# How to correctly account for country effects in logistic regression?

I use a database with entries at firm-level in 12 countries in 2008. I try to estimate innovation (0/1) based on few firm-level variables. I also want to see if / how much innovation is also due to country-level effects. Thus I want to control for country effects. If I introduce i.country in my logistic regression I get negative z values for each country. I feel this is not right because when I look at data, only one country has 0 for innovation more frequently than 1.

Countries take values as 52, 54, 55.. and 92 Bellow is a split of innovation responses by firm-countries. I tries two things: one is to have i.country in regression and other is to use dummies. I created dummies for countries and I introduced them all in regression. Which is correct and how I interpret this?

. tabulate Country INNOV

| NEW PROD LAST 3 yr?

Country |         0          1 |     Total
-----------+----------------------+----------
52 |         4         28 |        32
54 |        25         48 |        73
55 |        40         48 |        88
58 |        40         96 |       136
59 |         4         40 |        44
60 |        14         29 |        43
61 |        39         55 |        94
62 |        35         47 |        82
75 |        10         54 |        64
78 |        28         51 |        79
90 |        29        138 |       167
92 |       105         69 |       174
-----------+----------------------+----------
Total |       373        703 |     1,076



Here I look by one country no independent variables. The odds of innovation if country is 90 (Germany) is positive. If I repeat this country by country, only 92 gets z as negative


. logistic INNOV if Country==90

Logistic regression                               Number of obs   =        167
LR chi2(0)      =      -0.00
Prob > chi2     =          .
Log likelihood = -77.092379                       Pseudo R2       =    -0.0000

------------------------------------------------------------------------------
INNOV | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons |   4.758621   .9720773     7.64   0.000       3.1886    7.101696
------------------------------------------------------------------------------



Here I run regression with one independent variable and while controlling (??) for country effects .. z values for countries are negative (why?)


. logistic INNOV i.Country Mang_MNEexperience

Logistic regression                               Number of obs   =        481
LR chi2(12)     =      61.89
Prob > chi2     =     0.0000
Log likelihood = -283.25686                       Pseudo R2       =     0.0985

------------------------------------------------------------------------------------
INNOV | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
Country |
54  |   .3689431   .3062865    -1.20   0.230     .0724962    1.877602
55  |   .2295013   .1909388    -1.77   0.077     .0449375    1.172091
58  |   .4457037   .3627449    -0.99   0.321      .090423    2.196917
59  |   1.689363   1.597736     0.55   0.579     .2646602    10.78344
60  |   .7459045   .7228328    -0.30   0.762     .1116376    4.983748
61  |   .1580636   .1313537    -2.22   0.026     .0310076    .8057415
62  |   .3256028   .2674703    -1.37   0.172     .0650816    1.628988
75  |   .9975062    1.10341    -0.00   0.998     .1141151    8.719431
78  |   .6885038   .6454499    -0.40   0.691     .1096308    4.323944
90  |   .5391077   .4787809    -0.70   0.487     .0945637    3.073453
92  |   .0549765   .0542165    -2.94   0.003     .0079569    .3798489
|
Mang_MNEexperience |   1.083192   .0309218     2.80   0.005      1.02425    1.145525
_cons |   4.357274   3.409211     1.88   0.060     .9401977    20.19345
------------------------------------------------------------------------------------



Here I use dummies to control for countries

. logistic INNOV countrydummy1 countrydummy2 countrydummy3 countrydummy4 countrydummy5 countrydummy6
> countrydummy7 countrydummy8 countrydummy9 countrydummy10 countrydummy11 countrydummy12 Mang_MNEexpe
> rience
note: countrydummy12 omitted because of collinearity

Logistic regression                               Number of obs   =        481
LR chi2(12)     =      61.89
Prob > chi2     =     0.0000
Log likelihood = -283.25686                       Pseudo R2       =     0.0985

------------------------------------------------------------------------------------
INNOV | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
countrydummy1 |   18.18959   17.93813     2.94   0.003     2.632625    125.6773
countrydummy2 |   6.710925   4.467707     2.86   0.004     1.820148    24.74333
countrydummy3 |   4.174535    2.79421     2.13   0.033     1.124241     15.5009
countrydummy4 |   8.107169   5.216314     3.25   0.001     2.297149    28.61207
countrydummy5 |   30.72882   24.17314     4.35   0.000     6.575663    143.5993
countrydummy6 |    13.5677   11.30987     3.13   0.002     2.648225    69.51165
countrydummy7 |   2.875114   1.907619     1.59   0.111     .7832285    10.55411
countrydummy8 |   5.922583   3.865446     2.73   0.006     1.648026    21.28425
countrydummy9 |   18.14423   17.87654     2.94   0.003     2.630846    125.1358
countrydummy10 |   12.52361   9.977246     3.17   0.002     2.627836    59.68436
countrydummy11 |    9.80615   6.794078     3.30   0.001     2.522048    38.12797
countrydummy12 |          1  (omitted)
Mang_MNEexperience |   1.083192   .0309218     2.80   0.005      1.02425    1.145525
_cons |   .2395476   .1453217    -2.36   0.018     .0729475    .7866357
------------------------------------------------------------------------------------


1. Which way is the correct one?
2. Why in using i.country z is negative and in using dummies z is positive
3. How do I interpret country effects?

It's the same model. Look at the overall statistics: the log-likelihood, the corresponding chi-square statistic, and so forth.

The difference is an accident of which indicator (dummy) is omitted, as at least one of them must be. In the first output, it's country 52; in the second output it's country 92.

So, there isn't really any issue about which model is correct. A model call using Stata's factor variable notation is, at a minimum, a better way to do it in the important sense that the output is easier to read. (The names of the country indicators are under your control: even if you don't like the names some command gives them, you can always rename them.)

So, country by country results can't be paired off: they are relative to different base levels.

Stata's factor variable notation includes an option to set the base level.

@kjetil b halvorsen's general warnings about over-dispersion, Hauck-Donner and the like are well meant and you'd do well to keep them in mind, but they don't seem to bear directly on the question.

• Dear @NickCox: thank you a million for your comment. I am more than grateful and relieved. I do see now exactly what happens, i.e. why in first case I only have negative and in the second only positive z values. In the first case the base level is the first country that is one of the most innovative and by contrast all the others are less. In the second case the base level is the last listed country, also the least innovative. I had not seen that in the first regression 52 was missing.Thank you for pointing to this. Also for your very clear explanation. – MonicaR Nov 9 '19 at 20:37

Country is a categorical variable, so you should definitely use dummy encoding. I do not know Stata, so I am not sure what Stata did in the other case, but nevertheless it does not matter, since you should only do the analysis with Country represented as a dummy. Looking at the odds ratios (and their standard errors), it certainly looks like Country is an important variable, but note that with logistic regression, those asymptotic results (based on a normal approximation to the log likelihood function) can be terrible, so don't trust them as is. This is the Hauck-Donner phenomenon. What you should do is to test the variable Country as a whole, which you can do by fitting a model without that variable, then with it (otherwise identical), and compare the loglikelihoods. There could be a direct way of doing it in Stata.

But there are also other problems with binomial GLMs (generalized linear models), so you need some serious study before using them! For instance, overdispersion. You should check for that also, as a matter of routine.

You could also have a look at Principled way of collapsing categorical variables with many levels?.

• Dear @kjetil b halvorsen: many many thanks for your clear answer and for suggesting to fit a model without the country variable, then with it (otherwise identical), and compare the loglikelihoods. Thank you also for the link, I will do my best to get the best out of this reading. – MonicaR Nov 9 '19 at 20:36