Comparing effects across predictors
Example 4.2 of Mize and Han (2025): effect sizes within a single model
What social factors most strongly pattern political views? Comparing effect sizes across predictors is complicated when they are on different metrics (e.g., age versus income), are of different types (binary, nominal, continuous), or have nonlinear effects. Mize and Han (2025) suggest putting every predictor on the same footing: the effect of the entire range of the variable.
- For a binary predictor, the 0 versus 1 contrast already summarizes the whole of its effect.
- For a nominal predictor, the ME inequality – the average absolute difference in the outcome across its categories – summarizes its effect in one number (see
meinequality). - For a continuous predictor, use the change across its trimmed range, from the 5th to the 95th percentile. Like the binary contrast and the ME inequality, this expresses the effect of the entire range of the variable, while protecting against outliers. A two-standard-deviation change (Gelman 2008) is an alternative that is sometimes recommended for comparing continuous with binary predictors; see the end of this page.
mecompare calculates all three kinds of effect in a single call, and metest then tests any pair of effects against each other. The example uses the 2021 GSS: a linear regression of political views (1 = extremely liberal to 7 = extremely conservative) on age (with a squared term), gender, race-ethnicity, and social class.
1. Fit and store the model
use "https://tdmize.github.io/data/data/cda_gss", clear(cda_gss.dta | GSS 1972-2021 CDA - Categorical Data Analysis | date created 2023)keep if year == 2021(64,814 observations deleted)drop if missing(polviews, race4, woman, class, age)(424 observations deleted)clonevar conpolviews = polviews. quietly regress conpolviews c.age##c.age i.woman i.race4 i.class, vce(robust)
estimates store polmod2. One call for every predictor
amount(trimrange) applies to the continuous variables in the varlist (here, age); meinequality adds the ME inequality above the contrasts of each nominal variable (race-ethnicity and class). Binary variables need nothing extra.
mecompare age woman race4 class, models(polmod) amount(trimrange) meinequalityPredicting: Linear prediction
Marginal effects (N_polmod=3608)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
age(5-95%) |
polmod | 1 0.784 0.083 0.000
---------------------------------+---------------------------------------
woman |
Women - Men |
polmod | 2 -0.175 0.051 0.001
---------------------------------+---------------------------------------
race4 |
ME Inequality | 3 0.172 0.049 0.000
Black - White |
polmod | 4 -0.331 0.078 0.000
Other - White |
polmod | 5 -0.129 0.105 0.216
Hispanic - White |
polmod | 6 0.011 0.078 0.886
---------------------------------+---------------------------------------
class |
ME Inequality | 7 0.273 0.063 0.000
working cla - lower clas |
polmod | 8 -0.021 0.091 0.814
middle clas - lower clas |
polmod | 9 -0.279 0.091 0.002
upper class - lower clas |
polmod | 10 -0.536 0.162 0.001Reading the table:
- Row 1 is the trimmed-range effect of age: everyone is set to the 5th percentile of age, then to the 95th, and the average difference in predicted political views is the marginal effect. The effect of age is nonlinear, but this summarizes it in a single number.
- Row 2 is the gender gap: the contrast for a binary variable.
- Rows 3 and 7 are the ME inequalities for race-ethnicity and class: on average, how far apart the racial-ethnic groups (or the social classes) are in their political views. The rows beneath each are the contrasts with the base category that the ME inequality summarizes. Add
pwcompareto see all pairwise contrasts, ormeinequality(all)to also report the unweighted ME inequality; the Options page shows both.
The 5th and 95th percentiles that define the trimmed range of age are:
centile age, centile(5 95) Binom. interp.
Variable | Obs Percentile Centile [95% conf. interval]
-------------+-------------------------------------------------------------
age | 3,608 5 25 25 26
| 95 79 79 803. Test the differences in effect size
To compare effect sizes and ignore direction, use the absolute value of a signed effect; here the gender gap is negative. add collects the tests in one table, and rowname() labels each row.
metest, clear
metest 1 - abs(2), add rowname("age - woman") | estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000 metest 1 - 3, add rowname("age - race4") | estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000
age - race4 | 0.612 0.094 0.000 metest 1 - 7, add rowname("age - class") | estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000
age - race4 | 0.612 0.094 0.000
age - class | 0.511 0.101 0.000 metest 3 - abs(2), add rowname("race4 - woman") | estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000
age - race4 | 0.612 0.094 0.000
age - class | 0.511 0.101 0.000
race4 - woman | -0.003 0.069 0.971 metest 3 - 7, add rowname("race4 - class") | estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000
age - race4 | 0.612 0.094 0.000
age - class | 0.511 0.101 0.000
race4 - woman | -0.003 0.069 0.971
race4 - class | -0.101 0.081 0.212 metest 7 - abs(2), add rowname("class - woman") | estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000
age - race4 | 0.612 0.094 0.000
age - class | 0.511 0.101 0.000
race4 - woman | -0.003 0.069 0.971
race4 - class | -0.101 0.081 0.212
class - woman | 0.098 0.077 0.202 metest, title("Effect size comparison of predictors of political views")Effect size comparison of predictors of political views
| estimate se pvalue
---------------------------------+--------------------------------
age - woman | 0.609 0.098 0.000
age - race4 | 0.612 0.094 0.000
age - class | 0.511 0.101 0.000
race4 - woman | -0.003 0.069 0.971
race4 - class | -0.101 0.081 0.212
class - woman | 0.098 0.077 0.202 Age has a larger effect on political views than does gender, race-ethnicity, or social class. The effects of gender, race-ethnicity, and class are similar in size, with no significant differences among them.
Alternative: a two-standard-deviation change
amount(2sd) is the other common way to make a continuous variable comparable with a binary one. A two-standard-deviation change is centered on each observation’s own age (one SD below to one SD above); the trimmed-range change is the same change, from the 5th to the 95th percentile, for everyone. With a nonlinear effect the two can differ:
mecompare age, models(polmod) amount(2sd)Predicting: Linear prediction
Marginal effects (N_polmod=3608)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
age + 2SD (centered) |
polmod | 1 0.496 0.053 0.000mecompare age, models(polmod) amount(trimrange)Predicting: Linear prediction
Marginal effects (N_polmod=3608)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
age(5-95%) |
polmod | 1 0.784 0.083 0.000Mize and Han (2025) suggest the trimmed range as the more robust choice: it always reflects most of the range of the continuous variable’s effect, as a binary variable’s 0 to 1 effect always reflects its full range.
References
Mize, Trenton D. and Bing Han. 2025. “Inequality and Total Effect Summary Measures for Nominal and Ordinal Variables.” Sociological Science 12: 115–157.
Gelman, Andrew. 2008. “Scaling Regression Inputs by Dividing by Two Standard Deviations.” Statistics in Medicine 27(15): 2865–2873.