[Richard Williams]

Also, here is an example using clogit. Dummy variable coding and effect coding produce identical fits. Again my guess is that Cordula is making a mistake somewhere (easy enough to do if you have 40 interactions). If you really really want effect coding then you may want to download the xi3 command.

. webuse lowbirth2, clear
(Applied Logistic Regression, Hosmer & Lemeshow)

. clogit low lwt  ptd ht ui i.smoke##i.race, group(pairid) nolog

Conditional (fixed-effects) logistic regression

                                                Number of obs     =        112
                                                LR chi2(9)        =      26.34
                                                Prob > chi2       =     0.0018
Log likelihood = -25.643997                     Pseudo R2         =     0.3393

------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         lwt |   -.017926   .0101855    -1.76   0.078    -.0378892    .0020371
         ptd |   1.797776    .815141     2.21   0.027     .2001289    3.395423
          ht |   2.228638   1.149753     1.94   0.053    -.0248361    4.482111
          ui |   1.370714   .6920241     1.98   0.048     .0143716    2.727056
     1.smoke |   1.917216   1.168335     1.64   0.101    -.3726783     4.20711
             |
        race |
      black  |   1.144002   1.263177     0.91   0.365    -1.331779    3.619783
      other  |   .2858877   .9932426     0.29   0.773    -1.660832    2.232607
             |
  smoke#race |
    1#black  |  -.9362929   1.745752    -0.54   0.592    -4.357905    2.485319
    1#other  |   -.760635   2.037016    -0.37   0.709    -4.753113    3.231843
------------------------------------------------------------------------------

. xi3: clogit low lwt  ptd ht ui e.smoke*e.race, group(pairid) nolog
e.smoke           _Ismoke_0-1         (naturally coded; _Ismoke_0 omitted)
e.race            _Irace_1-3          (naturally coded; _Irace_1 omitted)

Conditional (fixed-effects) logistic regression

                                                Number of obs     =        112
                                                LR chi2(9)        =      26.34
                                                Prob > chi2       =     0.0018
Log likelihood = -25.643997                     Pseudo R2         =     0.3393

------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         lwt |   -.017926   .0101855    -1.76   0.078    -.0378892    .0020371
         ptd |   1.797776    .815141     2.21   0.027     .2001289    3.395423
          ht |   2.228638   1.149753     1.94   0.053    -.0248361    4.482111
          ui |   1.370714   .6920241     1.98   0.048     .0143716    2.727056
   _Ismoke_1 |   .6757866   .3292875     2.05   0.040      .030395    1.321178
    _Irace_2 |   .4820471   .5072945     0.95   0.342    -.5122319    1.476326
    _Irace_3 |  -.2882385   .5479771    -0.53   0.599    -1.362254    .7857769
   _Ism1Xra2 |  -.1853251   .4913708    -0.38   0.706    -1.148394     .777744
   _Ism1Xra3 |  -.0974962   .5772872    -0.17   0.866    -1.228958    1.033966
------------------------------------------------------------------------------

.

[Cordula Kiel]

Dear Richard and William,

thanks a lot for your helpful input!

I will try this out now und will give feedback on my results.
I just install xi3 and will work on that.
I also tried -fvvarlist- as in your last example, but it seems not to work with effects coding. I get the following error message: "factor variables may not contain negative values".
xi3 does not seem to make problems in this regard.

[Roman Mostazir]

Just to supplement here, your cited paper by Kugler et al. (2012), consults effect coded data from studies which followed fractional fractorial design. The paper assumes that when your study adopted fractional factorial designs, by effect coding, you can estimate main fixed effects (equivalent to anova fixed effect), given, they are 'aliased' with 2nd order effects and any two-way/ three-way interactions are aliased with higher order effects. The estimable effects are designed at study design phase. If your study is not a fractional factorial deisgn, this may not be a suitable paper to follow, as William pointed out above, multiplying two effect code may be flawed if you are not careful to what you are doing. For example, those in -1 and -1, will get a +1 when multiplied, which is not true in your dataset.

[Cordula Kiel]

Dear Roman,
thanks a lot for your comment!
It is indeed a fractional factorial design, but I did not design it, so I am not very sure if this has been considered in the design phase.

[Cordula Kiel]

So here are my results for using xi3 and dummy coding, which match the results from my previous idea to multiply the variables with each other.
The second results block shows the results for effects coding though, which do not match the results from the multiplication. Moreover, there are interaction variables omitted.

Conditional (fixed-effects) logistic regression   Number of obs   =      15600
                                                  Wald chi2(38)   =     713.66
                                                  Prob > chi2     =     0.0000
Log pseudolikelihood = -4627.5266                 Pseudo R2       =     0.1900

                                     (Std. Err. adjusted for 325 clusters in ID)
--------------------------------------------------------------------------------
               |               Robust
  Choice_Dummy |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
     optoutvar |   .9169907   .1529449     6.00   0.000     .6172242    1.216757
     Pangasius |   .1841965   .0660292     2.79   0.005     .0547815    .3136114
    Bangladesh |  -.1587668   .0730642    -2.17   0.030      -.30197   -.0155636
       Germany |    .747786   .0853922     8.76   0.000     .5804204    .9151516
           ASC |   1.004653   .4099213     2.45   0.014     .2012218    1.808084
     Naturland |   .6169105   .4266317     1.45   0.148    -.2192724    1.453093
         Brand |   .0261319   .0428466     0.61   0.542    -.0578459    .1101097
     FairLabel |   .3201833   .3811105     0.84   0.401    -.4267796    1.067146
         Price |  -.1464912   .0131636   -11.13   0.000    -.1722913    -.120691
      CETSCALE |          0  (omitted)
   _IGermany_1 |          0  (omitted)
      _ICEXGe1 |  -.0197657   .0902066    -0.22   0.827    -.1965673    .1570359
 _IBanglades_1 |          0  (omitted)
      _ICEXBa1 |  -.0777312   .0860788    -0.90   0.367    -.2464424    .0909801
         CIBV1 |          0  (omitted)
      _ICIXBa1 |   .0455831   .0788603     0.58   0.563    -.1089801    .2001464
         CIBV2 |          0  (omitted)
     _I1CIXBa1 |   .5792647   .0783303     7.40   0.000     .4257402    .7327893
    CI_Germany |          0  (omitted)
      _ICIXGe1 |   .5842659   .0932755     6.26   0.000     .4014493    .7670826
  sust_concern |          0  (omitted)
       _IASC_1 |          0  (omitted)
      _IsuXAS1 |  -.1610985   .0759576    -2.12   0.034    -.3099727   -.0122243
 _INaturland_1 |          0  (omitted)
      _IsuXNa1 |    -.17425   .0667061    -2.61   0.009    -.3049917   -.0435084
 _IFairLabel_1 |          0  (omitted)
      _IsuXFa1 |  -.0381624   .0558967    -0.68   0.495     -.147718    .0713932
Naturland_know |          0  (omitted)
      _INaXNa1 |   .5511232    .167491     3.29   0.001      .222847    .8793995
 ASC_knowledge |          0  (omitted)
      _IASXAS1 |   .0594404   .1492938     0.40   0.691      -.23317    .3520508
     Fair_know |          0  (omitted)
      _IFaXFa1 |   .2782418   .2925279     0.95   0.342    -.2951024    .8515859
           age |          0  (omitted)
      _IagXAS1 |  -.0134218   .0064565    -2.08   0.038    -.0260763   -.0007674
      _IagXNa1 |   -.011124   .0063063    -1.76   0.078    -.0234842    .0012361
      _IagXFa1 |  -.0019994   .0045573    -0.44   0.661    -.0109316    .0069328
        female |          0  (omitted)
      _IfeXAS1 |   .1067799   .1415325     0.75   0.451    -.1706187    .3841785
      _IfeXNa1 |  -.0493308   .1458635    -0.34   0.735     -.335218    .2365565
      _IfeXFa1 |    .000975   .1162149     0.01   0.993    -.2268021    .2287521
        degree |          0  (omitted)
      _IdeXAS1 |  -.2736318   .1462077    -1.87   0.061    -.5601936    .0129299
      _IdeXNa1 |  -.1422414   .1402038    -1.01   0.310    -.4170358    .1325529
      _IdeXFa1 |  -.1746861   .1205484    -1.45   0.147    -.4109567    .0615844
   high_income |          0  (omitted)
      _IhiXAS1 |   .6154653   .2308042     2.67   0.008     .1630974    1.067833
      _IhiXNa1 |   .4486477   .2539027     1.77   0.077    -.0489924    .9462878
      _IhiXFa1 |   .1074731   .1618008     0.66   0.507    -.2096506    .4245967
 medium_income |          0  (omitted)
      _ImeXAS1 |   .3184165   .2249913     1.42   0.157    -.1225584    .7593915
      _ImeXNa1 |   .4487657   .2549927     1.76   0.078    -.0510108    .9485423
      _ImeXFa1 |  -.1290489    .159808    -0.81   0.419    -.4422668    .1841691
    low_income |          0  (omitted)
      _IloXAS1 |   .3187577   .2574398     1.24   0.216     -.185815    .8233305
      _IloXNa1 |   .2676172   .2824475     0.95   0.343    -.2859698    .8212042
      _IloXFa1 |   .0226336   .1916792     0.12   0.906    -.3530507    .3983178
--------------------------------------------------------------------------------

Conditional (fixed-effects) logistic regression   Number of obs   =      15600
                                                  Wald chi2(52)   =     794.43
                                                  Prob > chi2     =     0.0000
Log pseudolikelihood = -4535.4306                 Pseudo R2       =     0.2061

                                     (Std. Err. adjusted for 325 clusters in ID)
--------------------------------------------------------------------------------
               |               Robust
  Choice_Dummy |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
     optoutvar |  -.6943901   .3757697    -1.85   0.065    -1.430885     .042105
     Pangasius |   .0912928   .0333422     2.74   0.006     .0259432    .1566424
    Bangladesh |  -.3400772    .044947    -7.57   0.000    -.4281716   -.2519828
       Germany |   .5762999   .0520594    11.07   0.000     .4742653    .6783345
           ASC |     .41867   .1681387     2.49   0.013     .0891241    .7482158
     Naturland |    .250001   .1457855     1.71   0.086    -.0357335    .5357354
         Brand |   .0132831   .0216861     0.61   0.540    -.0292209    .0557871
     FairLabel |   .0648911   .1067234     0.61   0.543    -.1442828    .2740651
         Price |  -.1470447   .0132501   -11.10   0.000    -.1730143    -.121075
      CETSCALE |          0  (omitted)
   _IGermany_2 |          0  (omitted)
   _IGermany_3 |          0  (omitted)
      _ICEXGe2 |  -.0528318   .0461784    -1.14   0.253    -.1433398    .0376763
      _ICEXGe3 |   -.066348   .0930468    -0.71   0.476    -.2487163    .1160203
 _IBanglades_2 |          0  (omitted)
 _IBanglades_3 |          0  (omitted)
      _ICEXBa2 |   .0730134   .1004248     0.73   0.467    -.1238157    .2698424
      _ICEXBa3 |          0  (omitted)
         CIBV1 |          0  (omitted)
      _ICIXBa2 |  -.0400594   .0532513    -0.75   0.452      -.14443    .0643112
      _ICIXBa3 |   .0059347   .0429349     0.14   0.890    -.0782161    .0900856
         CIBV2 |          0  (omitted)
     _I1CIXBa2 |  -.3585839   .0564153    -6.36   0.000    -.4691558   -.2480119
     _I1CIXBa3 |   .2798877   .0440544     6.35   0.000     .1935427    .3662327
    CI_Germany |          0  (omitted)
      _ICIXGe2 |  -.3628431   .0612579    -5.92   0.000    -.4829062   -.2427799
      _ICIXGe3 |   .2691362   .0559045     4.81   0.000     .1595654    .3787071
  sust_concern |          0  (omitted)
       _IASC_2 |          0  (omitted)
       _IASC_3 |          0  (omitted)
      _IsuXAS2 |  -.0208589   .0374398    -0.56   0.577    -.0942395    .0525217
      _IsuXAS3 |  -.1459618   .1298444    -1.12   0.261    -.4004521    .1085286
 _INaturland_2 |          0  (omitted)
 _INaturland_3 |          0  (omitted)
      _IsuXNa2 |   .1268654   .1229295     1.03   0.302     -.114072    .3678029
      _IsuXNa3 |          0  (omitted)
 _IFairLabel_2 |          0  (omitted)
 _IFairLabel_3 |          0  (omitted)
      _IsuXFa2 |   .0403018   .0495544     0.81   0.416     -.056823    .1374267
      _IsuXFa3 |          0  (omitted)
Naturland_know |          0  (omitted)
      _INaXNa2 |  -.0540129   .0535044    -1.01   0.313    -.1588796    .0508538
      _INaXNa3 |   .1848831   .0487736     3.79   0.000     .0892886    .2804776
 ASC_knowledge |          0  (omitted)
      _IASXAS2 |   .0608079    .048589     1.25   0.211    -.0344247    .1560405
      _IASXAS3 |   .0602842   .0405792     1.49   0.137    -.0192495    .1398179
     Fair_know |          0  (omitted)
      _IFaXFa2 |  -.0225302   .1124191    -0.20   0.841    -.2428676    .1978073
      _IFaXFa3 |    .083848   .0634799     1.32   0.187    -.0405703    .2082663
           age |          0  (omitted)
      _IagXAS2 |   .0002514   .0033672     0.07   0.940    -.0063483     .006851
      _IagXAS3 |  -.0076856   .0103092    -0.75   0.456    -.0278912    .0125201
      _IagXNa2 |   .0064819   .0097489     0.66   0.506    -.0126257    .0255895
      _IagXNa3 |          0  (omitted)
      _IagXFa2 |   .0037477   .0044094     0.85   0.395    -.0048945      .01239
      _IagXFa3 |          0  (omitted)
        female |          0  (omitted)
      _IfeXAS2 |  -.0232481   .0421483    -0.55   0.581    -.1058573    .0593611
      _IfeXAS3 |   .0583612   .1287663     0.45   0.650     -.194016    .3107385
      _IfeXNa2 |  -.0005147   .1258322    -0.00   0.997    -.2471413    .2461118
      _IfeXNa3 |          0  (omitted)
      _IfeXFa2 |   .0352629   .0541949     0.65   0.515    -.0709571    .1414829
      _IfeXFa3 |          0  (omitted)
        degree |          0  (omitted)
      _IdeXAS2 |   .0554175   .0411081     1.35   0.178     -.025153    .1359879
      _IdeXAS3 |  -.1262618   .1300025    -0.97   0.331     -.381062    .1285385
      _IdeXNa2 |   .1208431   .1253005     0.96   0.335    -.1247413    .3664275
      _IdeXNa3 |          0  (omitted)
      _IdeXFa2 |   .0197423   .0583005     0.34   0.735    -.0945245    .1340091
      _IdeXFa3 |          0  (omitted)
   high_income |          0  (omitted)
      _IhiXAS2 |   .0286063   .0649587     0.44   0.660    -.0987105     .155923
      _IhiXAS3 |   .3606554   .1963841     1.84   0.066    -.0242504    .7455611
      _IhiXNa2 |  -.2428902   .1965705    -1.24   0.217    -.6281612    .1423808
      _IhiXNa3 |          0  (omitted)
      _IhiXFa2 |    .020506   .0718198     0.29   0.775    -.1202584    .1612703
      _IhiXFa3 |          0  (omitted)
 medium_income |          0  (omitted)
      _ImeXAS2 |   .0983636    .071469     1.38   0.169    -.0417132    .2384403
      _ImeXAS3 |   .0859899   .1826656     0.47   0.638    -.2720281    .4440078
      _ImeXNa2 |  -.0425245   .1862755    -0.23   0.819    -.4076177    .3225687
      _ImeXNa3 |          0  (omitted)
      _ImeXFa2 |  -.0709475   .0703346    -1.01   0.313    -.2088008    .0669058
      _ImeXFa3 |          0  (omitted)
    low_income |          0  (omitted)
      _IloXAS2 |   .0676129   .0751598     0.90   0.368    -.0796976    .2149234
      _IloXAS3 |   .2470005    .215953     1.14   0.253    -.1762596    .6702606
      _IloXNa2 |  -.1414138   .2159974    -0.65   0.513     -.564761    .2819333
      _IloXNa3 |          0  (omitted)
      _IloXFa2 |   .0399832   .0832019     0.48   0.631    -.1230894    .2030559
      _IloXFa3 |          0  (omitted)
--------------------------------------------------------------------------------

[Richard Williams]

Cordula, you should show the commands as well. The 2nd model has 14 more degrees of freedom but without seeing the commands it is hard to know why.

[Richard Williams]

Also looking at your code it appears you tried to enter some variables twice, e.g. you have Germany and _IGermany_1. You don't show your code so I don't know exactly what you did but I suspect you have coding problems.

[Cordula Kiel]

Yes, I did not want to get those variables omitted (what happens if I do not enter them separately in addition to the interactions).
I input the following:

xi3: clogit Choice_Dummy optoutvar Pangasius Bangladesh Germany ASC Naturland Brand FairLabel Price $hypvarsxi3, group(Case) vce(cluster ID)

with

***xi3 interaction variables (hypotheses only)
#delimit ;
global hypvarsxi3
CETSCALE*e.Germany
CETSCALE*e.Bangladesh
CIBV1*e.Bangladesh
CIBV2*e.Bangladesh
CI_Germany*e.Germany
sust_concern*e.ASC
sust_concern*e.Naturland
sust_concern*e.FairLabel
e.Naturland_know*e.Naturland
e.ASC_knowledge*e.ASC
e.Fair_know*e.FairLabel
age*e.ASC
age*e.Naturland
age*e.FairLabel
e.female*e.ASC
e.female*e.Naturland
e.female*e.FairLabel
e.degree*e.ASC
e.degree*e.Naturland
e.degree*e.FairLabel
e.high_income*e.ASC
e.high_income*e.Naturland
e.high_income*e.FairLabel
e.medium_income*e.ASC
e.medium_income*e.Naturland
e.medium_income*e.FairLabel
e.low_income*e.ASC
e.low_income*e.Naturland
e.low_income*e.FairLabel
;

For the second example.
(For the first output, I did the same but replaced the -e- prefix with -i- and used the dummy coded versions of the variables.)

[Richard Williams]

I suspect you are getting a mix of dummy coded variables with effect coded variables, e.g. Germany is coded 0/1 but then e.Germany gets coded -1/1. I'm not sure what the impact of that is but I imagine you should be consistent. I would make the first part of the command have e.Germany e.Bangladesh etc.

I am guessing too that a lot of these are not mutually exclusive, e.g. if You are a 1 on Germany you must be a 0 on Bangladesh; if you are a 1 on high_income you must be a zero on medium and low income. If so I would create and use variables like Country where 1 = Germany, 2 = Bangladesh, etc.; and Income where 1 = low_income, 2 = Moderate_income, etc.

Anyway, try the first suggestion first. i.e. put e. in front of every categorical variable. That may take care of the inconsistencies you are seeing. Or at least cut down on all those 0 (omitted) messages.

[Richard Williams]

Also put i. in front of the categorical variables in the dummy variable coding. It could be that is the one that is wrong.

[Cordula Kiel]

Thanks for your suggestions!
I think I did the -i- and -e- thing correctly (as I wrote above at the bottom of my post.)

For the other point: I did not know that it is possible to use e.g. a country variable which includes different levels for each country.
I thought I have to use dummy variables for each level of categorical variables.
Does this apply only to models where I only look at the main effects of variables?

[Richard Williams]

You said your code was

xi3: clogit Choice_Dummy optoutvar Pangasius Bangladesh Germany ASC Naturland Brand FairLabel Price $hypvarsxi3, group(Case) vce(cluster ID)

You ought to be using things like i.Germany or e.Germany. The way you are doing it creates the possibility that dummy variable coding is used in some parts while effect coding is used in other parts.

How are your variables coded now? If you are already using effect coding (e.g. some vars are coded -1, 0, 1) then things may get screwed up as you try to effect code a variable that is already effect coded.

Yes, i. or e. create the dummies for you. So, i.Country would create, say, 4 dummies if Country had 5 possible values. Or else e.Country would create 4 effect coded variables. This should also generate the correct number of interactions. If you created a bunch of effect coded variables, I would try to go back to the earlier variables and use them. Stata is less likely to make mistakes than you are.

I'll also go back to the advice from way back when -- I am not sure this effect coding is worth it. I bet you could get what you want from using factor variable coding and margins. But, if you are going to use effect coding, you have to make sure you are doing it right.

[Cordula Kiel]

Yes, the variables I assigned an -e- were already effect coded (and the variables I assigned an -i- were dummy coded. I worked with two datasets accordingly). I thought this has to be the case.
That was then a lack of understanding from my side, I though the declaration has to fit the coding, I did not see that the prefix actually does the coding for me.

I will give it another try now as you suggested with the taking the original variables and then doing the xi3 again.
I also would prefer dummy coding.

There are two reasons why I thought effect coding might be better for my case:
First, I would like to be able to interpete the alternative-specific constant of "opting out". (Background information: I did a discrete choice experiment in which participants could either select one of two product alternatives or decide to choose nothing at all. As a lot of people chose this "opt out option", I would like to evaluate it as a separate attribute, and dummy coding might be misleading in these situations, as described by Bech&Gyrd-Hansen (2005): "Effects coding in discrete choice experiments".)
The other reason is that I would like to be able to evaluate the coefficients (and later the willingness-to-pay) not relative to the base alternative but more to a zero alternative.
But I am not sure whether my understanding is correct here. For example, if my base alternative for the country is Vietnam, and I use dummy coding, then my coefficients for Bangladesh and Germany would be evaluated against Vietnam, and not more generally.
So I thought if I take dummy coding and estimate the WTP for the different product attributes, then the WTP for Bangladesh would mean the WTP for switching from Vietnam to Bangladesh.
And I thought if I take effects coding, the WTP for Bangladesh would mean a more absolute WTP, as compared to a zero mean (receiving nothing).
But I don't know if I got that wrong. Do you have an idea on that?

[Richard Williams]

Ok, that probably explains a lot, including why the effect coding was estimating so many more parameters. Effect coding a variable coded -1, 0, 1 will create two variables from the original 1.

Use the data set where vars were dummy coded. If you use the effect coding commands, I suspect you'll find that effect coding and dummy variable coding produce identical results.

Better yet, if it exists, go back to the data set that had Country and Income as categorical vars and use them.

I don't use effect coding enough to have an opinion on its merits. I do know that commands like margins, contrast, and pwcompare let me do a lot of things and I doubt that effect coding could tell me much more. But get the effect coding right and then you can experiment from there.

[Cordula Kiel]

Now that's unfortunately not working out as planned, as I have some interactions that don't fit together. (E.g. a variable I only want to interact with for example Bangladesh, but not with all the countries because it doesn't make sense).
I think I will keep the dummy solution I produced before which led to the same results as the "mulitiplication" solution. Hopefully this is not completely wrong. I am a bit confused about all that and hope I will manage to interpret the results.