Dear Statalisters,
For my dissertation a have a database of 1575 individuals from a gender attitudes survey. My dependent variable is "Attitudes on maternity leave", with three categories (Too long = 0, Long enough = Too short = 2). My independent variables are also categorical (sociodemographic or attitude scales). The main explanatory variable is sex, which is interacted with a dummy for having had children.
I'm running a generalized ordinal logit regression since I have evidence from omodel, brant and the autofit option that not all variables satisfy the parallel lines (PL) assumption. However, I'd like to use margins to help interpretation, and this is where I ran into trouble.
I know margins requires that factor variables be identified by the i. prefix in the regression command, but I am getting different results from estimating the model using the full factorial operator (##) and the xi: prefix to create the interaction between the "sex" and "having children" dummies. I want both the main effects of the two variables and its interaction to be in the model. Here are the results for both options:
With the xi prefix:
With the ## operator:
As you can see, the autofit identifies different variables as violating the PL assumption for what seems to be the same model. What's more, when using the full factorial interaction operator, autofit seems unable to relax the PL assumption for the variables involved in the interaction, as shown by Step 16 of the autofit routine in the code above. Indeed, when explicitly telling what variables don't satisfy the proportional odds assumption with the npl option on gologit (the ones identified by autofit), the coefficients diverge for these variables in the two equations, as it should be:
The predicted probabilities from margins are different for all three models above. However, I have also noticed that the results from margins are different when run on the xi prefix version of the model and on the version using ## along with npl to relax the same variables autofit identifies for the former model.
To illustrate, here are the results from margins on the xi prefix model version:
And here is the output from margins on the model using the npl option to relax the PL assumption on the same 3 variables autofit appoints for the xi prefix model as violating said assumption. For the model,
This is what margins returns:
From these diverging results, my questions are:
Larissa
For my dissertation a have a database of 1575 individuals from a gender attitudes survey. My dependent variable is "Attitudes on maternity leave", with three categories (Too long = 0, Long enough = Too short = 2). My independent variables are also categorical (sociodemographic or attitude scales). The main explanatory variable is sex, which is interacted with a dummy for having had children.
I'm running a generalized ordinal logit regression since I have evidence from omodel, brant and the autofit option that not all variables satisfy the parallel lines (PL) assumption. However, I'd like to use margins to help interpretation, and this is where I ran into trouble.
I know margins requires that factor variables be identified by the i. prefix in the regression command, but I am getting different results from estimating the model using the full factorial operator (##) and the xi: prefix to create the interaction between the "sex" and "having children" dummies. I want both the main effects of the two variables and its interaction to be in the model. Here are the results for both options:
With the xi prefix:
Code:
. xi: gologit2 att_maternity_leave i.sex*i.children i.occupation i.agegroup i.educ_lvl ///
> i.hh_income i.personal_income i.nonwhite i.att_male_breadwinner i.religion_sub, or autofit(0.05)
i.sex _Isex_0-1 (naturally coded; _Isex_0 omitted)
i.children _Ichildren_0-1 (naturally coded; _Ichildren_0 omitted)
i.sex*i.child~n _IsexXchi_#_# (coded as above)
i.occupation _Ioccupatio_1-4 (naturally coded; _Ioccupatio_3 omitted)
i.agegroup _Iagegroup_1-4 (naturally coded; _Iagegroup_4 omitted)
i.educ_lvl _Ieduc_lvl_1-4 (naturally coded; _Ieduc_lvl_1 omitted)
i.hh_income _Ihh_income_0-1 (naturally coded; _Ihh_income_0 omitted)
i.personal_in~e _Ipersonal__0-1 (naturally coded; _Ipersonal__0 omitted)
i.nonwhite _Inonwhite_0-1 (naturally coded; _Inonwhite_0 omitted)
i.att_male_br~r _Iatt_male__0-1 (naturally coded; _Iatt_male__0 omitted)
i.religion_sub _Ireligion__0-3 (naturally coded; _Ireligion__0 omitted)
------------------------------------------------------------------------------
Testing parallel lines assumption using the .05 level of significance...
[output omitted]
Step 17: Constraints for parallel lines are not imposed for
_Isex_1 (P Value = 0.03197)
_Ioccupatio_4 (P Value = 0.00242)
_Iatt_male__1 (P Value = 0.04947)
Wald test of parallel lines assumption for the final model:
[output omitted]
chi2( 16) = 12.99
Prob > chi2 = 0.6734
[output omitted]
------------------------------------------------------------------------------
Generalized Ordered Logit Estimates Number of obs = 1,218
LR chi2(22) = 127.00
Prob > chi2 = 0.0000
Log likelihood = -852.76406 Pseudo R2 = 0.0693
( 1) [Too_long]_Ihh_income_1 - [Long_enough]_Ihh_income_1 = 0
( 2) [Too_long]_Ireligion__1 - [Long_enough]_Ireligion__1 = 0
( 3) [Too_long]_Iagegroup_3 - [Long_enough]_Iagegroup_3 = 0
( 4) [Too_long]_Ioccupatio_1 - [Long_enough]_Ioccupatio_1 = 0
( 5) [Too_long]_Ichildren_1 - [Long_enough]_Ichildren_1 = 0
( 6) [Too_long]_Ireligion__3 - [Long_enough]_Ireligion__3 = 0
( 7) [Too_long]_Ipersonal__1 - [Long_enough]_Ipersonal__1 = 0
( 8) [Too_long]_Ieduc_lvl_4 - [Long_enough]_Ieduc_lvl_4 = 0
( 9) [Too_long]_Ireligion__2 - [Long_enough]_Ireligion__2 = 0
(10) [Too_long]_IsexXchi_1_1 - [Long_enough]_IsexXchi_1_1 = 0
(11) [Too_long]_Iagegroup_2 - [Long_enough]_Iagegroup_2 = 0
(12) [Too_long]_Ieduc_lvl_3 - [Long_enough]_Ieduc_lvl_3 = 0
(13) [Too_long]_Ieduc_lvl_2 - [Long_enough]_Ieduc_lvl_2 = 0
(14) [Too_long]_Ioccupatio_2 - [Long_enough]_Ioccupatio_2 = 0
(15) [Too_long]_Iagegroup_1 - [Long_enough]_Iagegroup_1 = 0
(16) [Too_long]_Inonwhite_1 - [Long_enough]_Inonwhite_1 = 0
-------------------------------------------------------------------------------
att_materni~e | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
Too_long |
_Isex_1 | 1.459372 .6379658 0.86 0.387 .6195301 3.437712
_Ichildren_1 | 2.220308 .5357684 3.31 0.001 1.383615 3.562963
_IsexXchi_1_1 | .4096042 .1231099 -2.97 0.003 .227263 .738244
_Ioccupatio_1 | 1.590816 .2869034 2.57 0.010 1.117135 2.265343
_Ioccupatio_2 | 1.216887 .2054963 1.16 0.245 .8739917 1.694311
_Ioccupatio_4 | .5414892 .3013457 -1.10 0.270 .181922 1.611738
_Iagegroup_1 | 2.069052 .4881915 3.08 0.002 1.302959 3.285578
_Iagegroup_2 | 1.676878 .3346224 2.59 0.010 1.134079 2.479473
_Iagegroup_3 | 1.405077 .2542377 1.88 0.060 .9855571 2.003172
_Ieduc_lvl_2 | .9643911 .1681367 -0.21 0.835 .6852524 1.357237
_Ieduc_lvl_3 | 1.037131 .1841125 0.21 0.837 .7323649 1.468723
_Ieduc_lvl_4 | 2.40276 .7288476 2.89 0.004 1.325894 4.354235
_Ihh_income_1 | .9410948 .1519851 -0.38 0.707 .6857501 1.291519
_Ipersonal__1 | .9216517 .2427805 -0.31 0.757 .5499766 1.544505
_Inonwhite_1 | .6563793 .0882331 -3.13 0.002 .5043511 .8542338
_Iatt_male__1 | .3365761 .1180777 -3.10 0.002 .169225 .6694251
_Ireligion__1 | 1.302164 .1958484 1.76 0.079 .9697131 1.748592
_Ireligion__2 | 1.120148 .2814178 0.45 0.652 .6845823 1.832842
_Ireligion__3 | 1.629313 .4062187 1.96 0.050 .9995025 2.655983
_cons | 26.62686 12.11285 7.21 0.000 10.91689 64.94429
--------------+----------------------------------------------------------------
Long_enough |
_Isex_1 | 3.229216 .8583958 4.41 0.000 1.917915 5.437071
_Ichildren_1 | 2.220308 .5357684 3.31 0.001 1.383615 3.562963
_IsexXchi_1_1 | .4096042 .1231099 -2.97 0.003 .227263 .738244
_Ioccupatio_1 | 1.590816 .2869034 2.57 0.010 1.117135 2.265343
_Ioccupatio_2 | 1.216887 .2054963 1.16 0.245 .8739917 1.694311
_Ioccupatio_4 | 2.430166 .7991999 2.70 0.007 1.27557 4.629856
_Iagegroup_1 | 2.069052 .4881915 3.08 0.002 1.302959 3.285578
_Iagegroup_2 | 1.676878 .3346224 2.59 0.010 1.134079 2.479473
_Iagegroup_3 | 1.405077 .2542377 1.88 0.060 .9855571 2.003172
_Ieduc_lvl_2 | .9643911 .1681367 -0.21 0.835 .6852524 1.357237
_Ieduc_lvl_3 | 1.037131 .1841125 0.21 0.837 .7323649 1.468723
_Ieduc_lvl_4 | 2.40276 .7288476 2.89 0.004 1.325894 4.354235
_Ihh_income_1 | .9410948 .1519851 -0.38 0.707 .6857501 1.291519
_Ipersonal__1 | .9216517 .2427805 -0.31 0.757 .5499766 1.544505
_Inonwhite_1 | .6563793 .0882331 -3.13 0.002 .5043511 .8542338
_Iatt_male__1 | .6608023 .0935378 -2.93 0.003 .5007055 .8720888
_Ireligion__1 | 1.302164 .1958484 1.76 0.079 .9697131 1.748592
_Ireligion__2 | 1.120148 .2814178 0.45 0.652 .6845823 1.832842
_Ireligion__3 | 1.629313 .4062187 1.96 0.050 .9995025 2.655983
_cons | .4965651 .1431003 -2.43 0.015 .2822778 .8735257
-------------------------------------------------------------------------------
With the ## operator:
Code:
. gologit2 att_maternity_leave i.sex##i.children i.occupation i.agegroup i.educ_lvl ///
> i.hh_income i.personal_income i.nonwhite i.att_male_breadwinner i.religion_sub, or autofit(0.05)
------------------------------------------------------------------------------
Testing parallel lines assumption using the .05 level of significance...
[output omitted]
Step 16: Constraints for parallel lines are not imposed for
4.occupation (P Value = 0.00125)
1.sex (P Value = .)
1.children (P Value = .)
1.sex#1.children (P Value = .)
Wald test of parallel lines assumption for the final model:
[output omitted]
chi2( 18) = 20.37
Prob > chi2 = 0.3125
[output omitted]
------------------------------------------------------------------------------
Generalized Ordered Logit Estimates Number of obs = 1,218
LR chi2(20) = 119.04
Prob > chi2 = 0.0000
Log likelihood = -856.74263 Pseudo R2 = 0.0650
( 1) [Too_long]1.hh_income - [Long_enough]1.hh_income = 0
( 2) [Too_long]1.sex - [Long_enough]1.sex = 0
( 3) [Too_long]1.children - [Long_enough]1.children = 0
( 4) [Too_long]1.sex#1.children - [Long_enough]1.sex#1.children = 0
( 5) [Too_long]1.occupation - [Long_enough]1.occupation = 0
( 6) [Too_long]2.occupation - [Long_enough]2.occupation = 0
( 7) [Too_long]1.agegroup - [Long_enough]1.agegroup = 0
( 8) [Too_long]2.agegroup - [Long_enough]2.agegroup = 0
( 9) [Too_long]3.agegroup - [Long_enough]3.agegroup = 0
(10) [Too_long]2.educ_lvl - [Long_enough]2.educ_lvl = 0
(11) [Too_long]3.educ_lvl - [Long_enough]3.educ_lvl = 0
(12) [Too_long]4.educ_lvl - [Long_enough]4.educ_lvl = 0
(13) [Too_long]1.personal_income - [Long_enough]1.personal_income = 0
(14) [Too_long]1.nonwhite - [Long_enough]1.nonwhite = 0
(15) [Too_long]1.att_male_breadwinner - [Long_enough]1.att_male_breadwinner = 0
(16) [Too_long]1.religion_sub - [Long_enough]1.religion_sub = 0
(17) [Too_long]2.religion_sub - [Long_enough]2.religion_sub = 0
(18) [Too_long]3.religion_sub - [Long_enough]3.religion_sub = 0
---------------------------------------------------------------------------------------------------------
att_maternity_leave | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
----------------------------------------+----------------------------------------------------------------
Too_long |
sex |
Female (childless) | 3.074111 .8091185 4.27 0.000 1.835185 5.149431
|
children |
Has children (male) | 2.181106 .5196852 3.27 0.001 1.367299 3.479283
|
sex#children |
Female (childless)#Has children (male) | .4127405 .1233798 -2.96 0.003 .2297359 .7415242
|
occupation |
Formal worker | 1.582103 .2845895 2.55 0.011 1.112039 2.250864
Informal worker/self-employed | 1.217552 .205481 1.17 0.243 .8746496 1.694889
Unemployed | .4785535 .2693825 -1.31 0.190 .1587745 1.442382
|
agegroup |
18 to 29 years old | 2.068957 .4879833 3.08 0.002 1.303129 3.284849
30 to 44 years old | 1.686548 .3369284 2.62 0.009 1.14012 2.494862
45 to 59 years old | 1.413806 .2563532 1.91 0.056 .9909438 2.017116
|
educ_lvl |
Schooling: basic | .9651876 .1682604 -0.20 0.839 .6858395 1.358317
Schooling: high school | 1.038984 .1843314 0.22 0.829 .7338261 1.471041
Schooling: university | 2.401723 .7281533 2.89 0.004 1.325733 4.351007
|
hh_income |
Household income up to 3 min wages | .9433197 .1520738 -0.36 0.717 .6877579 1.293845
|
personal_income |
Personal income up to 3 min wages | .9155759 .2403605 -0.34 0.737 .5473103 1.531634
|
nonwhite |
Non-white | .6562465 .0881965 -3.13 0.002 .5042774 .854013
|
att_male_breadwinner |
Agrees with male breadwinner model | .6353918 .0888878 -3.24 0.001 .4830179 .8358339
|
religion_sub |
Protestant | 1.298127 .1954185 1.73 0.083 .9664476 1.743637
Other religion | 1.113869 .2802215 0.43 0.668 .6802885 1.823791
No religion but believes in God | 1.632276 .4058423 1.97 0.049 1.002661 2.657252
|
_cons | 12.5624 4.075055 7.80 0.000 6.652047 23.72409
----------------------------------------+----------------------------------------------------------------
Long_enough |
sex |
Female (childless) | 3.074111 .8091185 4.27 0.000 1.835185 5.149431
|
children |
Has children (male) | 2.181106 .5196852 3.27 0.001 1.367299 3.479283
|
sex#children |
Female (childless)#Has children (male) | .4127405 .1233798 -2.96 0.003 .2297359 .7415242
|
occupation |
Formal worker | 1.582103 .2845895 2.55 0.011 1.112039 2.250864
Informal worker/self-employed | 1.217552 .205481 1.17 0.243 .8746496 1.694889
Unemployed | 2.41457 .7944307 2.68 0.007 1.267014 4.601487
|
agegroup |
18 to 29 years old | 2.068957 .4879833 3.08 0.002 1.303129 3.284849
30 to 44 years old | 1.686548 .3369284 2.62 0.009 1.14012 2.494862
45 to 59 years old | 1.413806 .2563532 1.91 0.056 .9909438 2.017116
|
educ_lvl |
Schooling: basic | .9651876 .1682604 -0.20 0.839 .6858395 1.358317
Schooling: high school | 1.038984 .1843314 0.22 0.829 .7338261 1.471041
Schooling: university | 2.401723 .7281533 2.89 0.004 1.325733 4.351007
|
hh_income |
Household income up to 3 min wages | .9433197 .1520738 -0.36 0.717 .6877579 1.293845
|
personal_income |
Personal income up to 3 min wages | .9155759 .2403605 -0.34 0.737 .5473103 1.531634
|
nonwhite |
Non-white | .6562465 .0881965 -3.13 0.002 .5042774 .854013
|
att_male_breadwinner |
Agrees with male breadwinner model | .6353918 .0888878 -3.24 0.001 .4830179 .8358339
|
religion_sub |
Protestant | 1.298127 .1954185 1.73 0.083 .9664476 1.743637
Other religion | 1.113869 .2802215 0.43 0.668 .6802885 1.823791
No religion but believes in God | 1.632276 .4058423 1.97 0.049 1.002661 2.657252
|
_cons | .5220965 .1488314 -2.28 0.023 .2986091 .9128482
---------------------------------------------------------------------------------------------------------
Code:
. gologit2 att_maternity_leave i.sex##i.children i.occupation i.agegroup i.educ_lvl ///
> i.hh_income i.personal_income i.nonwhite i.att_male_breadwinner i.religion_sub , or npl(1.sex 1.children 1.sex#1.children
> 4.occupation)
Generalized Ordered Logit Estimates Number of obs = 1,218
LR chi2(23) = 124.03
Prob > chi2 = 0.0000
Log likelihood = -854.24631 Pseudo R2 = 0.0677
[output omitted]
---------------------------------------------------------------------------------------------------------
att_maternity_leave | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
----------------------------------------+----------------------------------------------------------------
Too_long |
sex |
Female (childless) | 1.126295 .7506986 0.18 0.858 .3050066 4.159061
|
children |
Has children (male) | 2.287915 1.475059 1.28 0.199 .6466296 8.095139
|
sex#children |
Female (childless)#Has children (male) | .6197827 .4973397 -0.60 0.551 .1285877 2.987304
|
occupation |
Formal worker | 1.58724 .2864341 2.56 0.010 1.114383 2.260741
Informal worker/self-employed | 1.218529 .2061066 1.17 0.243 .874703 1.697506
Unemployed | .5792418 .3306499 -0.96 0.339 .1892198 1.773182
|
agegroup |
18 to 29 years old | 2.071854 .4893674 3.08 0.002 1.304089 3.291631
30 to 44 years old | 1.68437 .3370393 2.61 0.009 1.137925 2.493225
45 to 59 years old | 1.413854 .2565961 1.91 0.056 .990655 2.017839
|
educ_lvl |
Schooling: basic | .966153 .1688555 -0.20 0.844 .6859313 1.360853
Schooling: high school | 1.038784 .1848084 0.21 0.831 .7329752 1.472181
Schooling: university | 2.405845 .730765 2.89 0.004 1.326536 4.363314
|
hh_income |
Household income up to 3 min wages | .9406668 .1520812 -0.38 0.705 .6852023 1.291376
|
personal_income |
Personal income up to 3 min wages | .9153579 .2415289 -0.34 0.737 .5457459 1.535293
|
nonwhite |
Non-white | .6560566 .08834 -3.13 0.002 .5038769 .8541973
|
att_male_breadwinner |
Agrees with male breadwinner model | .6314628 .0885609 -3.28 0.001 .4796994 .8312399
|
religion_sub |
Protestant | 1.303651 .1966212 1.76 0.079 .9700192 1.752034
Other religion | 1.116723 .2809709 0.44 0.661 .6819945 1.828565
No religion but believes in God | 1.638381 .4089523 1.98 0.048 1.004496 2.672275
|
_cons | 18.0539 10.0048 5.22 0.000 6.093501 53.49032
----------------------------------------+----------------------------------------------------------------
Long_enough |
sex |
Female (childless) | 3.272128 .8764313 4.43 0.000 1.9357 5.53124
|
children |
Has children (male) | 2.215837 .5428784 3.25 0.001 1.370863 3.581637
|
sex#children |
Female (childless)#Has children (male) | .4002188 .1216815 -3.01 0.003 .2205466 .726264
|
occupation |
Formal worker | 1.58724 .2864341 2.56 0.010 1.114383 2.260741
Informal worker/self-employed | 1.218529 .2061066 1.17 0.243 .874703 1.697506
Unemployed | 2.3864 .7860174 2.64 0.008 1.251353 4.550998
|
agegroup |
18 to 29 years old | 2.071854 .4893674 3.08 0.002 1.304089 3.291631
30 to 44 years old | 1.68437 .3370393 2.61 0.009 1.137925 2.493225
45 to 59 years old | 1.413854 .2565961 1.91 0.056 .990655 2.017839
|
educ_lvl |
Schooling: basic | .966153 .1688555 -0.20 0.844 .6859313 1.360853
Schooling: high school | 1.038784 .1848084 0.21 0.831 .7329752 1.472181
Schooling: university | 2.405845 .730765 2.89 0.004 1.326536 4.363314
|
hh_income |
Household income up to 3 min wages | .9406668 .1520812 -0.38 0.705 .6852023 1.291376
|
personal_income |
Personal income up to 3 min wages | .9153579 .2415289 -0.34 0.737 .5457459 1.535293
|
nonwhite |
Non-white | .6560566 .08834 -3.13 0.002 .5038769 .8541973
|
att_male_breadwinner |
Agrees with male breadwinner model | .6314628 .0885609 -3.28 0.001 .4796994 .8312399
|
religion_sub |
Protestant | 1.303651 .1966212 1.76 0.079 .9700192 1.752034
Other religion | 1.116723 .2809709 0.44 0.661 .6819945 1.828565
No religion but believes in God | 1.638381 .4089523 1.98 0.048 1.004496 2.672275
|
_cons | .5030049 .1456844 -2.37 0.018 .2851283 .8873689
---------------------------------------------------------------------------------------------------------
To illustrate, here are the results from margins on the xi prefix model version:
Code:
. margins, at( _Isex_1=(0 1) _Ichildren_1=(0 1))
Predictive margins Number of obs = 1,218
Model VCE : OIM
1._predict : Pr(att_maternity_leave==0), predict(pr outcome(0))
2._predict : Pr(att_maternity_leave==1), predict(pr outcome(1))
3._predict : Pr(att_maternity_leave==2), predict(pr outcome(2))
1._at : _Isex_1 = 0
_Ichildren_1 = 0
2._at : _Isex_1 = 0
_Ichildren_1 = 1
3._at : _Isex_1 = 1
_Ichildren_1 = 0
4._at : _Isex_1 = 1
_Ichildren_1 = 1
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_predict#_at |
1 1 | .0683289 .0274118 2.49 0.013 .0146028 .122055
1 2 | .0332513 .0109025 3.05 0.002 .0118828 .0546197
1 3 | .0488709 .0121997 4.01 0.000 .02496 .0727818
1 4 | .0232943 .0048849 4.77 0.000 .0137201 .0328684
2 1 | .5800066 .0426765 13.59 0.000 .4963622 .663651
2 2 | .4460295 .0302051 14.77 0.000 .3868287 .5052304
2 3 | .3503337 .0295183 11.87 0.000 .2924788 .4081886
2 4 | .2240374 .0195662 11.45 0.000 .1856884 .2623864
3 1 | .3516645 .0583139 6.03 0.000 .2373714 .4659576
3 2 | .5207192 .0335566 15.52 0.000 .4549495 .5864889
3 3 | .6007954 .0359067 16.73 0.000 .5304196 .6711713
3 4 | .7526683 .0209214 35.98 0.000 .7116631 .7936736
------------------------------------------------------------------------------
Code:
gologit2 att_maternity_leave i.sex##i.children i.occupation i.agegroup i.educ_lvl /// > i.hh_income i.personal_income i.nonwhite i.att_male_breadwinner i.religion_sub, or npl(1.sex 4.occupation 1.att_male_brea > dwinner)
Code:
. margins, at(sex=(0 1) children=(0 1))
Predictive margins Number of obs = 1,218
Model VCE : OIM
1._predict : Pr(att_maternity_leave==0), predict(pr outcome(0))
2._predict : Pr(att_maternity_leave==1), predict(pr outcome(1))
3._predict : Pr(att_maternity_leave==2), predict(pr outcome(2))
1._at : sex = 0
children = 0
2._at : sex = 0
children = 1
3._at : sex = 1
children = 0
4._at : sex = 1
children = 1
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_predict#_at |
1 1 | .0418671 .0136235 3.07 0.002 .0151656 .0685686
1 2 | .0196605 .0060389 3.26 0.001 .0078244 .0314966
1 3 | .029371 .0078227 3.75 0.000 .0140388 .0447032
1 4 | .0321284 .0064621 4.97 0.000 .019463 .0447938
2 1 | .5181767 .0401801 12.90 0.000 .4394252 .5969282
2 2 | .3603127 .0259047 13.91 0.000 .3095404 .411085
2 3 | .2730377 .0337376 8.09 0.000 .2069132 .3391622
2 4 | .2891611 .0178571 16.19 0.000 .2541619 .3241603
3 1 | .4399562 .0449395 9.79 0.000 .3518764 .528036
3 2 | .6200268 .0269224 23.03 0.000 .5672598 .6727938
3 3 | .6975913 .0385831 18.08 0.000 .6219697 .7732129
3 4 | .6787105 .0186828 36.33 0.000 .6420929 .7153281
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- What is the most appropriate way of creating a factorial interaction in this scenario?
- Should I be worried about autofit not relaxing the PL assumption in the model using the full factorial interaction operator? Is running gologit2, npl later to manually do this just as valid?
- What do I make of the diverging margin outputs for apparently the same model?
Larissa
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