Mean ratio for linear regression

[Ly Tran]

Hi all,
I have a survey data with y is continuous variable, x1: binary variable, x2...x5 are either continuous or categorical variables. I used linear regression with the following code:
svy: regress y x1 x2 x3 x4 x5
I have a result with coefficient for each independent variable. For the main binary independent variable x1, the coefficient shows the mean difference between 2 groups. However, my advisor wants to report mean ratio instead of mean difference but I don't know how. Could you please help me?
Thanks.

[Carlo Lazzaro]

Ly:
you may want to consider -nlcom-:

. use "C:\Program Files\Stata16\ado\base\a\auto.dta"
(1978 Automobile Data)

. regress price i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =      0.17
       Model |  1507382.66         1  1507382.66   Prob > F        =    0.6802
    Residual |   633558013        72  8799416.85   R-squared       =    0.0024
-------------+----------------------------------   Adj R-squared   =   -0.0115
       Total |   635065396        73  8699525.97   Root MSE        =    2966.4

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   312.2587   754.4488     0.41   0.680    -1191.708    1816.225
       _cons |   6072.423    411.363    14.76   0.000     5252.386     6892.46
------------------------------------------------------------------------------

. nlcom (_cons+_b[1.foreign]/_cons), post

       _nl_1:  _cons+_b[1.foreign]/_cons

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   313.2587   754.4488     0.42   0.678    -1165.434    1791.951
------------------------------------------------------------------------------

. testnl ( _cons+_b[1.foreign]/_cons)=0

  (1)  ( _cons+_b[1.foreign]/_cons) = 0

               chi2(1) =        0.17
           Prob > chi2 =        0.6780

.

[Ly Tran]

Thanks Carlo. May I ask how I interpret the coef. in the nlcom: 313.26. Is it a mean ratio between foreign group (1 vs. 0)?

[Carlo Lazzaro]

Ly:
-nlcom- replace _cons with 1 (313.2587 vs 312.2587); hence, this may not be what your supervisor wants you to do.
-nlcom- confirms (as expected) that the difference between the mean (conditional) price for domestic and foreign does not differ (or, better, that we cannot rule out that the difference is not 0).

[Ly Tran]

Thanks Carlo. So, can I use the following code to get mean ratio between groups?
nlcom ((_b[_cons]+_b[1.foreign])/_b[_cons]).

[Carlo Lazzaro]

Ly:
the formula you copied and pasted in #5 replaces _cons with 1 (313.2587 vs 312.2587); hence, this may not be what your supervisor wants you to do.
I do hope that what follows can give you some indications:

. use "C:\Program Files\Stata16\ado\base\a\auto.dta"
(1978 Automobile Data)

. regress price i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =      0.17
       Model |  1507382.66         1  1507382.66   Prob > F        =    0.6802
    Residual |   633558013        72  8799416.85   R-squared       =    0.0024
-------------+----------------------------------   Adj R-squared   =   -0.0115
       Total |   635065396        73  8699525.97   Root MSE        =    2966.4

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   312.2587   754.4488     0.41   0.680    -1191.708    1816.225
       _cons |   6072.423    411.363    14.76   0.000     5252.386     6892.46
------------------------------------------------------------------------------

. predict fitted, xb

. egen mean_domestic=mean(fitted) if foreign==0
(22 missing values generated)

. egen mean_foreign=mean(fitted) if foreign==1
(52 missing values generated)




. sum mean_domestic mean_foreign

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
mean_domes~c |         52    6072.423           0   6072.423   6072.423
mean_foreign |         22    6384.682           0   6384.682   6384.682


. sum mean_domestic

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
mean_domes~c |         52    6072.423           0   6072.423   6072.423


. scalar m1=r(mean)

. sum mean_foreign

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
mean_foreign |         22    6384.682           0   6384.682   6384.682

. scalar m2=r(mean)

. di scalar(m1)/scalar(m2)
.9510925

.

That said, I still fail to get what your supervisor is aiming at via mean ratios.

[Anustup Kundu]

Hi,
My question doesn't relate to mean ratio for linear regression but towards nlcom

I am trying to estimate the Intergenerational Correlation (IGC) in education using nlcom but cannot figure out how to

\[ IGC : \rho_{IG}= \beta1 * \frac{\sigma_{parent}}{\sigma_{child}} \]

Where P_IG = Intergenerational Correlation (IGC),

Beta1 = intergenerational regression coefficient (IGRC) coming from estimating

\[ Edu_{i,g} = \beta_{0}+ \beta_{1}Edu_{i,parent}+\beta_{2}Edu_{i,grandparen t} + \epsilon_{ig} \]

and Sigma= standard deviation of the parent/child