Matrix rows and columns in McDonald and Moffit calculation

[Teresa Mungazi]

Hi,

Please see below an example McDonald and Moffit calculation:


gen one=1
mkmat whrs, matrix(y)
mkmat one, matrix(ones)
mkmat one kl6 k618 wa we, matrix(X)
matrix Xb=inv(ones'*ones)*ones'*X
matrix b = e(b)
matrix beta = b[1,5],b[1,1], b[1,2],b[1,3],b[1,4]
matrix BXoverS=Xb * beta'/b[1,6]
scalar Z=el(BXoverS,1,1)
scalar Mu=normalden(Z)/normal(Z)
scalar P=normal(Z)
scalar P1=P*(1-Z*Mu-Mu^2)
scalar P2=normalden(Z*Z+normalden(Z)*Mu)
display Mu
display P
display P1
display P2

My question is specifically on this command: matrix beta = b[1,5],b[1,1], b[1,2],b[1,3],b[1,4]. I'd like to know how the figures in the example command were determined. I understand that figures represent rows and columns for elements of the matrix b, but how do I determine the number and ordering of the elements?

I hope someone can assist.

[Andrew Musau]

From the code, it appears that you select \(k\)−1 coefficients from the matrix of coefficients, e(b), and normalize these by dividing by the \(k\)^th coefficient, where \(k\) is the number of slope coefficients. I don't think the order should matter, but you can test this by trying out different orderings. There is no way to tell what coefficients are in e(b) apart from directly examining the matrix or looking at the regression command.

matrix list e(b)

[Teresa Mungazi]

Thank you so much Andrew. I seem to be getting an error message when I move to the command. Would you know where the issue is?

code:
matrix list e(b)

e(b)[1,26]
aware_count: aware_count: aware_count: aware_count: aware_count: aware_count: aware_count:
0b. 1. 2. 3. 0. 1b. 2.
age_catego~s age_catego~s age_catego~s age_catego~s education education education
y1 0 -.20132751 -.6625963 -.87057099 .1804277 0 .2116552

aware_count: aware_count: aware_count: aware_count: aware_count: aware_count: aware_count:
3. 4. 0. 1. 2. 3. 4.
education education income income income income income
y1 .10575347 .09571243 -.23376885 -.18024522 -.26007125 -.16936466 -.10334494

aware_count: aware_count: aware_count: aware_count: aware_count: aware_count: aware_count:
5. 6b. 0b. 1. 2. 4.
income income gender~emale poli~t_other poli~t_other poli~t_other poli~t_other
y1 -.05831255 0 .0136834 0 -.03834463 .10754739 .25653429

aware_count: aware_count: aware_count: aware_count: /:

gn_sus_q1 gn_sus_q3 gn_sus_q4 _cons var(e.awa~nt)
y1 -.60788258 .2009674 .51922832 1.991675 1.389505

. matrix beta = b[1,25],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12]
> ,b[1,13],b[1,14],b[1,15],b[1,15],b[1,15],b[1,16],b[1,17],b[1,18],b[1,19],b[1,20],b[1,21],b[1,22],b[1,23],b[1,
> 24]

. matrix BXoverS=Xb * beta'/b[1,26]
conformability error
r(503);

[Teresa Mungazi]

From what I figured, it is because the rows and columns of the matrices Xb and beta that I'm trying to multiply are not aligned. How do I fix this?

[Andrew Musau]

Before trying to replicate the code, you should take the time to understand what it is doing. I am not familiar with this decomposition, so my comments come from examining the code in #1. My understanding is limited since I do not have access to the dataset and the estimation results that the code uses. If you have access to the code but not to the data and estimation results, find these so that you can fully understand the code. The conformability error is straightforward to diagnose. In the original code, the author creates an \(X\) matrix that is N \(×\) 5, where N is the sample size.

mkmat one kl6 k618 wa we, matrix(X)

The matrix beta is 1 \(\times\) 5 since the author takes the first five coefficients and divides by the sixth.

matrix beta = b[1,5],b[1,1], b[1,2],b[1,3],b[1,4]

By transposing the beta matrix, he is able to multiply it with the Xb matrix.

matrix BXoverS=Xb * beta'/b[1,6]

Also, note that in the coefficients matrix generated by tobit or regress, the last element is the coefficient on the constant term. So it is important to know which coefficient is used in the normalization.

[Teresa Mungazi]

Thank you so much for your assistance Andrew, I think I got it. Only issue is now on the last 4 display commands. Nothing is displaying.

[Andrew Musau]

I wouldn't know what the issue is without seeing your data and codes. Use matrix list to view the matrices and display to view the scalars that lead up to the definition of Mu, P, P1 and P2. This way, you can identify where the issue arises.

[Teresa Mungazi]

[CODE] tobit aware_count age_35_54 age_55_74 age75_ education_no_high_school education_college_nodegree education_degree education_postgrad
> gender_binary_female political_affiliation_dem political_affiliation_ind political_affiliation_not gn_sus_q1 gn_sus_q3 gn_sus_q4, l
> l(0)

Refining starting values:

Grid node 0: Log likelihood = -3253.3592

Fitting full model:

Iteration 0: Log likelihood = -3253.3592
Iteration 1: Log likelihood = -3163.0364
Iteration 2: Log likelihood = -3158.9434
Iteration 3: Log likelihood = -3158.915
Iteration 4: Log likelihood = -3158.915

Tobit regression Number of obs = 1,984
Uncensored = 1,532
Limits: Lower = 0 Left-censored = 452
Upper = +inf Right-censored = 0

LR chi2(14) = 498.33
Prob > chi2 = 0.0000
Log likelihood = -3158.915 Pseudo R2 = 0.0731

--------------------------------------------------------------------------------------------
aware_count | Coefficient Std. err. t P>|t| [95% conf. interval]
---------------------------+----------------------------------------------------------------
age_35_54 | -.2339827 .0832773 -2.81 0.005 -.3973035 -.0706618
age_55_74 | -.8769795 .0908383 -9.65 0.000 -1.055129 -.6988303
age75_ | -1.209102 .1687665 -7.16 0.000 -1.540082 -.8781229
education_no_high_school | .1204809 .1753226 0.69 0.492 -.2233563 .464318
education_college_nodegree | .2832136 .0927022 3.06 0.002 .101409 .4650183
education_degree | .1967588 .088696 2.22 0.027 .022811 .3707067
education_postgrad | .2714768 .1144488 2.37 0.018 .0470233 .4959304
gender_binary_female | .0215732 .0683191 0.32 0.752 -.112412 .1555584
political_affiliation_dem | -.0343242 .0883404 -0.39 0.698 -.2075747 .1389263
political_affiliation_ind | .164384 .0947906 1.73 0.083 -.0215164 .3502844
political_affiliation_not | .2303417 .1272139 1.81 0.070 -.0191462 .4798295
gn_sus_q1 | -.7852713 .0938499 -8.37 0.000 -.9693267 -.6012158
gn_sus_q3 | .2486098 .1055488 2.36 0.019 .0416108 .4556088
gn_sus_q4 | .6036098 .1044214 5.78 0.000 .3988218 .8083978
_cons | 1.686088 .1220211 13.82 0.000 1.446784 1.925393
---------------------------+----------------------------------------------------------------
var(e.aware_count)| 2.099159 .0798288 1.948296 2.261702
--------------------------------------------------------------------------------------------

.
. gen one=1
variable one already defined
r(110);

. mkmat aware_count, matrix(y)

. mkmat one, matrix(ones)

. mkmat one age_35_54 age_55_74 age75_ education_no_high_school education_college_nodegree education_degree education_postgrad gender_
> binary_female political_affiliation_dem political_affiliation_ind political_affiliation_not gn_sus_q1 gn_sus_q3 gn_sus_q4, matrix(X)
>

.
. matrix Xb=inv(ones'*ones)*ones'*X

. matrix beta = b[1,15],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12],b[1,13],b[1,14]

.
. matrix beta = b[1,15],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12],b[1,13],b[1,14]

. matrix BXoverS=Xb * beta'/b[1,16]

. scalar Z=el(BXoverS,1,1)

. scalar Mu=normalden(Z)/normal(Z)

. scalar P=normal(Z)

. scalar P1=P*(1-Z*Mu-Mu^2)

.
.
. scalar P2=normalden(Z*Z+normalden(Z)*Mu)

. display Mu
.

. display P
.

.
. display P1
.

. display P2
.

/CODE]

[Teresa Mungazi]

  matrix list e(b)

e(b)[1,16]
      aware_count:   aware_count:   aware_count:   aware_count:   aware_count:   aware_count:   aware_count:
        age_35_54      age_55_74         age75_   e~no_high_~l   educ~odegree   educ~_degree   education_~d
y1     -.18891066     -.66473667     -.85717894      .09891194      .23891776      .17052525      .20320376

      aware_count:   aware_count:   aware_count:   aware_count:   aware_count:   aware_count:   aware_count:
     gender~emale   political~em   political_~d   political_~t      gn_sus_q1      gn_sus_q3      gn_sus_q4
y1     -.00830027     -.04716346      .11752833      .19827956     -.58755837      .21870967       .5474535

      aware_count:             /:
            _cons  var(e.awa~nt)
y1      1.8041728      1.3923365

[Teresa Mungazi]

 matrix list beta 

beta[1,15]
            c1          c2          c3          c4          c5          c6          c7          c8          c9
r1    .5474535  -.18891066  -.66473667  -.85717894   .09891194   .23891776   .17052525   .20320376  -.00830027

           c10         c11         c12         c13         c14         c15
r1  -.04716346   .11752833   .19827956  -.58755837   .21870967   .21870967

[Teresa Mungazi]

 tobit aware_count age_35_54 age_55_74 age75_ education_no_high_school education_college_nodegree education_degree education_postgrad
>  gender_binary_female political_affiliation_dem political_affiliation_ind political_affiliation_not gn_sus_q1 gn_sus_q3 gn_sus_q4, l
> l(0)

Refining starting values:

Grid node 0:  Log likelihood = -3253.3592

Fitting full model:

Iteration 0:  Log likelihood = -3253.3592  
Iteration 1:  Log likelihood = -3163.0364  
Iteration 2:  Log likelihood = -3158.9434  
Iteration 3:  Log likelihood =  -3158.915  
Iteration 4:  Log likelihood =  -3158.915  

Tobit regression                                    Number of obs     =  1,984
                                                           Uncensored =  1,532
Limits: Lower =    0                                    Left-censored =    452
        Upper = +inf                                   Right-censored =      0

                                                    LR chi2(14)       = 498.33
                                                    Prob > chi2       = 0.0000
Log likelihood = -3158.915                          Pseudo R2         = 0.0731

--------------------------------------------------------------------------------------------
               aware_count | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------------------+----------------------------------------------------------------
                 age_35_54 |  -.2339827   .0832773    -2.81   0.005    -.3973035   -.0706618
                 age_55_74 |  -.8769795   .0908383    -9.65   0.000    -1.055129   -.6988303
                    age75_ |  -1.209102   .1687665    -7.16   0.000    -1.540082   -.8781229
  education_no_high_school |   .1204809   .1753226     0.69   0.492    -.2233563     .464318
education_college_nodegree |   .2832136   .0927022     3.06   0.002      .101409    .4650183
          education_degree |   .1967588    .088696     2.22   0.027      .022811    .3707067
        education_postgrad |   .2714768   .1144488     2.37   0.018     .0470233    .4959304
      gender_binary_female |   .0215732   .0683191     0.32   0.752     -.112412    .1555584
 political_affiliation_dem |  -.0343242   .0883404    -0.39   0.698    -.2075747    .1389263
 political_affiliation_ind |    .164384   .0947906     1.73   0.083    -.0215164    .3502844
 political_affiliation_not |   .2303417   .1272139     1.81   0.070    -.0191462    .4798295
                 gn_sus_q1 |  -.7852713   .0938499    -8.37   0.000    -.9693267   -.6012158
                 gn_sus_q3 |   .2486098   .1055488     2.36   0.019     .0416108    .4556088
                 gn_sus_q4 |   .6036098   .1044214     5.78   0.000     .3988218    .8083978
                     _cons |   1.686088   .1220211    13.82   0.000     1.446784    1.925393
---------------------------+----------------------------------------------------------------
         var(e.aware_count)|   2.099159   .0798288                      1.948296    2.261702
--------------------------------------------------------------------------------------------

. 
.  gen one=1
variable one already defined
r(110);

. mkmat aware_count, matrix(y)

. mkmat one, matrix(ones)

. mkmat one age_35_54 age_55_74 age75_ education_no_high_school education_college_nodegree education_degree education_postgrad gender_
> binary_female political_affiliation_dem political_affiliation_ind political_affiliation_not gn_sus_q1 gn_sus_q3 gn_sus_q4, matrix(X)
>  

. 
. matrix Xb=inv(ones'*ones)*ones'*X

.  matrix beta = b[1,15],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12],b[1,13],b[1,14]

. 
. matrix beta = b[1,15],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12],b[1,13],b[1,14]

. matrix BXoverS=Xb * beta'/b[1,16]

. scalar Z=el(BXoverS,1,1)

. scalar Mu=normalden(Z)/normal(Z)

. scalar P=normal(Z)

. scalar P1=P*(1-Z*Mu-Mu^2)

. 
. 
. scalar P2=normalden(Z*Z+normalden(Z)*Mu)

. display Mu
.

. display P
.

. 
.  display P1
.

.  display P2
.

[Teresa Mungazi]

This is my output Andrew, please ignore the bit where I din't use code delimeters. I coudn't figure out how to delete.

[Andrew Musau]

matrix beta = b[1,15],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12],b[1,13],b[1,14]
matrix beta = b[1,15],b[1,1], b[1,2],b[1,3],b[1,4],b[1,5],b[1,6],b[1,7],b[1,8],b[1,9],b[1,10],b[1,11],b[1,12],b[1,13],b[1,14]

I do not see a matrix b defined in your code. There may yet be other issues.