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st: Mediation analysis with SEM command: Why do coefficients of SEM standard output and the output of 'estat teffetcs' differ?


From   Johannes Kotte <johannes.kotte@st.ovgu.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Mediation analysis with SEM command: Why do coefficients of SEM standard output and the output of 'estat teffetcs' differ?
Date   Thu, 17 Jan 2013 17:17:00 +0100

Dear Stata and SEM experts,

I am trying to test for mediation using the estat teffects command a described in http://www.ats.ucla.edu/stat/stata/faq/sem_mediation.htm.

In this online tutorial (which is really great), I find that the coefficients of the structureal model in the standard output of the SEM-command are exactly the same as the direct effects of the structurel model depicted using the 'estat teffects' command. This makes perfect sense as they are reporting the same thing.

However, IN MY CASE 'estat teffects' returns different coefficients from the ones under the standard output of the SEM-command. The are directionally the same, but not exactly. Does anybody know an answer wy this is happening?

The last time I posted sth, I learned that I should walways attach the output of tmy model. So, for those who find it useful, please find the (somewhat lengthy) output below.

Thanks for your help!
Johannes

--
Johannes Kotte
Otto-von-Guericke-Universität | Fakultät Wirtschaftswissenschaften | Lehrstuhl für Unternehmensführung und Organisation (Prof. Dr. Thomas Spengler) | Postfach 4120, 39016 Magdeburg | www.ufo.ovgu.de

Telefon: +49-173-6371955  | E-Mail: johannes.kotte@st.ovgu.de


OUTPUT:

. sem (bk_aanztrps bk_aqualtrps bk_aanzvors <- BK_A1) ///
    (bk_apraxerfs bk_apatents bk_anetzws bk_pmgmts <- BK_A2) ///
    (pr_anerkprs pr_aktprobls pr_erkneus pr_veraends <- PRAXREL) ///
    (BK_A1  BK_A2 <- kv_diszipl3s) ///
    (PRAXREL <- BK_A1 BK_A2 kv_diszipl3s) ///
        , standardized method(mlmv)

note: The following observed variable name will be treated as a latent variable: DR. If this is not your intention use the nocapslatent option, or identify the latent variable names in the latent() option.

Endogenous variables

Measurement: bk_aanztrps bk_aqualtrps bk_aanzvors bk_apraxerfs bk_apatents bk_anetzws bk_pmgmts pr_anerkprs pr_aktprobls pr_erkneus
              pr_veraends
Latent:       BK_A1 BK_A2 PRAXREL

Exogenous variables

Observed:     kv_diszipl3s

Fitting saturated model:

Iteration 0:   log likelihood = -5231.4245
Iteration 1:   log likelihood = -5216.7911
Iteration 2:   log likelihood =   -5216.52
Iteration 3:   log likelihood = -5216.5197

Fitting baseline model:

Iteration 0:   log likelihood = -6412.2715
Iteration 1:   log likelihood = -6411.8514
Iteration 2:   log likelihood =  -6411.851

Fitting target model:

Iteration 0:   log likelihood = -5382.9062
Iteration 1:   log likelihood = -5377.2997
Iteration 2:   log likelihood = -5376.6983
Iteration 3:   log likelihood = -5376.6969
Iteration 4:   log likelihood = -5376.6969

Structural equation model                       Number of obs      =       386
Estimation method  = mlmv
Log likelihood     = -5376.6969

 ( 1)  [bk_aanztrps]BK_A1 = 1
 ( 2)  [bk_apraxerfs]BK_A2 = 1
 ( 3)  [pr_anerkprs]PRAXREL = 1
-----------------------------------------------------------------------------------
                  |                 OIM
Standardized | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Structural        |
  BK_A1 <-        |
kv_diszipl3s | -.392863 .0479105 -8.20 0.000 -.4867657 -.2989602 ----------------+----------------------------------------------------------------
  BK_A2 <-        |
kv_diszipl3s | -.7435796 .0252151 -29.49 0.000 -.7930004 -.6941588 ----------------+----------------------------------------------------------------
  PRAXREL <-      |
BK_A1 | .2269224 .0704285 3.22 0.001 .0888851 .3649596 BK_A2 | .6325189 .0941227 6.72 0.000 .4480418 .816996 kv_diszipl3s | .1767666 .0809536 2.18 0.029 .0181004 .3354328
------------------+----------------------------------------------------------------
Measurement       |
  bk_aanztrps <-  |
BK_A1 | .7942326 .0298642 26.59 0.000 .7356997 .8527654 _cons | -.0007354 .048606 -0.02 0.988 -.0960013 .0945306 ----------------+----------------------------------------------------------------
  bk_aqualtrps <- |
BK_A1 | .7155012 .0337091 21.23 0.000 .6494326 .7815697 _cons | -.0027355 .0491141 -0.06 0.956 -.0989974 .0935263 ----------------+----------------------------------------------------------------
  bk_aanzvors <-  |
BK_A1 | .7705115 .0308117 25.01 0.000 .7101217 .8309013 _cons | .0004053 .0486785 0.01 0.993 -.0950027 .0958133 ----------------+----------------------------------------------------------------
  bk_apraxerfs <- |
BK_A2 | .8554182 .0192422 44.46 0.000 .8177041 .8931324 _cons | .0011565 .0394769 0.03 0.977 -.0762168 .0785299 ----------------+----------------------------------------------------------------
  bk_apatents <-  |
BK_A2 | .8019013 .0233597 34.33 0.000 .7561172 .8476854 _cons | -.0327433 .0422423 -0.78 0.438 -.1155367 .0500502 ----------------+----------------------------------------------------------------
  bk_anetzws <-   |
BK_A2 | .7255948 .0280429 25.87 0.000 .6706318 .7805578 _cons | .0024823 .0431817 0.06 0.954 -.0821522 .0871168 ----------------+----------------------------------------------------------------
  bk_pmgmts <-    |
BK_A2 | .6257822 .0341661 18.32 0.000 .5588178 .6927466 _cons | .0008299 .0452681 0.02 0.985 -.087894 .0895538 ----------------+----------------------------------------------------------------
  pr_anerkprs <-  |
PRAXREL | .7450922 .0281925 26.43 0.000 .6898359 .8003485 _cons | -.0071731 .0495114 -0.14 0.885 -.1042136 .0898674 ----------------+----------------------------------------------------------------
  pr_aktprobls <- |
PRAXREL | .7068533 .0301077 23.48 0.000 .6478433 .7658634 _cons | -.0048397 .0497006 -0.10 0.922 -.1022511 .0925718 ----------------+----------------------------------------------------------------
  pr_erkneus <-   |
PRAXREL | .7504649 .0267139 28.09 0.000 .6981067 .8028232 _cons | -.0040622 .0494015 -0.08 0.934 -.1008874 .0927631 ----------------+----------------------------------------------------------------
  pr_veraends <-  |
PRAXREL | .8666708 .0205953 42.08 0.000 .8263047 .9070369 _cons | -.0046912 .0486317 -0.10 0.923 -.1000077 .0906252
------------------+----------------------------------------------------------------
Variance          |
e.bk_aanztrps | .3691946 .0474383 .2870009 .4749276 e.bk_aqualtrps | .4880581 .0482378 .4021074 .5923808 e.bk_aanzvors | .4063121 .0474815 .3231384 .5108941 e.bk_apraxerfs | .2682596 .0329203 .2109101 .3412033 e.bk_apatents | .3569543 .0374643 .2905858 .438481 e.bk_anetzws | .4735122 .0406955 .4001065 .5603854 e.bk_pmgmts | .6083966 .0427611 .5301028 .698254 e.pr_anerkprs | .4448376 .0420121 .3696672 .5352936 e.pr_aktprobls | .5003584 .0425635 .423519 .5911389 e.pr_erkneus | .4368024 .0400957 .3648801 .5229015 e.pr_veraends | .2488817 .0356988 .1878882 .3296753 e.BK_A1 | .8456587 .0376445 .7750039 .9227548 e.BK_A2 | .4470893 .0374989 .3793159 .526972 e.PRAXREL | .6311146 .0490543 .5419352 .7349692
-----------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(50)  =    320.35, Prob > chi2 = 0.0000



.         estat gof, stats (all)

----------------------------------------------------------------------------
Fit statistic        |      Value   Description
---------------------+------------------------------------------------------
Likelihood ratio     |
         chi2_ms(50) |    320.354   model vs. saturated
            p > chi2 |      0.000
         chi2_bs(66) |   2390.663   baseline vs. saturated
            p > chi2 |      0.000
---------------------+------------------------------------------------------
Population error     |
               RMSEA |      0.118   Root mean squared error of approximation
 90% CI, lower bound |      0.106
         upper bound |      0.131
              pclose |      0.000   Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
                 AIC |  10829.394   Akaike's information criterion
                 BIC |  10979.716   Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison  |
                 CFI |      0.884   Comparative fit index
                 TLI |      0.846   Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals    |
                  CD |      0.595   Coefficient of determination
----------------------------------------------------------------------------
Note: SRMR is not reported because of missing values.



.         estat teffects


Direct effects
-----------------------------------------------------------------------------------
                  |                 OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Measurement       |
  bk_aanztrps <-  |
            BK_A1 |          1  (constrained)
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  bk_aqualtrps <- |
BK_A1 | .9011669 .0722078 12.48 0.000 .7596422 1.042692
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  bk_aanzvors <-  |
BK_A1 | .9703308 .0726611 13.35 0.000 .8279176 1.112744
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  bk_apraxerfs <- |
            BK_A2 |          1  (constrained)
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  bk_apatents <-  |
BK_A2 | .9323889 .0547558 17.03 0.000 .8250695 1.039708
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  bk_anetzws <-   |
BK_A2 | .8478419 .0540133 15.70 0.000 .7419778 .953706
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  bk_pmgmts <-    |
BK_A2 | .7314473 .0571697 12.79 0.000 .6193967 .8434978
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  pr_anerkprs <-  |
            BK_A1 |          0  (no path)
            BK_A2 |          0  (no path)
          PRAXREL |          1  (constrained)
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  pr_aktprobls <- |
            BK_A1 |          0  (no path)
            BK_A2 |          0  (no path)
PRAXREL | .9502792 .0685786 13.86 0.000 .8158677 1.084691
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  pr_erkneus <-   |
            BK_A1 |          0  (no path)
            BK_A2 |          0  (no path)
PRAXREL | 1.007179 .0707514 14.24 0.000 .8685084 1.145849
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  pr_veraends <-  |
            BK_A1 |          0  (no path)
            BK_A2 |          0  (no path)
PRAXREL | 1.155885 .0738158 15.66 0.000 1.011209 1.300561
     kv_diszipl3s |          0  (no path)
------------------+----------------------------------------------------------------
Structural        |
  BK_A1 <-        |
kv_diszipl3s | -.3119383 .0433476 -7.20 0.000 -.396898 -.2269786 ----------------+----------------------------------------------------------------
  BK_A2 <-        |
kv_diszipl3s | -.6359115 .0385622 -16.49 0.000 -.711492 -.5603309 ----------------+----------------------------------------------------------------
  PRAXREL <-      |
BK_A1 | .2088858 .0654598 3.19 0.001 .080587 .3371845 BK_A2 | .5405844 .0922168 5.86 0.000 .3598427 .721326 kv_diszipl3s | .1291991 .0595418 2.17 0.030 .0124993 .2458989
-----------------------------------------------------------------------------------


Indirect effects
-----------------------------------------------------------------------------------
                  |                 OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Measurement       |
  bk_aanztrps <-  |
            BK_A1 |          0  (no path)
kv_diszipl3s | -.3119383 .0433476 -7.20 0.000 -.396898 -.2269786 ----------------+----------------------------------------------------------------
  bk_aqualtrps <- |
            BK_A1 |          0  (no path)
kv_diszipl3s | -.2811085 .0415697 -6.76 0.000 -.3625836 -.1996333 ----------------+----------------------------------------------------------------
  bk_aanzvors <-  |
            BK_A1 |          0  (no path)
kv_diszipl3s | -.3026834 .0435164 -6.96 0.000 -.387974 -.2173927 ----------------+----------------------------------------------------------------
  bk_apraxerfs <- |
            BK_A2 |          0  (no path)
kv_diszipl3s | -.6359115 .0385622 -16.49 0.000 -.711492 -.5603309 ----------------+----------------------------------------------------------------
  bk_apatents <-  |
            BK_A2 |          0  (no path)
kv_diszipl3s | -.5929168 .0407822 -14.54 0.000 -.6728484 -.5129852 ----------------+----------------------------------------------------------------
  bk_anetzws <-   |
            BK_A2 |          0  (no path)
kv_diszipl3s | -.5391524 .0377912 -14.27 0.000 -.6132219 -.465083 ----------------+----------------------------------------------------------------
  bk_pmgmts <-    |
            BK_A2 |          0  (no path)
kv_diszipl3s | -.4651357 .038785 -11.99 0.000 -.541153 -.3891185 ----------------+----------------------------------------------------------------
  pr_anerkprs <-  |
BK_A1 | .2088858 .0654598 3.19 0.001 .080587 .3371845 BK_A2 | .5405844 .0922168 5.86 0.000 .3598427 .721326
          PRAXREL |          0  (no path)
kv_diszipl3s | -.2797242 .0402703 -6.95 0.000 -.3586525 -.2007959 ----------------+----------------------------------------------------------------
  pr_aktprobls <- |
BK_A1 | .1984998 .062205 3.19 0.001 .0765801 .3204194 BK_A2 | .5137061 .0876317 5.86 0.000 .341951 .6854611
          PRAXREL |          0  (no path)
kv_diszipl3s | -.2658161 .0381786 -6.96 0.000 -.3406448 -.1909873 ----------------+----------------------------------------------------------------
  pr_erkneus <-   |
BK_A1 | .2103853 .0659297 3.19 0.001 .0811655 .3396051 BK_A2 | .544465 .0928788 5.86 0.000 .3624259 .7265042
          PRAXREL |          0  (no path)
kv_diszipl3s | -.2817322 .0402595 -7.00 0.000 -.3606394 -.202825 ----------------+----------------------------------------------------------------
  pr_veraends <-  |
BK_A1 | .2414479 .075664 3.19 0.001 .0931493 .3897466 BK_A2 | .6248534 .106592 5.86 0.000 .4159369 .83377
          PRAXREL |          0  (no path)
kv_diszipl3s | -.323329 .0444497 -7.27 0.000 -.4104488 -.2362093
------------------+----------------------------------------------------------------
Structural        |
  BK_A1 <-        |
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  BK_A2 <-        |
     kv_diszipl3s |          0  (no path)
----------------+----------------------------------------------------------------
  PRAXREL <-      |
            BK_A1 |          0  (no path)
            BK_A2 |          0  (no path)
kv_diszipl3s | -.4089233 .0557593 -7.33 0.000 -.5182095 -.299637
-----------------------------------------------------------------------------------


Total effects
-----------------------------------------------------------------------------------
                  |                 OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Measurement       |
  bk_aanztrps <-  |
            BK_A1 |          1  (constrained)
kv_diszipl3s | -.3119383 .0433476 -7.20 0.000 -.396898 -.2269786 ----------------+----------------------------------------------------------------
  bk_aqualtrps <- |
BK_A1 | .9011669 .0722078 12.48 0.000 .7596422 1.042692 kv_diszipl3s | -.2811085 .0415697 -6.76 0.000 -.3625836 -.1996333 ----------------+----------------------------------------------------------------
  bk_aanzvors <-  |
BK_A1 | .9703308 .0726611 13.35 0.000 .8279176 1.112744 kv_diszipl3s | -.3026834 .0435164 -6.96 0.000 -.387974 -.2173927 ----------------+----------------------------------------------------------------
  bk_apraxerfs <- |
            BK_A2 |          1  (constrained)
kv_diszipl3s | -.6359115 .0385622 -16.49 0.000 -.711492 -.5603309 ----------------+----------------------------------------------------------------
  bk_apatents <-  |
BK_A2 | .9323889 .0547558 17.03 0.000 .8250695 1.039708 kv_diszipl3s | -.5929168 .0407822 -14.54 0.000 -.6728484 -.5129852 ----------------+----------------------------------------------------------------
  bk_anetzws <-   |
BK_A2 | .8478419 .0540133 15.70 0.000 .7419778 .953706 kv_diszipl3s | -.5391524 .0377912 -14.27 0.000 -.6132219 -.465083 ----------------+----------------------------------------------------------------
  bk_pmgmts <-    |
BK_A2 | .7314473 .0571697 12.79 0.000 .6193967 .8434978 kv_diszipl3s | -.4651357 .038785 -11.99 0.000 -.541153 -.3891185 ----------------+----------------------------------------------------------------
  pr_anerkprs <-  |
BK_A1 | .2088858 .0654598 3.19 0.001 .080587 .3371845 BK_A2 | .5405844 .0922168 5.86 0.000 .3598427 .721326
          PRAXREL |          1  (constrained)
kv_diszipl3s | -.2797242 .0402703 -6.95 0.000 -.3586525 -.2007959 ----------------+----------------------------------------------------------------
  pr_aktprobls <- |
BK_A1 | .1984998 .062205 3.19 0.001 .0765801 .3204194 BK_A2 | .5137061 .0876317 5.86 0.000 .341951 .6854611 PRAXREL | .9502792 .0685786 13.86 0.000 .8158677 1.084691 kv_diszipl3s | -.2658161 .0381786 -6.96 0.000 -.3406448 -.1909873 ----------------+----------------------------------------------------------------
  pr_erkneus <-   |
BK_A1 | .2103853 .0659297 3.19 0.001 .0811655 .3396051 BK_A2 | .544465 .0928788 5.86 0.000 .3624259 .7265042 PRAXREL | 1.007179 .0707514 14.24 0.000 .8685084 1.145849 kv_diszipl3s | -.2817322 .0402595 -7.00 0.000 -.3606394 -.202825 ----------------+----------------------------------------------------------------
  pr_veraends <-  |
BK_A1 | .2414479 .075664 3.19 0.001 .0931493 .3897466 BK_A2 | .6248534 .106592 5.86 0.000 .4159369 .83377 PRAXREL | 1.155885 .0738158 15.66 0.000 1.011209 1.300561 kv_diszipl3s | -.323329 .0444497 -7.27 0.000 -.4104488 -.2362093
------------------+----------------------------------------------------------------
Structural        |
  BK_A1 <-        |
kv_diszipl3s | -.3119383 .0433476 -7.20 0.000 -.396898 -.2269786 ----------------+----------------------------------------------------------------
  BK_A2 <-        |
kv_diszipl3s | -.6359115 .0385622 -16.49 0.000 -.711492 -.5603309 ----------------+----------------------------------------------------------------
  PRAXREL <-      |
BK_A1 | .2088858 .0654598 3.19 0.001 .080587 .3371845 BK_A2 | .5405844 .0922168 5.86 0.000 .3598427 .721326 kv_diszipl3s | -.2797242 .0402703 -6.95 0.000 -.3586525 -.2007959
-----------------------------------------------------------------------------------


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