoms with anx/dep so the OR for a person with both is actually 0.52 * 30 = 15.6.
Alright this thread got out control.
I agree with Rogojel's post #19 and meanjoe's generalization in # 26.
I did the math and their approaches give the same result as my proposed method of stratifying on one of the variables and looking at the ratio of the two ORs.
Their appoach, calculate the expected OR via the product of the OR of W and OR of X6 = 18.86, then multiply that by 0.539, which equals actual OR in the model for outcome given both condtions present (i.e., odds of both present over odds of neither present). This value is 10.16. Which we can see is a negative multiplicative interaction.
The method I was proposing was to calculate the OR of W present versus not present in patients with X6 present, divided by, the OR of W present versus not present in patient with out x6 present.
Thus the OR of W*X6 = observed/expected, and since it is < 1, the observed was lower than expected if the two covariates were truly independent. And given my approach it means the percent lower the OR was when the second variable was present versus not present. Big picture the cross product term in the model represents the deviation of the two lines from being parallel (lines are the plotted log odds based on stratifying on one of the two covariates of interest).
Thanks everybody for bearing with me while I also tried to wrap my head around this!!
I agree with Rogojel's post #19 and meanjoe's generalization in # 26.
I did the math and their approaches give the same result as my proposed method of stratifying on one of the variables and looking at the ratio of the two ORs.
Their appoach, calculate the expected OR via the product of the OR of W and OR of X6 = 18.86, then multiply that by 0.539, which equals actual OR in the model for outcome given both condtions present (i.e., odds of both present over odds of neither present). This value is 10.16. Which we can see is a negative multiplicative interaction.
The method I was proposing was to calculate the OR of W present versus not present in patients with X6 present, divided by, the OR of W present versus not present in patient with out x6 present.
Thus the OR of W*X6 = observed/expected, and since it is < 1, the observed was lower than expected if the two covariates were truly independent. And given my approach it means the percent lower the OR was when the second variable was present versus not present. Big picture the cross product term in the model represents the deviation of the two lines from being parallel (lines are the plotted log odds based on stratifying on one of the two covariates of interest).
Thanks everybody for bearing with me while I also tried to wrap my head around this!!
rogojel,
There was no intercept, so you assumed the odds of (Y=1|W=0,X6=0) = 1 (I agree with this). Given this, would you still use the covariates in your calculations or are they already controlled for in the calculation of the beta coefficients. I originally wanted to incorporate the intercept and covariates in all of the conversions of betas to odds. I wanted to go:
b0 = 0;
b1 = 1.314;
b2 = 1.623;
b3 = -0.612;
b4 = 1.913; Sum of all of the covariates controlled for in the model.
So, for W=1 and X6 = 0.
p10 = 1/(1+exp(-(b0 + b1*1 + B4*1))); Probability
p10_odds = p10/(1-p10); Odds
You can see I incorporated the other covariates in the calculation. Is that correct or not, since the beta coefficient was 0?
There was no intercept, so you assumed the odds of (Y=1|W=0,X6=0) = 1 (I agree with this). Given this, would you still use the covariates in your calculations or are they already controlled for in the calculation of the beta coefficients. I originally wanted to incorporate the intercept and covariates in all of the conversions of betas to odds. I wanted to go:
b0 = 0;
b1 = 1.314;
b2 = 1.623;
b3 = -0.612;
b4 = 1.913; Sum of all of the covariates controlled for in the model.
So, for W=1 and X6 = 0.
p10 = 1/(1+exp(-(b0 + b1*1 + B4*1))); Probability
p10_odds = p10/(1-p10); Odds
You can see I incorporated the other covariates in the calculation. Is that correct or not, since the beta coefficient was 0?