Comparing non-nested models

[Deepika Deshpande]

Hi - I am using a dataset of US listed industrials (2000-2020) and studying the moderation impact of the global financial crisis on the relationship between geographic diversification of the firms and their performance (ROA.) I have operationalized geographic diversification in 2 ways:

1. Extent of Foreign sales (also called Foreign Market Penetration) - Ln_GSD (MODEL 1)
2. Extent of Foreign production (Foreign Production) - Ln_GSD_Asset (MODEL 2)

Based on the above 2 operationalizations, I have created two models (indicated as MODEL 1 and MODEL 2 above.) Pasted below the moderation results for both models. I am looking for a test to ascertain if the moderation impact of the crisis for FMP-Performance (Ln_GSD) or MODEL 1 is greater than the moderation impact of the crisis for FP-Performance (Ln_GSD_Asset) or MODEL 2.

• Could you please guide me as to which test I should use? I was thinking of using the likelihood ratio test, however, that works only for nested models.
• Since my 2 models are not nested models, should I use nnest instead (https://stats.oarc.ucla.edu/stata/co...nested-models/) ?
• Another option is to use estat ic but I believe that it works for log likelihood models only.

Would have any suggestions for me?

MODEL 1

xtreg Ln_EBIT_ROA Ln_Revenue Ln_LTD_to_Sales Ln_Intangible_Assets  CoAge wGDPpc wCPI wDCF wExpgr w
> GDPgr wCons Ln_PS_RD c.l1.Ln_GSD##c.l1.Ln_GSD##ib2.crisis if  CoAge>=0 & NATION=="UNITED STATES" &
>  NATIONCODE==840 & FSTS>=10 & FSTS <=100 & GENERALINDUSTRYCLASSIFICATION ==1 & Year_<2020 & Year_<
> YearInactive & Discr_GS_Rev!=1, fe cluster(n_WSID)

Fixed-effects (within) regression               Number of obs     =      1,080
Group variable: n_WSID                          Number of groups  =        215

R-sq:                                           Obs per group:
     within  = 0.1280                                         min =          1
     between = 0.0043                                         avg =        5.0
     overall = 0.0123                                         max =         19

                                                F(17,214)         =          .
corr(u_i, Xb)  = -0.7239                        Prob > F          =          .

                                             (Std. Err. adjusted for 215 clusters in n_WSID)
--------------------------------------------------------------------------------------------
                           |               Robust
               Ln_EBIT_ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                Ln_Revenue |   .5231021   .1499161     3.49   0.001     .2276008    .8186035
           Ln_LTD_to_Sales |   -.125481   .0419333    -2.99   0.003    -.2081362   -.0428258
      Ln_Intangible_Assets |  -.1103335   .0615829    -1.79   0.075    -.2317202    .0110532
                     CoAge |  -.0029363   .0166989    -0.18   0.861    -.0358517    .0299791
                    wGDPpc |   .0000298   .0000218     1.37   0.172    -.0000131    .0000727
                      wCPI |   .0060675   .0254869     0.24   0.812      -.04417     .056305
                      wDCF |   1.36e-13   1.27e-13     1.07   0.285    -1.14e-13    3.85e-13
                    wExpgr |   .0126791   .0125128     1.01   0.312    -.0119851    .0373433
                    wGDPgr |   .0115004   .0300052     0.38   0.702    -.0476431     .070644
                     wCons |  -2.27e-14   4.36e-14    -0.52   0.603    -1.09e-13    6.32e-14
                  Ln_PS_RD |    -.04777   .0474308    -1.01   0.315    -.1412614    .0457213
                           |
                    Ln_GSD |
                       L1. |    -.49074   .2583853    -1.90   0.059    -1.000046    .0185662
                           |
       cL.Ln_GSD#cL.Ln_GSD |    .177507   .1103887     1.61   0.109    -.0400813    .3950953
                           |
                    crisis |
                        1  |   .0000289   .1170896     0.00   1.000    -.2307677    .2308255
                        3  |   -.244763   .1386875    -1.76   0.079    -.5181314    .0286055
                           |
          crisis#cL.Ln_GSD |
                        1  |  -.0697625   .1898751    -0.37   0.714    -.4440274    .3045024
                        3  |  -.1822128   .2083067    -0.87   0.383    -.5928084    .2283829
                           |
crisis#cL.Ln_GSD#cL.Ln_GSD |
                        1  |  -.2631727   .1049846    -2.51   0.013    -.4701091   -.0562364
                        3  |  -.2041293   .0970556    -2.10   0.037    -.3954366   -.0128219
                           |
                     _cons |   -13.0135   2.823174    -4.61   0.000    -18.57829   -7.448709
---------------------------+----------------------------------------------------------------
                   sigma_u |  1.1013267
                   sigma_e |  .59130596
                       rho |  .77623771   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------

MODEL 2

. xtreg Ln_EBIT_ROA Ln_Revenue Ln_LTD_to_Sales Ln_Intangible_Assets  CoAge wGDPpc wCPI wDCF wExpgr w
> GDPgr wCons Ln_PS_RD c.l1.Ln_GSD_Asset##c.l1.Ln_GSD_Asset##ib2.crisis if  CoAge>=0 & NATION=="UNIT
> ED STATES" & NATIONCODE==840 & FSTS>=10 & FSTS <=100 & GENERALINDUSTRYCLASSIFICATION ==1 & Year_<2
> 020 & Year_<YearInactive & Discr_GS_Rev!=1, fe cluster(n_WSID)

Fixed-effects (within) regression               Number of obs     =        938
Group variable: n_WSID                          Number of groups  =        188

R-sq:                                           Obs per group:
     within  = 0.1327                                         min =          1
     between = 0.0051                                         avg =        5.0
     overall = 0.0096                                         max =         18

                                                F(17,187)         =          .
corr(u_i, Xb)  = -0.7147                        Prob > F          =          .

                                                  (Std. Err. adjusted for 188 clusters in n_WSID)
-------------------------------------------------------------------------------------------------
                                |               Robust
                    Ln_EBIT_ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------------------+----------------------------------------------------------------
                     Ln_Revenue |   .6324088   .1731603     3.65   0.000     .2908101    .9740075
                Ln_LTD_to_Sales |  -.1416329   .0584044    -2.43   0.016    -.2568491   -.0264167
           Ln_Intangible_Assets |  -.1816245   .0582329    -3.12   0.002    -.2965023   -.0667468
                          CoAge |  -.0027908   .0165359    -0.17   0.866    -.0354117    .0298302
                         wGDPpc |   .0000134   .0000174     0.77   0.443    -.0000209    .0000477
                           wCPI |  -.0212403   .0263041    -0.81   0.420    -.0731312    .0306507
                           wDCF |   2.58e-13   1.32e-13     1.95   0.052    -2.37e-15    5.19e-13
                         wExpgr |   .0171985   .0136959     1.26   0.211      -.00982    .0442169
                         wGDPgr |   .0045089   .0324868     0.14   0.890    -.0595788    .0685967
                          wCons |  -6.90e-14   4.54e-14    -1.52   0.130    -1.58e-13    2.05e-14
                       Ln_PS_RD |  -.0919234   .0727104    -1.26   0.208    -.2353614    .0515146
                                |
                   Ln_GSD_Asset |
                            L1. |   .0831113   .3679609     0.23   0.822    -.6427766    .8089992
                                |
cL.Ln_GSD_Asset#cL.Ln_GSD_Asset |   .2656332   .2406542     1.10   0.271    -.2091129    .7403792
                                |
                         crisis |
                             1  |   -.188022   .1496301    -1.26   0.210    -.4832019    .1071579
                             3  |  -.3896768   .1794329    -2.17   0.031    -.7436496    -.035704
                                |
         crisis#cL.Ln_GSD_Asset |
                             1  |  -.5481548   .3419877    -1.60   0.111    -1.222805     .126495
                             3  |   -.523638   .3525392    -1.49   0.139    -1.219103     .171827
                                |
         crisis#cL.Ln_GSD_Asset#|
                cL.Ln_GSD_Asset |
                             1  |  -.3290189   .2468779    -1.33   0.184    -.8160426    .1580048
                             3  |  -.3656444   .2437182    -1.50   0.135    -.8464348     .115146
                                |
                          _cons |  -13.58189   3.460469    -3.92   0.000    -20.40846   -6.755312
--------------------------------+----------------------------------------------------------------
                        sigma_u |  1.1117421
                        sigma_e |  .59800123
                            rho |  .77559559   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------------

[Joseph Coveney]

I am looking . . . to ascertain if the moderation impact of the crisis for FMP-Performance (Ln_GSD) . . . is greater than the moderation impact of the crisis for FP-Performance (Ln_GSD_Asset) . . .

Is there a reason why you cannot put them both into an omnibus model and compare the magnitudes of the respective coefficients? Does that lag thingy prevent that? As it stands now with two separate regression models, you're fitting the models to two separate sets of the data (you can fix that problem without resorting to an omnibus model, but it still would leave comparability problematic; you could also examine their covariation in the joint model's -e(V)-.) Also, you might want to scale them both by their observed ranges (or theoretical maximum excursions) so that a comparison can be made more readily. Likewise, although the least-squares algorithm that Stata uses might be reasonably robust to numerical ill-conditioning, you've got quite a discrepancy in the scales of your other predictors. It might be good to scale them, too.

Again, I don't know what kind of monkey wrench the lagging business throws into things, but maybe something along the following lines as a first-pass try, if it's feasible.

#delimit ;
keep if
    CoAge >= 0 &
    NATION=="UNITED STATES" &
    NATIONCODE == 840 &
    FSTS >= 10 &
    FSTS <= 100 &
    GENERALINDUSTRYCLASSIFICATION == 1 &
    Year_ < 2020 & Year_ < YearInactive &
    Discr_GS_Rev != 1;
#delimit cr
// A few of those seem redundant

local kitchen_sink Ln_Revenue Ln_LTD_to_Sales Ln_Intangible_Assets  ///
    CoAge wGDPpc wCPI wDCF wExpgr wGDPgr wCons Ln_PS_RD
foreach var of varlist `kitchen_sink' {
    summarize `var', meanonly
    replace `var' = (`var' - r(min)) / (r(max) - r(min))
}

// Might as well do the same for the outcome variable, too
forech var of varlist Ln_EBIT_ROA Ln_GSD Ln_GSD_Asset {
    summarize `var', meanonly
    replace `var' = (`var' - r(min)) / (r(max) - r(min))
}

// And finally here
xtreg Ln_EBIT_ROA `kitchen_sink" ///
    c.l1.Ln_GSD##c.l1.Ln_GSD##ib2.crisis ////
    c.l1.Ln_GSD_Asset##c.l1.Ln_GSD_Asset##ib2.crisis, ///
        i(n_WSID) fe vce(bootstrap, reps(1000) nodots)
estat bootstrap, percentile

[Deepika Deshpande]

Thanks for your response, I have given it some thought and tried the omnibus model (without scaling them.) The results are even harder to interpret, Under the omnibus model both terms below produce non-significant coefficients:
c.l1.Ln_GSD##c.l1.Ln_GSD##ib2.crisis c.l1.Ln_GSD_Asset##c.l1.Ln_GSD_Asset##ib2.crisis
I am not sure if this is because of the lack of scaling problem. I will try that now. Separately, would nnest work? Thanks so much, Apologies in advance for asking these basic questions.

[Joseph Coveney]

Under the omnibus model both terms below produce non-significant coefficients:

So what. Those NHSTs don't address your research question, which as you originally stated it has nothing to do with "significance" of the coefficients, but rather whether their respective "moderation impact" is greater or lesser than that of the other.

I construe this "moderation impact" to be represented by the relative magnitude of the regression coefficients, which depend not only on their ability to predict the outcome but also on the relative scale of the two predictors. So that's why I recommended to re-scale them to what is observed in order to be more comparable (or to re-scale them to their theoretical ranges that may be observed in practice).

That your regression coefficients are now "non-significant" in the omnibus model I'm guessing relates to their near linear dependence.

To illustrate all of these points, I've put together a do file below that you can run. I've chosen a simpler model in order to more clearly illustrate the points, but the principles ought to still apply to your case. I've annotated the code to cover each point: why I recommend re-scaling the coefficients, why I recommend including both in an omnibus model and what I mean by the possible source of the sudden loss of "statistical significance" when both are included.

version 17.0

clear *

// seedem
set seed 2502913

tempname Corr
matrix define `Corr' = J(3, 3, 0.5) + I(3) * 0.5

drawnorm y x1 x2, double corr(`Corr') ///
    sd(1 2 1) n(250)

// True "importance" toward predicting outcome (essentially the same: 0.53 versus 0.55)
correlate y x1
correlate y x2

*
* Unrescaled
*
regress y c.x1
estimates store X1
regress y c.x2
estimates store X2
quietly suest X1 X2
* suest , coeflegend
lincom  _b[X2_mean:x2] - _b[X1_mean:x1] // (Huge difference, but completely artefact of scale difference)
estimates drop _all

regress y c.(x?)
lincom _b[x2] - _b[x1] // (Still big difference, and also artefact, but attenuated by covariance of predictors)

*
* Rescaled
*
preserve
foreach var of varlist x? {
    summarize `var', meanonly
    quietly replace `var' = (`var' - r(min)) / (r(max) - r(min))
}
regress y c.x1
estimates store X1
regress y c.x2
estimates store X2
quietly suest X1 X2
lincom  _b[X2_mean:x2] - _b[X1_mean:x1] // Similar importance now that both are re-scaled apples-to-apples
estimates drop _all

regress y c.(x?)
lincom _b[x2] - _b[x1] // Including both in an omnibus model presents even more accurate picture
restore

*
* Near collinearity
*
quietly replace x2 = x1 / 2 in 2/250
regress y c.x1 // "Highly significant" coefficient
regress y c.x2 // Ditto, "Highly significant"

regress y c.(x?) // Together, both now "non-significant"

exit

[Deepika Deshpande]

Thank you, Joseph. Your feedback is immensely helpful (- apologies for taking time to respond... its been a while since I studied statistics at university and hence I wanted to understand the surrounding statistical concepts thoroughly.) I not understand why you recommended standardizing the IVs of interest and the DV.

Based on your feedback, I have standardized the IVs (of interest) and the DV and ran an omnibus model. So far so good. However, I think something is wrong with my lincom command. Any suggestions would be very helpful. Thanks.

. xtreg stLn_EBIT_ROA Ln_Revenue Ln_LTD_to_Sales Ln_Intangible_Assets  CoAge wGDPpc wCPI wDCF wExpgr
>  wGDPgr wCons Ln_PS_RD c.l1.stLn_GSD##c.l1.stLn_GSD##ib2.crisis c.l1.stLn_GSD_Asset##c.l1.stLn_GSD
> _Asset##ib2.crisis if  CoAge>=0 & NATION=="UNITED STATES" & NATIONCODE==840 & FSTS>=10 & FSTS <=10
> 0 & GENERALINDUSTRYCLASSIFICATION ==1 & Year_<2020 & Year_<YearInactive & Discr_GS_Rev!=1, fe clus
> ter(n_WSID)

Fixed-effects (within) regression               Number of obs     =        926
Group variable: n_WSID                          Number of groups  =        188

R-sq:                                           Obs per group:
     within  = 0.1552                                         min =          1
     between = 0.0024                                         avg =        4.9
     overall = 0.0068                                         max =         18

                                                F(23,187)         =          .
corr(u_i, Xb)  = -0.7446                        Prob > F          =          .

                                                 (Std. Err. adjusted for 188 clusters in n_WSID)
------------------------------------------------------------------------------------------------
                               |               Robust
                 stLn_EBIT_ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------------------+----------------------------------------------------------------
                    Ln_Revenue |   .0245912   .0066984     3.67   0.000     .0113772    .0378053
               Ln_LTD_to_Sales |  -.0058658   .0023662    -2.48   0.014    -.0105336    -.001198
          Ln_Intangible_Assets |  -.0068704   .0024209    -2.84   0.005    -.0116462   -.0020947
                         CoAge |  -.0001842   .0006843    -0.27   0.788    -.0015342    .0011658
                        wGDPpc |   1.33e-06   8.73e-07     1.53   0.128    -3.87e-07    3.06e-06
                          wCPI |  -.0010576   .0010169    -1.04   0.300    -.0030637    .0009484
                          wDCF |   6.03e-15   5.04e-15     1.20   0.233    -3.92e-15    1.60e-14
                        wExpgr |    .000601   .0005293     1.14   0.258    -.0004433    .0016452
                        wGDPgr |   .0001661   .0012917     0.13   0.898     -.002382    .0027142
                         wCons |  -1.03e-15   1.76e-15    -0.59   0.558    -4.49e-15    2.43e-15
                      Ln_PS_RD |  -.0020041    .002838    -0.71   0.481    -.0076027    .0035944
                               |
                      stLn_GSD |
                           L1. |    -.57451   .4553334    -1.26   0.209     -1.47276    .3237404
                               |
       cL.stLn_GSD#cL.stLn_GSD |   .1883956   .2907277     0.65   0.518     -.385132    .7619232
                               |
                        crisis |
                            1  |  -.4569799   .3124271    -1.46   0.145    -1.073314    .1593546
                            3  |  -.4601988   .2564698    -1.79   0.074    -.9661447    .0457471
                               |
            crisis#cL.stLn_GSD |
                            1  |   .7185452   .4607122     1.56   0.121    -.1903161    1.627406
                            3  |    .487764   .4050218     1.20   0.230     -.311235    1.286763
                               |
crisis#cL.stLn_GSD#cL.stLn_GSD |
                            1  |   -.357259   .2781143    -1.28   0.201    -.9059036    .1913856
                            3  |  -.2306706   .2617277    -0.88   0.379    -.7469891    .2856478
                               |
                stLn_GSD_Asset |
                           L1. |   -.359221   .7368407    -0.49   0.626     -1.81281    1.094368
                               |
             cL.stLn_GSD_Asset#|
             cL.stLn_GSD_Asset |   .2460803   .4487124     0.55   0.584    -.6391085    1.131269
                               |
      crisis#cL.stLn_GSD_Asset |
                            1  |   .3356031   .7352778     0.46   0.649    -1.114902    1.786108
                            3  |   .5517952   .7587673     0.73   0.468    -.9450485    2.048639
                               |
      crisis#cL.stLn_GSD_Asset#|
             cL.stLn_GSD_Asset |
                            1  |  -.2548082   .4477104    -0.57   0.570     -1.13802     .628404
                            3  |  -.3704474   .4619013    -0.80   0.424    -1.281654    .5407597
                               |
                         _cons |   .4437262   .2979755     1.49   0.138    -.1440993    1.031552
-------------------------------+----------------------------------------------------------------
                       sigma_u |  .04523247
                       sigma_e |  .02298206
                           rho |  .79481585   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------------

. 
end of do-file

. lincom _b[c.l1.stLn_GSD##c.l1.stLn_GSD##ib2.crisis] - _b[c.l1.stLn_GSD_Asset##c.l1.stLn_GSD_Asset#
> #ib2.crisis]
invalid matrix stripe;
c.l1.stLn_GSD##c.l1.stLn_GSD##ib2.crisis
r(198);

[Joseph Coveney]

So far so good. However, I think something is wrong with my lincom command. Any suggestions would be very helpful.

You must specify levels of factor variables individually with -lincom-. Likewise, you must specify the components of the interaction terms individually. In general, specify the predictors in the manner that you see them presented in the regression output table. See below for an example (scroll down to the comments), and refer to the user's manual entry for -lincom- for more details.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ1560649071

.ÿ
.ÿquietlyÿsysuseÿauto

.ÿ
.ÿsummarizeÿrep78,ÿmeanonly

.ÿquietlyÿreplaceÿrep78ÿ=ÿruniformint(r(min),ÿr(max))ÿifÿmi(rep78)

.ÿ
.ÿxtregÿpriceÿi.foreign##c.mpg,ÿi(rep78)ÿre

Random-effectsÿGLSÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿ74
Groupÿvariable:ÿrep78ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿÿ5

R-squared:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿWithinÿÿ=ÿ0.2992ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ3
ÿÿÿÿÿBetweenÿ=ÿ0.2769ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ14.8
ÿÿÿÿÿOverallÿ=ÿ0.2888ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ32

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(3)ÿÿÿÿÿÿ=ÿÿÿÿÿÿ28.90
corr(u_i,ÿX)ÿ=ÿ0ÿ(assumed)ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000

-------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿpriceÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
--------------+----------------------------------------------------------------
ÿÿÿÿÿÿforeignÿ|
ÿÿÿÿÿForeignÿÿ|ÿÿ-139.1509ÿÿÿ2646.266ÿÿÿÿ-0.05ÿÿÿ0.958ÿÿÿÿ-5325.737ÿÿÿÿ5047.435
ÿÿÿÿÿÿÿÿÿÿmpgÿ|ÿÿ-333.9747ÿÿÿ75.30932ÿÿÿÿ-4.43ÿÿÿ0.000ÿÿÿÿ-481.5782ÿÿÿ-186.3711
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
foreign#c.mpgÿ|
ÿÿÿÿÿForeignÿÿ|ÿÿÿÿ83.3522ÿÿÿ112.3521ÿÿÿÿÿ0.74ÿÿÿ0.458ÿÿÿÿ-136.8538ÿÿÿÿ303.5582
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ12677.14ÿÿÿ1563.759ÿÿÿÿÿ8.11ÿÿÿ0.000ÿÿÿÿÿ9612.228ÿÿÿÿ15742.05
--------------+----------------------------------------------------------------
ÿÿÿÿÿÿsigma_uÿ|ÿÿ437.92483
ÿÿÿÿÿÿsigma_eÿ|ÿÿ2566.3844
ÿÿÿÿÿÿÿÿÿÿrhoÿ|ÿÿ.02829376ÿÿÿ(fractionÿofÿvarianceÿdueÿtoÿu_i)
-------------------------------------------------------------------------------

.ÿ
.ÿ//ÿCannotÿuseÿfactorÿvariablesÿlikeÿthisÿwithÿ-lincom-
.ÿcaptureÿlincomÿ_b[i.foreign##c.mpg]

.ÿdisplayÿinÿsmclÿasÿerrorÿ_rc
198

.ÿ
.ÿ//ÿMustÿspecifyÿtheÿlevels,ÿinteractionÿtermsÿetc.ÿindividually
.ÿlincomÿ_b[1.foreign]ÿ+ÿ_b[c.mpg]ÿ+ÿ_b[1.foreign#c.mpg]

ÿ(ÿ1)ÿÿ1.foreignÿ+ÿmpgÿ+ÿ1.foreign#c.mpgÿ=ÿ0

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿpriceÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿ(1)ÿ|ÿÿ-389.7733ÿÿÿ2581.744ÿÿÿÿ-0.15ÿÿÿ0.880ÿÿÿÿ-5449.899ÿÿÿÿ4670.352
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.