Bifactor Graded Model (Bifactor IRT)

[Maryam Bidgoli]

Hello everyone!

I have a 10 item questionnaire related to subjective financial wellbeing (SFWB) and I want to fit a bifactor graded model (bifactor IRT) using gsem in Stata 16. The general latent (G) is SFWB and two specific latent traits (S1 and S2; positively vs negatively worded items). The 10 items are below:

Table. Subjective Financial Wellbeing Item Content
variable	item
fwb1_exp	I could handle a major unexpected expense.
fwb3_secure	I am securing my financial future.
fwb6_enjoy	I can enjoy life because of the way I'm managing my money.
fwb2_getby	I am just getting by financially.
fwb4_concern	I am concerned that the money I have or will save won't last.
fwb9_strain	Giving a gift for a wedding, birthday or other occasion would put a strain on my finances for the month.
fwb5_never	Because of my money situation, I feel like I will never have the things I want in life.
fwb10_left	I have money left over at the end of the month.
fwb7_behind	I am behind with my finances.
fwb8_control	My finances control my life.

The code is:

mat V = I(4)

gsem ( SFWB -> fwb1_exp fwb2_getby fwb3_secure fwb4_concern fwb5_never fwb6_enjoy fwb7_behind fwb8_control fwb9_strain fwb10_left, ologit) ///
(S1 -> fwb1_exp fwb3_secure fwb6_enjoy fwb10_left, ologit) ///
(S2 -> fwb2_getby fwb4_concern fwb5_never fwb7_behind fwb8_control fwb9_strain, ologit), ///
latent (SFWB S1 S2)
covstructure(SFWB S1 S2, fixed(V)) ///
  intp(3) difficult

My questions are:

1. is the code correct?
2. the model is not concave. Any suggestion?

[Maryam Bidgoli]

There was a typo in my code. The following code worked:

mat V = I(3)

gsem ( SFWB -> fwb1_exp fwb2_getby fwb3_secure fwb4_concern fwb5_never fwb6_enjoy fwb7_behind fwb8_control fwb9_strain fwb10_left, ologit) ///
(S1 -> fwb1_exp fwb3_secure fwb6_enjoy fwb10_left, ologit) ///
(S2 -> fwb2_getby fwb4_concern fwb5_never fwb7_behind fwb8_control fwb9_strain, ologit), ///
latent (SFWB S1 S2) ///
covstructure(SFWB S1 S2, fixed(V)) ///
intp(3) difficult

However, there is no p-value and z score for the cut off points.

 mat V = I(3)

. 
. gsem ( SFWB -> fwb1_exp fwb2_getby fwb3_secure fwb4_concern fwb5_never fwb6_enjoy fwb7_behind fwb8_control fwb9_strain fwb10_left, ologit) ///
> (S1 -> fwb1_exp fwb3_secure fwb6_enjoy fwb10_left, ologit) ///
> (S2 -> fwb2_getby fwb4_concern fwb5_never fwb7_behind fwb8_control fwb9_strain, ologit), ///
> latent (SFWB S1 S2) ///
> covstructure(SFWB S1 S2, fixed(V)) ///
> intp(3) difficult

Fitting fixed-effects model:

Iteration 0:   log likelihood = -63739.607  
Iteration 1:   log likelihood = -63739.607  

Refining starting values:

Grid node 0:   log likelihood = -61020.697

Fitting full model:

Iteration 0:   log likelihood = -61020.697  (not concave)
Iteration 1:   log likelihood = -55851.943  (not concave)
Iteration 2:   log likelihood =  -54669.93  (not concave)
Iteration 3:   log likelihood = -54047.834  (not concave)
Iteration 4:   log likelihood = -53375.306  
Iteration 5:   log likelihood = -53274.617  (not concave)
Iteration 6:   log likelihood = -53248.898  
Iteration 7:   log likelihood = -53243.856  (not concave)
Iteration 8:   log likelihood = -53238.307  
Iteration 9:   log likelihood = -53232.463  
Iteration 10:  log likelihood = -53229.725  
Iteration 11:  log likelihood = -53229.356  
Iteration 12:  log likelihood = -53229.221  
Iteration 13:  log likelihood = -53229.205  
Iteration 14:  log likelihood = -53229.199  
Iteration 15:  log likelihood = -53229.198  

Generalized structural equation model           Number of obs     =      4,609

Response       : fwb1_exp                       Number of obs     =      4,571
Family         : ordinal
Link           : logit

Response       : fwb2_getby                     Number of obs     =      4,519
Family         : ordinal
Link           : logit

Response       : fwb3_secure                    Number of obs     =      4,517
Family         : ordinal
Link           : logit

Response       : fwb4_concern                   Number of obs     =      4,557
Family         : ordinal
Link           : logit

Response       : fwb5_never                     Number of obs     =      4,529
Family         : ordinal
Link           : logit

Response       : fwb6_enjoy                     Number of obs     =      4,542
Family         : ordinal
Link           : logit

Response       : fwb7_behind                    Number of obs     =      4,571
Family         : ordinal
Link           : logit

Response       : fwb8_control                   Number of obs     =      4,568
Family         : ordinal
Link           : logit

Response       : fwb9_strain                    Number of obs     =      4,582
Family         : ordinal
Link           : logit

Response       : fwb10_left                     Number of obs     =      4,568
Family         : ordinal
Link           : logit

Log likelihood = -53229.198

 ( 1)  [/]var(SFWB) = 1
 ( 2)  [/]var(S1) = 1
 ( 3)  [/]var(S2) = 1
-------------------------------------------------------------------------------
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
fwb1_exp      |
         SFWB |   2.639515   .0829198    31.83   0.000     2.476995    2.802035
           S1 |   1.823552   .0794761    22.94   0.000     1.667782    1.979323
--------------+----------------------------------------------------------------
fwb2_getby    |
         SFWB |   1.213218   .0430201    28.20   0.000       1.1289    1.297536
           S2 |   .5336184   .0539463     9.89   0.000     .4278856    .6393512
--------------+----------------------------------------------------------------
fwb3_secure   |
         SFWB |   3.515999    .151759    23.17   0.000     3.218557    3.813441
           S1 |   2.909161   .1454342    20.00   0.000     2.624115    3.194207
--------------+----------------------------------------------------------------
fwb4_concern  |
         SFWB |   2.376854   .1075676    22.10   0.000     2.166026    2.587683
           S2 |    1.46545   .1631709     8.98   0.000     1.145641    1.785259
--------------+----------------------------------------------------------------
fwb5_never    |
         SFWB |   2.053554   .0721625    28.46   0.000     1.912118     2.19499
           S2 |   .9756279   .0846641    11.52   0.000     .8096893    1.141566
--------------+----------------------------------------------------------------
fwb6_enjoy    |
         SFWB |   2.261273   .0639185    35.38   0.000     2.135996    2.386551
           S1 |   1.224857   .0557284    21.98   0.000     1.115631    1.334083
--------------+----------------------------------------------------------------
fwb7_behind   |
         SFWB |     2.6262   .1153044    22.78   0.000     2.400207    2.852192
           S2 |  -.5393334   .1159713    -4.65   0.000     -.766633   -.3120338
--------------+----------------------------------------------------------------
fwb8_control  |
         SFWB |   1.767583   .0542302    32.59   0.000     1.661294    1.873873
           S2 |   .1672053   .0691436     2.42   0.016     .0316864    .3027243
--------------+----------------------------------------------------------------
fwb9_strain   |
         SFWB |   2.302436   .0715461    32.18   0.000     2.162208    2.442664
           S2 |  -.0531245   .0662402    -0.80   0.423    -.1829529    .0767039
--------------+----------------------------------------------------------------
fwb10_left    |
         SFWB |   2.248496   .0643258    34.95   0.000     2.122419    2.374572
           S1 |   .5813085   .0488526    11.90   0.000     .4855592    .6770578
--------------+----------------------------------------------------------------
/fwb1_exp     |
         cut1 |  -3.923197   .1095892                     -4.137987   -3.708406
         cut2 |  -2.328526   .0851335                     -2.495385   -2.161668
         cut3 |   .9133986   .0708675                      .7745009    1.052296
         cut4 |   3.776938   .1081037                      3.565058    3.988817
--------------+----------------------------------------------------------------
/fwb2_getby   |
         cut1 |  -2.944535   .0659644                     -3.073822   -2.815247
         cut2 |  -1.639572    .046856                     -1.731409   -1.547736
         cut3 |   .0526678   .0392931                     -.0243453     .129681
         cut4 |   1.013667   .0431851                      .9290255    1.098308
--------------+----------------------------------------------------------------
/fwb3_secure  |
         cut1 |  -6.098861   .2331863                     -6.555898   -5.641825
         cut2 |  -3.538884   .1543199                     -3.841346   -3.236423
         cut3 |   1.236468     .10538                      1.029927    1.443009
         cut4 |   5.553632   .2264719                      5.109755    5.997509
--------------+----------------------------------------------------------------
/fwb4_concern |
         cut1 |  -4.354533   .1918661                     -4.730584   -3.978483
         cut2 |  -3.297541   .1509946                     -3.593485   -3.001597
         cut3 |  -.0473106    .059935                     -.1647811      .07016
         cut4 |    2.21833   .1090061                      2.004682    2.431978
--------------+----------------------------------------------------------------
/fwb5_never   |
         cut1 |  -4.901197   .1367705                     -5.169263   -4.633132
         cut2 |  -3.824839   .1081226                     -4.036756   -3.612923
         cut3 |  -1.088057   .0584659                     -1.202648   -.9734662
         cut4 |   1.087941   .0577737                      .9747069    1.201176
--------------+----------------------------------------------------------------
/fwb6_enjoy   |
         cut1 |  -4.782857   .1088629                     -4.996224   -4.569489
         cut2 |  -3.010867   .0798201                     -3.167311   -2.854422
         cut3 |    .341088   .0576153                      .2281641    .4540119
         cut4 |   3.185858   .0819193                      3.025299    3.346417
--------------+----------------------------------------------------------------
/fwb7_behind  |
         cut1 |  -6.172782   .2210433                     -6.606019   -5.739545
         cut2 |  -5.113688   .1832798                      -5.47291   -4.754466
         cut3 |  -2.883979    .113007                     -3.105469   -2.662489
         cut4 |  -.5895829   .0624202                     -.7119241   -.4672416
--------------+----------------------------------------------------------------
/fwb8_control |
         cut1 |  -4.126525   .0936194                     -4.310016   -3.943035
         cut2 |  -3.135057   .0729731                     -3.278082   -2.992033
         cut3 |  -1.243173   .0497445                      -1.34067   -1.145675
         cut4 |   .4892727   .0457554                      .3995937    .5789517
--------------+----------------------------------------------------------------
/fwb9_strain  |
         cut1 |   -4.87244   .1196732                     -5.106995   -4.637885
         cut2 |  -3.904622   .0979252                     -4.096552   -3.712693
         cut3 |  -1.783866   .0643351                      -1.90996   -1.657771
         cut4 |   .6644565   .0544258                      .5577838    .7711291
--------------+----------------------------------------------------------------
/fwb10_left   |
         cut1 |  -4.200151   .0953621                     -4.387058   -4.013245
         cut2 |  -2.552125   .0704455                     -2.690196   -2.414054
         cut3 |   -.420569   .0536458                     -.5257128   -.3154252
         cut4 |   1.280043   .0569573                      1.168409    1.391677
--------------+----------------------------------------------------------------
     var(SFWB)|          1  (constrained)
       var(S1)|          1  (constrained)
       var(S2)|          1  (constrained)
-------------------------------------------------------------------------------

. 
end of do-file