I need advice on the correct interpretation of an odds ratio of an interaction term.
Both the mixed-effect logistic regression output is below as well as the predicted odds values, which I calculate merely to help me visualize what the OR values in the output are referring to.
The dependent variable is whether a household owned a television. We are interested in the effects of household head gender (Female, Male), wealth status (Poor, Middle, Rich), and the interaction between these variables. This is hypothetical given the confidentiality of the dataset I'm working with. I've also excluded other predictors here to shorten the length of the post.
The base levels are set to Male and Rich. As we can see in the predicted odds values table below, the odds of Female#Rich owning a TV is 7.2; the odds of Male#Rich is 2.0. This is represented in the regression output under Female (OR: 3.58). Given gender is one component of the interaction term, it no longer represents the unique effects of head-gender, and is interpreted in relation to the base level for wealth (i.e., Rich). We can do the same for Female#Poor (OV: 3.99) and Male#Poor (OV: 4.2) [OR: 0.95, omitted from the regression ouput] and Female#Middle (OV: 2.8) and Male#Middle (OV: 2.6) [OR: 1.048, ommitted]. In both cases, the OR is much closer to 1 than at the rich level (3.58).
The regression output lists the OR in the interaction for Female#Poor and Female#Medium as 0.27 and 0.29, respectively.
Conceptually, it indicates the difference in the odds between female and males in owning a TV is much smaller at poor and middle wealth levels, compared to a rich level (where we know the gendered difference is much larger). I'm looking for help on how to interpret this in numerical terms. I had originally thought of writing the difference in the odds of owning a TV between male and female heads is 70% smaller at middle-class level, as compared to a rich level -- however, I don't think that intuition is right.
The predicted odds values are here:
Both the mixed-effect logistic regression output is below as well as the predicted odds values, which I calculate merely to help me visualize what the OR values in the output are referring to.
The dependent variable is whether a household owned a television. We are interested in the effects of household head gender (Female, Male), wealth status (Poor, Middle, Rich), and the interaction between these variables. This is hypothetical given the confidentiality of the dataset I'm working with. I've also excluded other predictors here to shorten the length of the post.
The base levels are set to Male and Rich. As we can see in the predicted odds values table below, the odds of Female#Rich owning a TV is 7.2; the odds of Male#Rich is 2.0. This is represented in the regression output under Female (OR: 3.58). Given gender is one component of the interaction term, it no longer represents the unique effects of head-gender, and is interpreted in relation to the base level for wealth (i.e., Rich). We can do the same for Female#Poor (OV: 3.99) and Male#Poor (OV: 4.2) [OR: 0.95, omitted from the regression ouput] and Female#Middle (OV: 2.8) and Male#Middle (OV: 2.6) [OR: 1.048, ommitted]. In both cases, the OR is much closer to 1 than at the rich level (3.58).
The regression output lists the OR in the interaction for Female#Poor and Female#Medium as 0.27 and 0.29, respectively.
Conceptually, it indicates the difference in the odds between female and males in owning a TV is much smaller at poor and middle wealth levels, compared to a rich level (where we know the gendered difference is much larger). I'm looking for help on how to interpret this in numerical terms. I had originally thought of writing the difference in the odds of owning a TV between male and female heads is 70% smaller at middle-class level, as compared to a rich level -- however, I don't think that intuition is right.
Code:
TV_owner | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------------------------+----------------------------------------------------------------
hhead_gender |
Female | 3.577116 1.585295 2.88 0.004 1.500722 8.5264
|
Status_Ladder_Cat |
Poor | 2.092556 .5473432 2.82 0.005 1.25323 3.494002
Middle | 1.309231 .3067593 1.15 0.250 .8271336 2.072321
|
hhead_gender#Status_Ladder_Cat |
Female#Poor | .2661135 .1304397 -2.70 0.007 .101821 .6954992
Female#Middle | .2930256 .1347962 -2.67 0.008 .1189433 .7218902
Code:
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------------------------+----------------------------------------------------------------
hhead_gender |
Female | 3.57335 1.00732 3.55 0.000 1.599038 5.547662
Male | 3.040049 .8109692 3.75 0.000 1.450579 4.62952
|
Status_Ladder_Cat |
Rich | 3.936832 1.453617 2.71 0.007 1.087794 6.78587
Poor | 4.122344 1.165546 3.54 0.000 1.837915 6.406773
Middle | 2.673619 .6924266 3.86 0.000 1.316488 4.03075
|
hhead_gender#Status_Ladder_Cat |
Female#Rich | 7.175792 3.313105 2.17 0.030 .6822246 13.66936
Female#Poor | 3.995892 1.269603 3.15 0.002 1.507515 6.484269
Female#Middle | 2.752908 .7712539 3.57 0.000 1.241278 4.264538
Male#Rich | 2.006027 .6562206 3.06 0.002 .7198586 3.292196
Male#Poor | 4.197724 1.252428 3.35 0.001 1.743011 6.652437
Male#Middle | 2.626354 .7001336 3.75 0.000 1.254117 3.99859
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