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  • LCA gsem output tables and intercept significance

    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:
      Code:
      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

    Code:
    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
    ---------------------------------------------------------------------------------------------

  • #2
    Wossenseged,

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

    Code:
    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) =

    Code:
    di invlogit(.9128742)
    .71358795
    We can replicate that result in post-estimation:
    Code:
    . 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)] =

    Code:
    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.

    Code:
    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
    --------------------------------------------------------------
    Please use the code delimiters to show code and results - use the # button on the formatting toolbar, between the " (double quote) and <> buttons.

    Please use the command -dataex- to show a representative sample of data; it is installed already if you have Stata 14.2 or 15.1, else you can install it by typing

    Code:
    ssc install dataex

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