Confusion about when to use SUR estimation (sureg) or Multivariate regression (mvreg)

[Michael Steiner]

I am having a problem deciding between seemingly unrelated regression (sureg) and multivariate regression (mv). And I’m unsure what method to use for my research problem.
I am using Stata 15 for Windows.

My goal is to analyze factors that drive consumers’ choice for different products. In order to do so, I conducted an experiment that presents respondents several product alternatives and I asked them to evaluate the products based on purchase likelihood values (ranging from 0 to 100).

I assume that factors such as price consciousness, brand, socio-demographics etc. influence customers likelihood to buy a certain product.

As result, I will have 6 equations, i.e. a demand system for food items. That is, the existence of one product should influence the evaluation of the others.
The IVs do not differ between the equations.

My goal is to test whether the significance of the factors differs between the equations.

In order to analyze such data, SUR estimation (sureg) but also multivariate regression (mvreg) seem to be applicable from my perspective. But I do not know which method I should use.

I hope that you can help making the decision for one of the methods?

Kind regards
Michael

[Joro Kolev]

Depends on your regressors in the 6 equations. If the regressors are the same, it does not matter whether you use seemingly unrelated, or multivariate regresssion.

If the regressors are different, you have not choice but to use seemingly unrelated regression.

In short, just use seemingly unrelated regression.

[Michael Steiner]

Thank you for your feedback!!

The IVs do not differ.

Indeed, my first intention was to use SUR ... but then I talked to some other researchers from my field and they all recommended mvreg because the IVs are the same. This left me puzzled ... and to be honest, I still am ... does it really make no difference? Is there any disadvantage of sureg compared to mvreg?

Is there any literature that compares mvreg and sureg?

[Joro Kolev]

There is not literature on comparing mvreg to sureg because when the regressors are different, you cannot use mvreg, and when the regressors are the same, they both give you numerically the same estimates. Here:

. sysuse auto, clear
(1978 Automobile Data)

. mvreg headroom trunk turn = price mpg displ gear_ratio length weight

Equation             Obs   Parms        RMSE    "R-sq"          F        P
--------------------------------------------------------------------------
headroom              74       7    .7390205    0.2996   4.777213   0.0004
trunk                 74       7    3.052314    0.5326    12.7265   0.0000
turn                  74       7    2.132377    0.7844   40.62042   0.0000

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
headroom     |
       price |  -.0000528    .000038    -1.39   0.168    -.0001286    .0000229
         mpg |  -.0093774   .0260463    -0.36   0.720     -.061366    .0426112
displacement |   .0031025   .0024999     1.24   0.219    -.0018873    .0080922
  gear_ratio |   .2108071   .3539588     0.60   0.553    -.4956976    .9173119
      length |    .015886    .012944     1.23   0.224    -.0099504    .0417223
      weight |  -.0000868   .0004724    -0.18   0.855    -.0010296    .0008561
       _cons |  -.4525117   2.170073    -0.21   0.835    -4.783995    3.878972
-------------+----------------------------------------------------------------
trunk        |
       price |   .0000445   .0001567     0.28   0.778    -.0002684    .0003573
         mpg |  -.0220919   .1075767    -0.21   0.838    -.2368159    .1926322
displacement |   .0032118   .0103251     0.31   0.757    -.0173971    .0238207
  gear_ratio |  -.2271321   1.461926    -0.16   0.877    -3.145149    2.690885
      length |    .170811   .0534615     3.20   0.002     .0641014    .2775206
      weight |  -.0015944    .001951    -0.82   0.417    -.0054885    .0022997
       _cons |  -13.28253   8.962868    -1.48   0.143    -31.17249    4.607429
-------------+----------------------------------------------------------------
turn         |
       price |  -.0002647   .0001095    -2.42   0.018    -.0004833   -.0000462
         mpg |  -.0492948   .0751542    -0.66   0.514    -.1993031    .1007136
displacement |   .0036977   .0072132     0.51   0.610    -.0106999    .0180953
  gear_ratio |  -.1048432   1.021316    -0.10   0.919    -2.143399    1.933712
      length |    .072128   .0373487     1.93   0.058    -.0024204    .1466764
      weight |   .0027059    .001363     1.99   0.051    -.0000145    .0054264
       _cons |   20.19157   6.261549     3.22   0.002     7.693467    32.68968
------------------------------------------------------------------------------

. sureg  (headroom price mpg displ gear_ratio length weight) (trunk price mpg displ gear_ratio length weight) (tur
> n price mpg displ gear_ratio length weight)

Seemingly unrelated regression
--------------------------------------------------------------------------
Equation             Obs   Parms        RMSE    "R-sq"       chi2        P
--------------------------------------------------------------------------
headroom              74       6    .7031986    0.2996      31.66   0.0000
trunk                 74       6    2.904362    0.5326      84.34   0.0000
turn                  74       6    2.029016    0.7844     269.19   0.0000
--------------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
headroom     |
       price |  -.0000528   .0000361    -1.46   0.143    -.0001236    .0000179
         mpg |  -.0093774   .0247838    -0.38   0.705    -.0579527    .0391979
displacement |   .0031025   .0023787     1.30   0.192    -.0015597    .0077646
  gear_ratio |   .2108071   .3368017     0.63   0.531     -.449312    .8709263
      length |    .015886   .0123166     1.29   0.197    -.0082541     .040026
      weight |  -.0000868   .0004495    -0.19   0.847    -.0009677    .0007942
       _cons |  -.4525117   2.064885    -0.22   0.827    -4.499612    3.594588
-------------+----------------------------------------------------------------
trunk        |
       price |   .0000445   .0001491     0.30   0.766    -.0002479    .0003368
         mpg |  -.0220919   .1023623    -0.22   0.829    -.2227182    .1785345
displacement |   .0032118   .0098246     0.33   0.744     -.016044    .0224676
  gear_ratio |  -.2271321   1.391064    -0.16   0.870    -2.953567    2.499302
      length |    .170811   .0508701     3.36   0.001     .0711074    .2705146
      weight |  -.0015944   .0018564    -0.86   0.390    -.0052329    .0020441
       _cons |  -13.28253    8.52842    -1.56   0.119    -29.99793    3.432864
-------------+----------------------------------------------------------------
turn         |
       price |  -.0002647   .0001042    -2.54   0.011     -.000469   -.0000605
         mpg |  -.0492948   .0715113    -0.69   0.491    -.1894543    .0908648
displacement |   .0036977   .0068635     0.54   0.590    -.0097546      .01715
  gear_ratio |  -.1048432   .9718108    -0.11   0.914    -2.009557    1.799871
      length |    .072128   .0355384     2.03   0.042     .0024741     .141782
      weight |   .0027059   .0012969     2.09   0.037     .0001641    .0052478
       _cons |   20.19157   5.958039     3.39   0.001      8.51403    31.86911
------------------------------------------------------------------------------

.

[Michael Steiner]

Thanks a lot for your feedback !! This is highly helpful !!