Problems with Multivariate multiple regression

[Qi vd Kolk]

Hi all,

I performed a multivariate multiple regression in Stata 16.1 with three dependent variables.
However, I can't find how to display the adjusted R-squared and I think it is important to report in my master thesis.
Is there a command to also display the adjusted r-squared when conducting a multivariate multiple regression?

Furthermore, I can't find how to test for multicollinearity and heteroscedascity, with multiple regression one uses estate vif and vce(robust) but what are the commands to do this with a multivariate multiple regression?

Thanks in advance!

[Rich Goldstein]

what command did you use? please read the FAQ and post what you did and what was returned following the FAQ advice;

[Carlo Lazzaro]

Qi:
I do share Rich's wise recommendations on posting in the most effective and efficient way.
That said, given the following toy-example, I think you can easily calculate the Adj-Rsq going back to -regress- repeated for each dependent variables in the left-hand side of the regression equation:

. use https://www.stata-press.com/data/r16/auto
(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
------------------------------------------------------------------------------

. reg headroom price mpg displ gear_ratio length weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(6, 67)        =      4.78
       Model |  15.6544852         6  2.60908087   Prob > F        =    0.0004
    Residual |  36.5921364        67  .546151289   R-squared       =    0.2996
-------------+----------------------------------   Adj R-squared   =    0.2369
       Total |  52.2466216        73  .715707146   Root MSE        =    .73902

------------------------------------------------------------------------------
    headroom |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       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
------------------------------------------------------------------------------

. di e(r2_a)
.23690675

.

[Qi vd Kolk]

Thanks for the reply!

I used the following commands:

1. manova Postcrisisrep_overall PostAng_overall PostCPI_overall = i.CompManupDummy##c.centered_Priorreputation_overa ll c.centered_CrisisResponsibility c.centered_CrisisInvolvement__ c.centered_Employment c.centered_Age
2. mvreg

If I use mvreg, vce(robust) Stata says: option vce() not allowed.
Also, when I want to use estat vif after using mvreg, Stata says: estat vif not valid


DV's = Postcrisisrep_overall PostAng_overall PostCPI_overal
IV = CompManupDummy
Controls = c.centered_CrisisResponsibility c.centered_CrisisInvolvement__ c.centered_Employment c.centered_Age
Moderator = centered_Priorreputation_overall

[Qi vd Kolk]

Thanks Carlo!
So if I understand correctly, I am allowed to use the adjusted R-squared that you get when running each dependent variable in a separate regression because this is the same when you run all all three dependent variables in one regression (mvreg)?

Furthermore, I read that one advantage of using the mvreg command is that tests of coefficients (IVs) across the DVs may be run. However, I barely have any significant values in my regression table, I was wondering whether It is necessary then to use the test command as the use of the test command is one of the compelling reasons for conducting a multivariate regression analysis.
The reason why I performed a multivariate multiple regression is because I have moderately correlated dependent variables.

Below my multivariate regression table: I runned three mvreg's regression to get model 1, 2 and 3 as I thought it would make sense to show a model(1) with only controls and the Dv's, a model(2) with controls + dv + IV and a model (3) that contains controls, DV, IV + interaction just like people often do when using a multiple regression.

	M1			M2			M3
	Post-Rep	Post-Ang	PostCPI	Post-rep	PostAng	PostCPI	Post-rep	PostAng	PostCPI
	b/se	b/se	b/se	b/se	b/se	b/se	b/se	b/se	b/se
Crisis responsibility	-0.060	0.313*	-0.073	-0.060	0.312*	-0.073	-0.011	0.263	-0.036
	(0.124)	(0.137)	(0.087)	(0.122)	(0.136)	(0.087)	(0.122)	(0.136)	(0.088)
Crisis Involvement	0.017	0.182	0.004	-0.014	0.214*	-0.006	-0.021	0.223*	0.010
	(0.092)	(0.102)	(0.065)	(0.092)	(0.102)	(0.066)	(0.088)	(0.097)	(0.063)
cGender	-0.112	0.161	0.105	-0.127	0.176	0.100
	(0.187)	(0.208)	(0.132)	(0.185)	(0.206)	(0.132)
Employment	0.138	0.044	0.089	0.111	0.073	0.080	0.126	0.048	0.067
	(0.128)	(0.142)	(0.090)	(0.128)	(0.142)	(0.091)	(0.123)	(0.137)	(0.089)
Age	-0.130*	0.015	-0.010	-0.134*	0.019	-0.012	-0.121*	0.001	-0.015
	(0.055)	(0.061)	(0.039)	(0.054)	(0.060)	(0.039)	(0.052)	(0.058)	(0.037)
Crisis strategy=1				-0.301	0.309	-0.101	-0.265	0.265	-0.087
				(0.160)	(0.178)	(0.114)	(0.157)	(0.174)	(0.113)
Prior reputation							0.343	-0.449*	0.181
							(0.180)	(0.200)	(0.130)
Crisis strategy#Priorreputation							-0.091	0.224	0.002
							(0.251)	(0.279)	(0.181)
Constant	3.149***	3.327***	2.680***	3.300***	3.173***	2.731***	3.283***	3.196***	2.721***
	(0.079)	(0.087)	(0.055)	(0.111)	(0.124)	(0.080)	(0.110)	(0.122)	(0.079)
R-squared	0.058	0.119	0.022	0.090	0.145	0.030	0.135	0.191	0.062
R-squared, adjusted
Observations	106			106			106
* p<0.05, ** p<0.01, *** p<0.001

[Carlo Lazzaro]

Qi:
yes, but a more substantive issue rests on the usefulness of Adj_R2 to be included in the -mvreg- output table (admittedly, I do not know, as I'm not a -mvreg- user); hence, check the literature in your reserch field.
-test- on all your dependent variables may be informative.

[Qi vd Kolk]

Thank you very much, really appreciate it!!