Outliers in logit regression: all positive outcomes

[Birte Olsen]

Dear all, I have a dataset on civil wars in the country-year format on a total of N = 2207. I am running a logit model estimating the effect of female empowerment on civil war outcome (binary measure about whether the challengers succeed in obtaining their aims). After this, I wanted to investigate any possible outliers defined by standardized Pearson residuals larger then 3 or smaller than - 3. My command looks like this:

logit war_outcome lagfpe lagpolyarchy lnlaggdp lnlagpop lnlagmilper i.region lagtimesv lagtimesv2 lagtimesv3 lagtimesnv lagtimesnv2 lagtimesnv3 coldwar, vce(cluster country_name)

predict rsta, rsta;

I then make a variable to list the observations listed as outliers.

.
gen residualv = 1 if rsta>3
replace residualv = 1 if rsta<-3
list location year war_outcome if residualv == 1

This produces this output:

      +------------------------------------------------+
      |                     location   year   war_outcome |
      |------------------------------------------------|
   3. |                       Uganda   1986          1 |
  28. |                      Namibia   1988          1 |
  42. |                      Algeria   1962          1 |
 107. |                       Rwanda   1994          1 |
 108. |                     Ethiopia   1991          1 |
      |------------------------------------------------|
 130. |                      Liberia   1990          1 |
 192. |                      Burundi   1992          1 |
 286. |                       Angola   1974          1 |
 353. |                   Mozambique   1974          1 |
 355. |                      Liberia   2003          1 |
      |------------------------------------------------|
 357. |                     Ethiopia   1991          1 |
 384. |                        Congo   1997          1 |
 400. |                      Somalia   1994          1 |
 441. |                      Tunisia   1954          1 |
 504. |                Guinea-Bissau   1974          1 |
      |------------------------------------------------|
 508. |                       Rwanda   1994          1 |
 523. |                         Chad   1990          1 |
 533. | Democratic Republic of Congo   1997          1 |
 539. |     Central African Republic   2013          1 |
 583. |                      Somalia   1991          1 |
      |------------------------------------------------|
 593. |                Guinea-Bissau   1999          1 |
 624. |                       Rwanda   1961          1 |
 703. |                        Chile   1973          1 |
 733. |                         Cuba   1959          1 |
 850. |                    Nicaragua   1979          1 |
      |------------------------------------------------|
 858. |                    Argentina   1955          1 |
1047. |                      Lebanon   1978          1 |
1143. |                        Yemen   1967          1 |
1150. |                     Cambodia   1979          1 |
1263. |                  Afghanistan   1978          1 |
      |------------------------------------------------|
1272. |                    Palestine   1948          1 |
1299. |                         Laos   1975          1 |
1305. |                         Laos   1949          1 |
1376. |                     Cambodia   1975          1 |
1620. |                    Indonesia   1949          1 |
      |------------------------------------------------|
1636. |                    Hyderabad   1948          1 |
1726. |                      Georgia   2008          1 |
1746. |         Cambodia (Kampuchea)   1954          1 |
1858. |                        China   1949          1 |
1882. |                  Afghanistan   1996          1 |
      |------------------------------------------------|
1884. |                  Afghanistan   1988          1 |
1896. |                     Pakistan   1971          1 |
1934. |                        Yemen   1948          1 |
1966. |                       Cyprus   1959          1 |
1974. |                      Vietnam   1954          1 |
      |------------------------------------------------|
2148. |                     Slovenia   1991          1 |
2195. |                      Romania   1989          1 |
2197. |                         Fiji   1987          1 |
      +------------------------------------------------+

However, as you see, I have a lot of outliers. All the outliers have the value 1 on war_outcome, and together make up almost all of my sample of positive outcomes for war_outcome (48 out of 56 instances). I am unsure how to interpret this, and whether the problem lies in my data or interpretation of the logit model/binary dependent variable or in my limited Stata knowledge.

Any help would be greatly appreciated!

(Stata SE 17)

[Nick Cox]

The way to answer this is to look more closely at the results, e.g. by using predict to get fitted probabilities too. For example, if most values are 0 and the fitted function is nearly flat then all the values of 1 will be associated with large residuals.

This demonstration is extreme to make the point.

clear
set obs 100
set seed 2803
gen y = runiform() < 0.1
gen x = _n
logit y x
predict rsta, rsta
predict fitted
su 

scatter rsta fitted 
scatter rsta y

[Birte Olsen]

That makes very much sense!

I will look more closely at my results - thank you Nick!