如何在逻辑回归中正确考虑国家影响？

Question

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?

Answer 1

I assume there is another array( at the top not included in your example code. Something like this?

function array_set_depth($array, $depth = -1)
{
  $subdepth = $depth + 1;
  if ($depth < 0) {
    foreach ($array as $key => $subarray) {
      $temp[$key] = array_set_depth(($subarray), $subdepth);
    }
  }
  if ($array['hasChildren'] && isset($array['children'])) {
    foreach ($array['children'] as $key => $subarray) {
      $temp[$key] = array_set_depth($subarray, $subdepth);
    }
    $array['children'] = $temp;
  }
  $array['depth'] = $depth;
  return $array;
}

Example usage, I set your array to the value $a:

$b = array_set_depth($a);
print_r($b);

Edit:

To set depth before the children for nice printing you can do this:

function array_set_depth($array, $depth = -1)
{
  $subdepth = $depth + 1;
  if ($depth < 0) {
    foreach ($array as $key => $subarray) {
      $temp[$key] = array_set_depth(($subarray), $subdepth);
    }
    return $temp;
  }
  $array['depth'] = $depth;
  if ($array['hasChildren'] && isset($array['children'])) {
    foreach ($array['children'] as $key => $subarray) {
      $temp[$key] = array_set_depth($subarray, $subdepth);
    }
    unset($array['children']);
    $array['children'] = $temp;
  }
  return $array;
}

Answer 2

A recursive function like this should do it?

function setDepth(&$a, $depth)
{
    $a['depth']=$depth;
    foreach($a as $key=>$value)
    {
        if (is_array($value))
           setDepth($a[$key], $depth+1);
    }

}

The thing to note is that the array is passed by reference, so that we can modify it. Note that we also use this reference in the recursive call to setDepth. Although I used foreach for convenience, the $value variable is a copy, and passing that to setDepth would only make short lived changes within the scope of the foreach loop.

Answer 3

Modified Pauls code to work with this example.

function setDepth(&$a, $depth = -1)
{
    if (($depth > -1) && !($depth % 2))
      $a['depth']= $depth / 2;
    foreach($a as $key=>$value)
    {
        if (is_array($value))
           setDepth($a[$key], $depth+1);
    }

}
setDepth($a);
print_r($a);

Answer 4

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 it is probably wrong. Looking at the odds ratios (and its standard errors), it certainly looks like Country is an important variable, but note that with logistic regresson, those asymptotic (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 glm's (generalized linear models), so you some serious stydu 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? .

Answer 5

sth like this should do the trick:

function setdepth($arr, $depth = 0)
{
    foreach ($arr as $key => $val)
    {
        $arr[$key]['depth'] = $depth;
        if ($arr[$key]['hasChildren'])
        {
            setdepth(&$arr[$key]['children'], $depth+1);
        }
    }
}

i would be easier if your array started with index not with values, so example usage could be like this:

$arr[0] = $website;
setdepth(&$arr, 0);

where website is the array from your example

Answer 6

This might be helpful:

function extend( $arr, $myArr=array() ) {

    foreach( $arr as $key => $value ) {
        if( is_array( $key ) ) {
            extend( $arr[ $key ] );
        } else {
            $myArr[ $key ] = $arr[ $key ];
        }
    }

    return $myArr;
}

Function called "extend" because it's not only copies array into new one, it can also extends existing arrays.

To extend an array you should put it as the second parameter, otherwise put an empty array. The function lopps through array properties and checks is it an array or not and if it is function envoked again otherwise it copies values into another array and returns it.