Fitting topological model of social mobility with design matrix in Stata

[Chen Samulsion]

Dear Stata users,

My question is about mobility table analysis, and the relevant commands including -poisson-, -glm-, and -loglin- (SSC). I want to replicate the result of John Goldthorpe who used level matrix or design matrix in fitting partitioning models (or called topological models). The model tells us that the log likelihood ratio, i.e. G² = 351 with 31 degrees of freedom. How can I fit this model and get significance test results in Stata? Thank you very much.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(father son count levels)
1 1 311 2
1 2 130 2
1 3  79 1
1 4  53 1
1 5  33 1
1 6  37 1
1 7  45 1
2 1 161 2
2 2 128 2
2 3  66 1
2 4  39 1
2 5  53 1
2 6  59 1
2 7  48 1
3 1 128 1
3 2 109 1
3 3  89 3
3 4  54 1
3 5  89 1
3 6 108 1
3 7 117 1
4 1 167 1
4 2 151 1
4 3 106 1
4 4 324 4
4 5 116 1
4 6 192 1
4 7 273 1
5 1 154 1
5 2 147 1
5 3 109 1
5 4  83 1
5 5 170 5
5 6 229 1
5 7 190 1
6 1 202 1
6 2 228 1
6 3 216 1
6 4 170 1
6 5 319 1
6 6 788 6
6 7 671 6
7 1 162 1
7 2 194 1
7 3 205 1
7 4 164 1
7 5 311 1
7 6 587 6
7 7 870 6
end
label values father class
label values son class
label def class 1 "I", modify
label def class 2 "II", modify
label def class 3 "III", modify
label def class 4 "IV", modify
label def class 5 "V", modify
label def class 6 "VI", modify
label def class 7 "VII", modify

*/ Show the Intergenerational class mobility
tabulate father son [fw=count]

*/ Show the Levels matrix (design matrix) for model
tabulate father son [fw=levels]

[Maarten Buis]

https://www.maartenbuis.nl/presentations/london15b.pdf

[Chen Samulsion]

Dear Maarten Buis thank you very much. I have noticed your presentation in 2015 and it really helps me a lot. I have wrongly inputted data in Class II of father and Class I of son cell that made me can't replicate the significance test result G² = 351. (The data I provide in 1# is right. However, I have wrong copy in my own disk.)

poisson count i.father##i.son
est store full
poisson count i.father i.son i.levels, irr
lrtest full
llingov, sat(full)

. lrtest full

Likelihood-ratio test                                 LR chi2(31) =    351.25
(Assumption: . nested in full)                        Prob > chi2 =    0.0000

. llgof, sat(full)

             |        LL         df          p        BIC          D 
-------------+-------------------------------------------------------
          r1 |  351.2547         31   6.09e-56   67.54032   .0765724

Now, my further question is when I examine specific partitioned table should I use one combined design matrix or should I use separate ones? I find that the lrtest gives different significance test results. For example:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(meduc feduc count diag move_sym move_asym full_matrix) byte _est_full
1 1 2068 1 0 0 1 1
1 2  703 0 1 2 2 1
1 3  426 0 0 0 0 1
1 4  122 0 0 0 0 1
1 5   60 0 0 0 0 1
2 1 4555 0 1 1 1 1
2 2 7200 2 0 0 2 1
2 3 2523 0 1 2 2 1
2 4  416 0 0 0 0 1
2 5  229 0 0 0 0 1
3 1 1032 0 0 0 0 1
3 2 1792 0 1 1 1 1
3 3 4845 3 0 0 3 1
3 4  856 0 1 2 2 1
3 5  544 0 0 0 0 1
4 1  334 0 0 0 0 1
4 2  472 0 0 0 0 1
4 3 1157 0 1 1 1 1
4 4 1100 4 0 0 4 1
4 5  471 0 1 2 2 1
5 1  389 0 0 0 0 1
5 2  740 0 0 0 0 1
5 3 1783 0 0 0 0 1
5 4  999 0 1 1 1 1
5 5 2418 5 0 0 5 1
end
label values meduc edu
label values feduc edu
label def edu 1 "low", modify
label def edu 2 "lower voc", modify
label def edu 3 "medium voc", modify
label def edu 4 "higher voc", modify
label def edu 5 "university", modify

. tabdisp meduc feduc, cell(count)

-----------------------------------------------------------------------
           |                           feduc                           
     meduc |        low   lower voc  medium voc  higher voc  university
-----------+-----------------------------------------------------------
       low |       2068         703         426         122          60
 lower voc |       4555        7200        2523         416         229
medium voc |       1032        1792        4845         856         544
higher voc |        334         472        1157        1100         471
university |        389         740        1783         999        2418
-----------------------------------------------------------------------


gen diag = (meduc==feduc)*meduc
gen move_sym = abs(feduc-meduc) == 1
gen move_asym = (meduc-feduc==1) + 2*(meduc-feduc==-1)
gen full_matrix=diag
replace full_matrix= move_asym if full_matrix==0

poisson count i.meduc##i.feduc
est store full

poisson count i.meduc i.feduc i.diag i.move_asym, nolog

Poisson regression                              Number of obs     =         25
                                                LR chi2(15)       =   35202.87
                                                Prob > chi2       =     0.0000
Log likelihood = -923.95537                     Pseudo R2         =     0.9501

------------------------------------------------------------------------------
       count |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       meduc |
  lower voc  |   1.155873   .0343001    33.70   0.000     1.088646      1.2231
 medium voc  |   .9144184   .0327381    27.93   0.000     .8502528    .9785839
 higher voc  |   .0403103   .0374226     1.08   0.281    -.0330366    .1136572
 university  |   .9259324   .0339594    27.27   0.000     .8593732    .9924916
             |
       feduc |
  lower voc  |  -.3596171   .0258192   -13.93   0.000    -.4102218   -.3090123
 medium voc  |   .0997877   .0223721     4.46   0.000     .0559393    .1436362
 higher voc  |  -1.049797   .0280252   -37.46   0.000    -1.104725   -.9948684
 university  |  -.9977161   .0329306   -30.30   0.000    -1.062259   -.9331732
             |
        diag |
          1  |   1.642732   .0394995    41.59   0.000     1.565314     1.72015
          2  |   2.093975   .0365023    57.37   0.000     2.022432    2.165519
          3  |   1.479891    .031555    46.90   0.000     1.418045    1.541738
          4  |   2.020947   .0481663    41.96   0.000     1.926543    2.115351
          5  |   1.870874   .0395989    47.25   0.000     1.793262    1.948487
             |
   move_asym |
          1  |     1.1175   .0204131    54.74   0.000     1.077491    1.157509
          2  |   .7335041   .0261475    28.05   0.000     .6822559    .7847522
             |
       _cons |   5.991605   .0328124   182.60   0.000     5.927294    6.055916
------------------------------------------------------------------------------

. lrtest full

Likelihood-ratio test                                 LR chi2(9)  =   1633.31
(Assumption: . nested in full)                        Prob > chi2 =    0.0000


poisson count i.meduc i.feduc i.full_matrix, nolog

Poisson regression                              Number of obs     =         25
                                                LR chi2(13)       =   32396.71
                                                Prob > chi2       =     0.0000
Log likelihood = -2327.0359                     Pseudo R2         =     0.8744

------------------------------------------------------------------------------
       count |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       meduc |
  lower voc  |   1.300971   .0194043    67.05   0.000      1.26294    1.339003
 medium voc  |   .5554793   .0244917    22.68   0.000     .5074763    .6034822
 higher voc  |   .0473744   .0282109     1.68   0.093    -.0079179    .1026668
 university  |   .8472129   .0273145    31.02   0.000     .7936774    .9007484
             |
       feduc |
  lower voc  |   .0776559   .0193121     4.02   0.000     .0398048     .115507
 medium voc  |  -.2826242   .0210531   -13.42   0.000    -.3238875   -.2413609
 higher voc  |  -1.139246   .0264795   -43.02   0.000    -1.191144   -1.087347
 university  |  -1.184959   .0328806   -36.04   0.000    -1.249403   -1.120514
             |
 full_matrix |
          1  |   1.079217   .0184555    58.48   0.000     1.043045    1.115389
          2  |    1.11327   .0230316    48.34   0.000     1.068129    1.158411
          3  |   2.117254   .0295994    71.53   0.000     2.059241    2.175268
          4  |   1.999344   .0456336    43.81   0.000     1.909903    2.088784
          5  |   2.032849   .0393746    51.63   0.000     1.955676    2.110021
             |
       _cons |   6.095593   .0235744   258.57   0.000     6.049388    6.141798
------------------------------------------------------------------------------

. lrtest full

Likelihood-ratio test                                 LR chi2(11) =   4439.47
(Assumption: . nested in full)                        Prob > chi2 =    0.0000

[Maarten Buis]

That just depends on the hypothesis you want to test.