[I have cross-posted this to Cross Validated here].
[I am using Stata 15.1]
I am interested in analyzing how the effect of a dichotomous variable on a dichotomous outcome changes by age. In reading this how-to article from UCLA's Institute for Digital Research & Education--"How Can I Use the Margins Command to Understand Multiple Interaction in Regression and Anova"--I noticed they adjusted for multiple comparisons using a Bonferroni adjustment because one of the terms in the interaction they used (female * prog) had three categories (.05/3 = .0167) and, later on, another (honors * read) had six (.05/6 = .0083), making it progressively less likely for the p-value to be significant.
In my example above, would I need to do this for every age in the sample? For instance, consider the following sample data in Stata and analysis:
The outcome, union, is binary, where 1 = the respondent is in a labor union. The independent variable, married, is binary, where 1 = the respondent is married. And the independent variable, age, is continuous, marking the age of the respondent, and ranging from 34 to 46.
Although the coefficients are not significant above, assuming they were, we would not need to employ Bonferroni's adjustment in this case, but we would need to apply it to the break down of the margins, correct? (Here it is my understanding that the margins post-estimation command calculates the predicted value of being in a union for both married and not married folk, at each value of age).
So would each of those p-values need to be Bonferroni adjusted for the number of age categories--which, here would be .05/13 = .0038? (Side question: why are all the p-values significant here but not in the actual regression model?)
What about if we went with the dydx option? (Here it is my understanding that, unlike with margins above, the dydx option calculates the marginal effect of being married at each value of age, on the outcome of being in a union).
My interpretation of these results is that from age 34 (_at 1) through age 37 (_at 4), there is no significant difference in unionization between married and single folks at the .05 level, but that at age 38 (_at 5), 39 (_at 6), and 40 (_at 7), there is. However, if we need to employ a Bonferroni adjustment here as before (.05/13 = .0038), then none of them are significant.
Is that the case? If so, how does one analyze the interaction effects of age in samples with a large range (e.g. polls of 18- to 90-year-olds)?
[I am using Stata 15.1]
I am interested in analyzing how the effect of a dichotomous variable on a dichotomous outcome changes by age. In reading this how-to article from UCLA's Institute for Digital Research & Education--"How Can I Use the Margins Command to Understand Multiple Interaction in Regression and Anova"--I noticed they adjusted for multiple comparisons using a Bonferroni adjustment because one of the terms in the interaction they used (female * prog) had three categories (.05/3 = .0167) and, later on, another (honors * read) had six (.05/6 = .0083), making it progressively less likely for the p-value to be significant.
In my example above, would I need to do this for every age in the sample? For instance, consider the following sample data in Stata and analysis:
Code:
* LOAD SAMPLE DATA sysuse nlsw88.dta * SUMMARY STATISTICS FOR THREE VARIABLES OF INTEREST summarize union married age
| Variable | Obs | Mean | Std. Dev. | Min | Max |
| union | 1,878 | .2454739 | .4304825 | 0 | 1 |
| married | 2,246 | .6420303 | .4795099 | 0 | 1 |
| age | 2,246 | 39.15316 | 3.060002 | 34 | 46 |
The outcome, union, is binary, where 1 = the respondent is in a labor union. The independent variable, married, is binary, where 1 = the respondent is married. And the independent variable, age, is continuous, marking the age of the respondent, and ranging from 34 to 46.
Code:
* LOGISTIC REGRESSION OF Y ON BINARY X*CONTINUOUS X logit union married##c.age, nolog
| union | Coef. | Std. Err. | z | P>z | [95% Conf. | Interval] |
| married | ||||||
| married | -.4123983 | 1.450548 | -0.28 | 0.776 | -3.255419 | 2.430623 |
| age | .0049886 | .0293678 | 0.17 | 0.865 | -.0525712 | .0625483 |
| married#c.age | ||||||
| married | .0042013 | .0368046 | 0.11 | 0.909 | -.0679343 | .076337 |
| _cons | -1.161027 | 1.158666 | -1.00 | 0.316 | -3.431971 | 1.109917 |
Although the coefficients are not significant above, assuming they were, we would not need to employ Bonferroni's adjustment in this case, but we would need to apply it to the break down of the margins, correct? (Here it is my understanding that the margins post-estimation command calculates the predicted value of being in a union for both married and not married folk, at each value of age).
Code:
margins married, at(age=(34(1)46))
| Margin | Delta-method Std. Err. |
z | P > [z] | [95% Conf. | Interval] | |
| _at#married | ||||||
| 1#single | .2706328 | .0354409 | 7.64 | 0.000 | .2011699 | .3400956 |
| 1#married | .2208075 | .0231087 | 9.56 | 0.000 | .1755153 | .2660996 |
| 2#single | .2716186 | .0305767 | 8.88 | 0.000 | .2116894 | .3315478 |
| 2#married | .2223927 | .0200148 | 11.11 | 0.000 | .1831645 | .2616209 |
| 3#single | .2726067 | .026051 | 10.46 | 0.000 | .2215476 | .3236657 |
| 3#married | .223986 | .017149 | 13.06 | 0.000 | .1903745 | .2575975 |
| [truncated] |
What about if we went with the dydx option? (Here it is my understanding that, unlike with margins above, the dydx option calculates the marginal effect of being married at each value of age, on the outcome of being in a union).
Code:
* MARGINAL EFFECT OF BEING MARRIED AT EACH AGE ON UNIONIZATION margins, dydx(married) at(age=(34(1)46))
| dy/dx | Delta-method Std. Err. |
z | P>[z] | [95% Conf. | Interval] | |
| 0.married | (base outcome) | |||||
| 1.married | ||||||
| _at | ||||||
| 1 | -.0498253 | .0423092 | -1.18 | 0.239 | -.1327498 | .0330992 |
| 2 | -.0492259 | .0365448 | -1.35 | 0.178 | -.1208524 | .0224006 |
| 3 | -.0486207 | .0311888 | -1.56 | 0.119 | -.1097497 | .0125083 |
| 4 | -.0480096 | .0265243 | -1.81 | 0.070 | -.0999963 | .0039771 |
| 5 | -.0473926 | .0230158 | -2.06 | 0.039 | -.0925028 | -.0022824 |
| 6 | -.0467698 | .021287 | -2.20 | 0.028 | -.0884917 | -.005048 |
| 7 | -.0461412 | .0218083 | -2.12 | 0.034 | -.0888847 | -.0033976 |
| [truncated] |
My interpretation of these results is that from age 34 (_at 1) through age 37 (_at 4), there is no significant difference in unionization between married and single folks at the .05 level, but that at age 38 (_at 5), 39 (_at 6), and 40 (_at 7), there is. However, if we need to employ a Bonferroni adjustment here as before (.05/13 = .0038), then none of them are significant.
Is that the case? If so, how does one analyze the interaction effects of age in samples with a large range (e.g. polls of 18- to 90-year-olds)?
