LCA gsem output tables and intercept significance

[Wossenseged Jemberie]

Hello dear all,
I was trying to understand the output tables especially the first one, mlogit model for C (I have attached the output below). I have searched on Stata documentation on SEM Release 15 and LCA example 50g, but to no avail. Ex 50g ignores those tables and continues with the output result from –estat lcmean- My questions are

1. what does the p-value for _cons in the first table indicate (in my case they are insignificant)? AIC and BIC values for 3 class solution are smaller than one class solution in my analysis
2. if the intercept coeficient for an item (x) remains insignificant as in:

   bin_ettor_life  //in my third class

   for one class but significant in the other classes, what does this indicate? This is related to the table output of logistic regression models of the third classes

The documentation for LCA is a bit lacking (subjective opinion) in practical examples wrt to other SEM documentations, or it may be that I am novice user.
thank you for your help

Generalized structural equation model           Number of obs     =      2,669
Log likelihood = -17965.754

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.C          |  (base outcome)
-------------+----------------------------------------------------------------
2.C          |
       _cons |   -.054045   .0738337    -0.73   0.464    -.1987563    .0906663
-------------+----------------------------------------------------------------
3.C          |
       _cons |  -.0547762   .0774471    -0.71   0.479    -.2065697    .0970174
------------------------------------------------------------------------------


Class          : 3

Response       : bin_problemDays_me~l           Number of obs     =      2,654
Family         : Bernoulli
Link           : logit

Response       : bin_sed_regUse_life            Number of obs     =      2,081
Family         : Bernoulli
Link           : logit

Response       : m_depress_life                 Number of obs     =      2,665
Family         : Bernoulli
Link           : logit

Response       : m_anxiety_life                 Number of obs     =      2,664
Family         : Bernoulli
Link           : logit

Response       : m_violence_life                Number of obs     =      2,663
Family         : Bernoulli
Link           : logit

Response       : bin_problemDays_drug           Number of obs     =      2,189
Family         : Bernoulli
Link           : logit

Response       : polydrug_life_wo_s~2           Number of obs     =      2,603
Family         : Bernoulli
Link           : logit

Response       : bin_reg_alkonsetage            Number of obs     =      2,656
Family         : Bernoulli
Link           : logit

Response       : bin_abuse_alkonset~e           Number of obs     =      2,367
Family         : Bernoulli
Link           : logit

Response       : bin_fam_conflict               Number of obs     =      2,632
Family         : Bernoulli
Link           : logit

Response       : bin_f2f5_combine               Number of obs     =      2,633
Family         : Bernoulli
Link           : logit

Response       : bin_ettor_life                 Number of obs     =      2,652
Family         : Bernoulli
Link           : logit

Response       : bin_problemDays_alc            Number of obs     =      2,637
Family         : Bernoulli
Link           : logit

---------------------------------------------------------------------------------------------
                            |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
bin_problemDays_medical     |
                      _cons |  -.1611242   .0762826    -2.11   0.035    -.3106353    -.011613
----------------------------+----------------------------------------------------------------
bin_sed_regUse_life         |
                      _cons |  -2.811561   .2081087   -13.51   0.000    -3.219446   -2.403675
----------------------------+----------------------------------------------------------------
m_depress_life              |
                      _cons |  -2.438758   .2544036    -9.59   0.000    -2.937379   -1.940136
----------------------------+----------------------------------------------------------------
m_anxiety_life              |
                      _cons |  -2.448186     .24694    -9.91   0.000    -2.932179   -1.964192
----------------------------+----------------------------------------------------------------
m_violence_life             |
                      _cons |  -2.656828   .1686088   -15.76   0.000    -2.987295    -2.32636
----------------------------+----------------------------------------------------------------
bin_problemDays_drug        |
                      _cons |  -5.713981    1.22993    -4.65   0.000    -8.124599   -3.303362
----------------------------+----------------------------------------------------------------
polydrug_life_wo_sed_cutat2 |
                      _cons |  -4.463023   .4840727    -9.22   0.000    -5.411788   -3.514258
----------------------------+----------------------------------------------------------------
bin_reg_alkonsetage         |
                      _cons |  -.4409185   .0859805    -5.13   0.000    -.6094371   -.2723998
----------------------------+----------------------------------------------------------------
bin_abuse_alkonsetage       |
                      _cons |   -.473027   .0947681    -4.99   0.000    -.6587691   -.2872849
----------------------------+----------------------------------------------------------------
bin_fam_conflict            |
                      _cons |   -2.16245   .1306248   -16.55   0.000     -2.41847    -1.90643
----------------------------+----------------------------------------------------------------
bin_f2f5_combine            |
                      _cons |  -1.205164   .0966388   -12.47   0.000    -1.394572   -1.015755
----------------------------+----------------------------------------------------------------
bin_ettor_life              |
                      _cons |    .076515   .0784798     0.97   0.330    -.0773027    .2303327
----------------------------+----------------------------------------------------------------
bin_problemDays_alc         |
                      _cons |   .5939501   .0790166     7.52   0.000     .4390803    .7488199
---------------------------------------------------------------------------------------------

[Weiwen Ng]

Wossenseged,

I'll respond using Stata's example data for example 50.

use http://www.stata-press.com/data/r15/gsem_lca1
gsem (accident play insurance stock <- ), logit lclass(C 2) nolog noheader
------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.C          |  (base outcome)
-------------+----------------------------------------------------------------
2.C          |
       _cons |  -.9482041   .2886333    -3.29   0.001    -1.513915   -.3824933
------------------------------------------------------------------------------

Class          : 1

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
accident     |
       _cons |   .9128742   .1974695     4.62   0.000     .5258411    1.299907
-------------+----------------------------------------------------------------
play         |
       _cons |  -.7099072   .2249096    -3.16   0.002    -1.150722   -.2690926
-------------+----------------------------------------------------------------
insurance    |
       _cons |  -.6014307   .2123096    -2.83   0.005     -1.01755   -.1853115
-------------+----------------------------------------------------------------
stock        |
       _cons |  -1.880142   .3337665    -5.63   0.000    -2.534312   -1.225972
------------------------------------------------------------------------------

Omitting the results for class 2 here. This example has 4 binary indicators. The above table gives the logit intercepts for the indicators in each class - the logit intercepts tell you the probability of endorsing that indicator in that class. The formulae are on pg 484 of the SEM manual, but to work through an example, P(accident = 1 | class = 1) = exp(.9128742) / (1 + exp(.9128742)) = invlogit(.9128742) =

di invlogit(.9128742)
.71358795

We can replicate that result in post-estimation:

. estat lcmean

Latent class marginal means                     Number of obs     =        216

--------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
1            |
    accident |   .7135879   .0403588      .6285126    .7858194
        play |   .3296193   .0496984      .2403573    .4331299
   insurance |   .3540164   .0485528      .2655049    .4538042
       stock |   .1323726   .0383331      .0734875    .2268872
-------------+------------------------------------------------
2            |
    accident |   .9931933   .0253243      .0863544    .9999956
        play |   .9397644   .0659957      .6135685    .9935191
   insurance |   .9265309   .0656538      .6557086    .9881667
       stock |    .769132   .0952072      .5380601    .9050206
--------------------------------------------------------------

As to your second question, the p-value describes the result of the usual hypothesis test that the logit intercept is equal to zero. Inverse logit 0 = 0.5. It doesn't really mean anything that the logit intercept is not significantly different from zero. We just take interest in the point estimate plus its confidence interval. In fact, we probably are more interested in the point estimate and CI of that logit intercept expressed in probability terms.

Your first question is related. The first set of logit intercepts in the header are the logit intercepts describing the proportion of each latent class (formula on the bottom of page 484). Again, the tests are asking if the logit intercept is significantly different from zero, and it doesn't matter if that p-value is significant. From the book, we know that the probability of being in latent class 2 is exp(gamma1) / [exp(gamma1) + exp(gamma2)]. gamma1 is zero (as it is in all multinomial logit models), so P(C = 2) = 1 / [1 + exp(-.9482041)] =

di invlogit(-.9482041)
.27924614

You can probably see where I am going with this: if we use the appropriate post-estimation command, we can replicate that probability.

estat lcprob

Latent class marginal probabilities             Number of obs     =        216

--------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
           C |
          1  |   .7207539   .0580926      .5944743    .8196407
          2  |   .2792461   .0580926      .1803593    .4055257
--------------------------------------------------------------