Usage and examples
Every form of metest, from the help file, with output
metest [exp] [, options]exp refers to marginal effects by the # shown in the mecompare table, or by their coefficient names, combined with +, -, *, /, parentheses, or =. A bare number is always an ME number; a literal number is written with a leading # (#2 is the number two, 2 is the second marginal effect). Non-whole numbers are always literals.
The examples below are the ones in the help file, run in order.
Setup: fit and store two models, then calculate the marginal effects
sysuse nlsw88, clear(NLSW, 1988 extract)drop if missing(union, married, age, race, wage)(368 observations deleted)
. logit union i.married age i.race, vce(robust)Iteration 0: Log pseudolikelihood = -1046.6242
Iteration 1: Log pseudolikelihood = -1038.8701
Iteration 2: Log pseudolikelihood = -1038.8354
Iteration 3: Log pseudolikelihood = -1038.8354
Logistic regression Number of obs = 1,878
Wald chi2(4) = 15.82
Prob > chi2 = 0.0033
Log pseudolikelihood = -1038.8354 Pseudo R2 = 0.0074
------------------------------------------------------------------------------
| Robust
union | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
married |
Married | -0.176 0.114 -1.549 0.121 -0.399 0.047
age | 0.011 0.018 0.637 0.524 -0.024 0.046
|
race |
Black | 0.372 0.120 3.093 0.002 0.136 0.608
Other | 0.553 0.439 1.260 0.208 -0.307 1.412
|
_cons | -1.570 0.711 -2.207 0.027 -2.964 -0.176
------------------------------------------------------------------------------est store m1
logit union i.married age i.race wage, vce(robust)Iteration 0: Log pseudolikelihood = -1046.6242
Iteration 1: Log pseudolikelihood = -1016.7478
Iteration 2: Log pseudolikelihood = -1016.3517
Iteration 3: Log pseudolikelihood = -1016.3517
Logistic regression Number of obs = 1,878
Wald chi2(5) = 59.14
Prob > chi2 = 0.0000
Log pseudolikelihood = -1016.3517 Pseudo R2 = 0.0289
------------------------------------------------------------------------------
| Robust
union | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
married |
Married | -0.119 0.116 -1.029 0.303 -0.345 0.108
age | 0.013 0.018 0.705 0.481 -0.023 0.048
|
race |
Black | 0.492 0.122 4.025 0.000 0.252 0.732
Other | 0.483 0.482 1.002 0.316 -0.462 1.427
|
wage | 0.084 0.012 6.819 0.000 0.060 0.108
_cons | -2.356 0.739 -3.189 0.001 -3.803 -0.908
------------------------------------------------------------------------------est store m2. mecompare age i.married, models(m1 m2)Predicting: Pr(union)
Marginal effects and cross-model differences (N_m1=1878) (N_m2=1878)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
age + 1 (centered) |
m1 | 1 0.002 0.003 0.524
m2 | 2 0.002 0.003 0.480
Difference | 3 -0.000 0.001 0.689
---------------------------------+---------------------------------------
married |
Married - Single |
m1 | 4 -0.033 0.021 0.126
m2 | 5 -0.021 0.021 0.308
Difference | 6 -0.011 0.004 0.003A single marginal effect, by number and by name
metest 1 | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 | 0.002 0.003 0.524 metest age:m1 | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 | 0.002 0.003 0.524 The cross-model difference, three equivalent ways
Note that mecompare already reports it as ME 3.
metest 1 - 2 | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 - m2 | -0.000 0.001 0.689 metest 3 | estimate se pvalue
---------------------------------+--------------------------------
age |
Difference | -0.000 0.001 0.689 metest _b[age:m1] - _b[age:m2] | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 - m2 | -0.000 0.001 0.689 A ratio and an average
Note the # on the divisor of the average, which makes it the number two rather than ME 2.
metest 1 / 2 | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 / m2 | 0.910 0.254 0.000 metest (1 + 2) / #2 | estimate se pvalue
---------------------------------+--------------------------------
age |
(m1 + m2) / 2 | 0.002 0.003 0.501 Scaling by a literal value
10 times the effect for a change in age:
metest 1 * #10 | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 * 10 | 0.021 0.033 0.524 Equality tests, including a joint test and two constraints at once
metest 1 = 2Tests of equality
| chi2 df pvalue
---------------------------------+--------------------------------
age |
m1 = m2 | 0.161 1.000 0.689 metest 1 = 2 = 3Tests of equality
| chi2 df pvalue
---------------------------------+--------------------------------
age |
m1 = m2 = Difference | 0.645 2.000 0.725 metest (1 = 2) (4 = 5)Tests of equality
| chi2 df pvalue
---------------------------------+--------------------------------
(age~1 = age~2)(mar~1 = mar~2) | 9.216 2.000 0.010 Building up a table
Estimates and equality tests are shown in separate tables.
metest, clear
metest 1 - 2 | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 - m2 | -0.000 0.001 0.689 metest 4 - 5, add | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 - m2 | -0.000 0.001 0.689
---------------------------------+--------------------------------
married |
m1 - m2 | -0.011 0.004 0.003 metest 1 = 2, add | estimate se pvalue
---------------------------------+--------------------------------
age |
m1 - m2 | -0.000 0.001 0.689
---------------------------------+--------------------------------
married |
m1 - m2 | -0.011 0.004 0.003
Tests of equality
| chi2 df pvalue
---------------------------------+--------------------------------
age |
m1 = m2 | 0.161 1.000 0.689 Redisplayed at any point, with a title, by typing metest on its own:
metest, title("Age and marriage")Age and marriage
| estimate se pvalue
---------------------------------+--------------------------------
age |
m1 - m2 | -0.000 0.001 0.689
---------------------------------+--------------------------------
married |
m1 - m2 | -0.011 0.004 0.003
Age and marriage
| chi2 df pvalue
---------------------------------+--------------------------------
age |
m1 = m2 | 0.161 1.000 0.689 All six statistics, and a label of your own
metest 1 - 2, stat(all) | estimate se zvalue pvalue ll ul
-------------+-----------------------------------------------------------------
age |
m1 - m2 | -0.000 0.001 -0.401 0.689 -0.001 0.001 metest 1 - 2, rowname("Age effect, m1 vs m2") | estimate se pvalue
---------------------------------+--------------------------------
Age effect, m1 vs m2 | -0.000 0.001 0.689 Options
| Option | Purpose |
|---|---|
statistics(list) |
Statistics to display: estimate, se, zvalue, pvalue, ll, ul, or all. The default is estimate se pvalue. Ignored for equality tests, which report the test statistic, its degrees of freedom, and the p-value. stats() is a synonym. |
allstats |
Same as statistics(all). |
add |
Adds the result as another row of the saved table rather than starting a new one. save is a synonym. |
clear |
Clears the saved table before running; metest, clear on its own clears it without running anything. |
rowname(string) |
Labels the row. A : in the label puts what comes before it on a row of its own, with the rest indented underneath, which is how several rows are grouped under one heading. label() is a synonym. |
decimals(#) |
Decimal places; the default is 3. |
width(#) |
Width of each statistic column; the default is 9. |
labwidth(#) |
Width of the label column; the maximum is 32. twidth() is a synonym. |
title(string) |
Title above the table. |
notable |
Suppresses the table. |
details |
Shows the underlying nlcom or test output. |
level(#) |
Confidence level for ll and ul. |
Results accumulate in the matrix _metest (estimates) and _metest_test (equality tests). metest is r-class: after an expression it returns r(estimate), r(se), r(zvalue), r(pvalue), r(ll), and r(ul); after an equality test, r(chi2) (or r(F)), r(df), and r(pvalue).
Use after other commands
metest also works after other estimation commands: a number refers to the nth coefficient in e(b), in the order of matrix list e(b), and coefficient names work as usual.
sysuse nlsw88, clear(NLSW, 1988 extract)regress wage age ttl_exp grade Source | SS df MS Number of obs = 2,244
-------------+---------------------------------- F(3, 2240) = 132.71
Model | 11221.4453 3 3740.48178 Prob > F = 0.0000
Residual | 63132.8852 2,240 28.1843237 R-squared = 0.1509
-------------+---------------------------------- Adj R-squared = 0.1498
Total | 74354.3305 2,243 33.1495009 Root MSE = 5.3089
------------------------------------------------------------------------------
wage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
age | -0.101 0.037 -2.735 0.006 -0.174 -0.029
ttl_exp | 0.271 0.025 10.819 0.000 0.222 0.320
grade | 0.641 0.045 14.106 0.000 0.552 0.730
_cons | -0.061 1.570 -0.039 0.969 -3.140 3.019
------------------------------------------------------------------------------metest 1 - 2 | estimate se pvalue
---------------------------------+--------------------------------
age - ttl_exp | -0.372 0.047 0.000 metest 1 / 2 | estimate se pvalue
---------------------------------+--------------------------------
age / ttl_exp | -0.374 0.136 0.006 metest 1 = 2 = 3Tests of equality
| F df pvalue
---------------------------------+--------------------------------
age = ttl_exp = grade | 88.241 2.000 0.000 metest abs(1) - abs(2) | estimate se pvalue
---------------------------------+--------------------------------
abs(age) - abs(ttl_exp) | -0.170 0.042 0.000 metest min(1,2) | estimate se pvalue
---------------------------------+--------------------------------
min(age,ttl_exp) | -0.101 0.037 0.006 metest _b[age] * #10 | estimate se pvalue
---------------------------------+--------------------------------
age * 10 | -1.011 0.370 0.006 After margins, post, a number refers to a row of the margins table. E.g., a risk ratio – the ratio of two predicted probabilities, averaging over observed values – in the Health and Retirement Study 2020:
use "https://tdmize.github.io/data/data/cda_hrs", clear(cda_hrs.dta | Health & Retirement Study 2020)drop if missing(cogB, marstatB, collegeB, woman, age)(761 observations deleted)
. logit cogB i.collegeB i.marstatB i.woman c.age, orIteration 0: Log likelihood = -2466.5782
Iteration 1: Log likelihood = -2311.9677
Iteration 2: Log likelihood = -2282.8575
Iteration 3: Log likelihood = -2282.3938
Iteration 4: Log likelihood = -2282.3924
Iteration 5: Log likelihood = -2282.3924
Logistic regression Number of obs = 14,962
LR chi2(4) = 368.37
Prob > chi2 = 0.0000
Log likelihood = -2282.3924 Pseudo R2 = 0.0747
---------------------------------------------------------------------------------------
cogB | Odds ratio Std. err. z P>|z| [95% conf. interval]
----------------------+----------------------------------------------------------------
collegeB |
bachelor's or higher | 0.233 0.037 -9.269 0.000 0.171 0.317
|
marstatB |
currently married | 0.556 0.051 -6.401 0.000 0.465 0.666
|
woman |
woman | 0.802 0.073 -2.428 0.015 0.671 0.958
age | 1.049 0.004 12.085 0.000 1.041 1.057
_cons | 0.003 0.001 -19.128 0.000 0.001 0.005
---------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.
. margins collegeB, postPredictive margins Number of obs = 14,962
Model VCE: OIM
Expression: Pr(cogB), predict()
---------------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
----------------------+----------------------------------------------------------------
collegeB |
no bachelor's | 0.048 0.002 23.986 0.000 0.044 0.052
bachelor's or higher | 0.012 0.002 6.758 0.000 0.008 0.015
---------------------------------------------------------------------------------------metest 1 / 2 | estimate se pvalue
---------------------------------+--------------------------------
0bn_collegeB / 1_collegeB | 4.065 0.626 0.000 Omitted (o.) coefficients are skipped when numbering, so check the numbers with matrix list e(b). After some commands test reports F rather than chi-squared; run metest, clear before accumulating results from a model of the other kind.