[转载]Stata: 使用 SEM 估计调节-中介效应

作者: stata连享会 | 来源:发表于2018-06-27 08:33 被阅读252次

[转载]Stata: 使用 SEM 估计调节-中介效应
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Source: STATA FAQ | HOW CAN I DO MODERATED MEDIATION WITH A CATEGORICAL MODERATOR USING SEM?

……Stata 现场培训报名中……

This page is just an extension of How can I do moderated mediation in Stata? to include a categorical moderator variables. We will call that page modmed. If you are unfamiliar with moderated mediation you should review the modmed FAQ page before continuing on with this page.

We will to use the same data and the same abbreviated variable names as were used on the modmed page. The model is not of substantive interest, it is merely used to show the steps involved in the analysis.

 rename science y  /* dependent variable   */
 rename math x     /* independent variable */
 rename read m     /* mediator variable    */
 rename female w   /* moderator variable with 2 levels */
 rename socst cv   /* continuous covariate */

The modmed page presented five different models for moderated mediation. This page will cover models 5, 2 and 3, to illustrate the use of categorical moderators. The diagram for model 5 looks like this:

Model 5

Image model5s

First pass using sem

The trick to using sem for moderated mediation with a categorical moderator is to do a multiple group analysis using the group option. Please note, there are no explicit interactions in the model. The interactions are implicit in the multiple group analysis itself. Here is our first try.

sem (m <- x cv)(y <- m x cv), group(w)
 Endogenous variables
 Observed:  m y
 Exogenous variables
 
 Observed:  x cv
 
 Fitting target model:
 
 Iteration 0:   log likelihood = -2792.7769  
 Iteration 1:   log likelihood = -2792.7769  
 
 Structural equation model                       Number of obs      =       200
 Grouping variable  = w                          Number of groups   =         2
 Estimation method  = ml
 Log likelihood     = -2792.7769
 
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4461113     .09393     4.75   0.000      .262012    .6302107
       female |   .5523602   .0843711     6.55   0.000     .3869959    .7177244
     cv       |
         male |   .3687237   .0800976     4.60   0.000     .2117353     .525712
       female |   .3444715   .0754397     4.57   0.000     .1966124    .4923306
     _cons    |
         male |   10.10814    4.69041     2.16   0.031     .9151099    19.30118
       female |   4.564765   3.855135     1.18   0.236    -2.991162    12.12069
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |   .4504614   .1045896     4.31   0.000     .2454696    .6554532
       female |    .211106   .0977165     2.16   0.031     .0195853    .4026267
     x        |
         male |   .3523138   .1046885     3.37   0.001     .1471281    .5574996
       female |    .452633   .1015976     4.46   0.000     .2535052    .6517607
     cv       |
         male |   .0497414   .0887335     0.56   0.575    -.1241731     .223656
       female |   .0458989   .0840018     0.55   0.585    -.1187416    .2105395
     _cons    |
         male |   8.206073   4.797652     1.71   0.087    -1.197152     17.6093
       female |   13.63157   3.958183     3.44   0.001     5.873677    21.38947
 -------------+----------------------------------------------------------------
 Variance     |
   e.m        |
         male |   55.76584   8.267278                        41.704    74.56907
       female |   41.59327   5.634104                      31.89494    54.24058
   e.y        |
         male |   55.51193   8.229635                      41.51411    74.22955
       female |   43.28974   5.863902                      33.19584     56.4529
 ------------------------------------------------------------------------------
 LR test of model vs. saturated: chi2(0)   =      0.00, Prob  chi2 =      .

This isn’t too bad. We are getting separate male and female coefficients for both x and m. However, we are also getting separate coefficients for cv and separate residual variances in each equations. In a traditional moderated mediation model these values are not part of the interaction. So, we will need to constrain the coefficients for cv and residual variances to be equal in both equations. Here is how to do that.

Model 5 constraining the covariate to be equal across groups

Equations that begin with 0: refer to the male group
Equations that begin with 1: refer to the female group.
To constrain values use a ‘@’ and a name. Terms with the same name will be constrained to be equal. For example, the term cv@c1 will be constrained to be equal in both equations.

sem (0: m <- x cv@c1)(0: y <- m x cv@c2)            ///
     (1: m <- x cv@c1)(1: y <- m x cv@c2), group(w) ///
     variance(0: e.m@v1 e.y@v2) ///
     variance(1: e.m@v1 e.y@v2)**
 
 Endogenous variables
 Observed:  m y
 
 Exogenous variables
 Observed:  x cv
 
 Fitting target model:
 Iteration 0:   log likelihood = -2795.5195  
 Iteration 1:   log likelihood = -2794.6484  
 Iteration 2:   log likelihood = -2794.6438  
 Iteration 3:   log likelihood = -2794.6438  
 
 Structural equation model                       Number of obs      =       200
 Grouping variable  = w                          Number of groups   =         2
 Estimation method  = ml
 Log likelihood     = -2794.6438
 
  ( 1)  [m]0bn.w#c.cv - [m]1.w#c.cv = 0
  ( 2)  [y]0bn.w#c.cv - [y]1.w#c.cv = 0
  ( 3)  [var(e.m)]0bn.w - [var(e.m)]1.w = 0
  ( 4)  [var(e.y)]0bn.w - [var(e.y)]1.w = 0
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4525824   .0821032     5.51   0.000      .291663    .6135017
       female |   .5435942   .0815035     6.67   0.000     .3838503    .7033381
     cv       |
          [*] |   .3576463   .0548017     6.53   0.000     .2502369    .4650556
     _cons    |
         male |   10.33924   4.225914     2.45   0.014     2.056605    18.62188
       female |   4.326879   4.000737     1.08   0.279    -3.514422    12.16818
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |   .4513773   .0937037     4.82   0.000     .2677214    .6350331
       female |   .2101483   .0992473     2.12   0.034     .0156271    .4046694
     x        |
         male |   .3527524   .0972145     3.63   0.000     .1622155    .5432893
       female |   .4520144   .1061237     4.26   0.000     .2440157    .6600131
     cv       |
          [*] |   .0479536   .0608685     0.79   0.431    -.0713466    .1672537
     _cons    |
         male |   8.227069   4.450954     1.85   0.065    -.4966419    16.95078
       female |    13.6048   4.117905     3.30   0.001     5.533856    21.67575
 -------------+----------------------------------------------------------------
 Variance     |
   e.m        |
          [*] |   48.05346   4.805346                      39.50068    58.45812
   e.y        |
          [*] |   48.85108   4.885108                      40.15633    59.42843
 ------------------------------------------------------------------------------
 Note: [*] identifies parameter estimates constrained to be equal across
       groups.
 LR test of model vs. saturated: chi2(4)   =      3.73, Prob  chi2 = 0.4432

Now we can use the estat teffects to calculate the indirect effects for both males and females.

estat teffects
 
 Direct effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4525824   .0821032     5.51   0.000      .291663    .6135017
       female |   .5435942   .0815035     6.67   0.000     .3838503    .7033381
     cv       |
         male |   .3576463   .0548017     6.53   0.000     .2502369    .4650556
       female |   .3576463   .0548017     6.53   0.000     .2502369    .4650556
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |   .4513773   .0937037     4.82   0.000     .2677214    .6350331
       female |   .2101483   .0992473     2.12   0.034     .0156271    .4046694
     x        |
         male |   .3527524   .0972145     3.63   0.000     .1622155    .5432893
       female |   .4520144   .1061237     4.26   0.000     .2440157    .6600131
     cv       |
         male |   .0479536   .0608685     0.79   0.431    -.0713466    .1672537
       female |   .0479536   .0608685     0.79   0.431    -.0713466    .1672537
 ------------------------------------------------------------------------------
 
 Indirect effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
          [*] |          0  (no path)
     cv       |
          [*] |          0  (no path)
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
          [*] |          0  (no path)
     x        |
         male |   .2042854   .0563196     3.63   0.000     .0939009    .3146699
       female |   .1142354   .0566038     2.02   0.044     .0032939    .2251768
     cv       |
         male |   .1614334   .0416532     3.88   0.000     .0797947    .2430722
       female |   .0751587    .037317     2.01   0.044     .0020188    .1482986
 ------------------------------------------------------------------------------
 Note: [*] identifies parameter estimates constrained to be equal across
       groups.
 
 Total effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4525824   .0821032     5.51   0.000      .291663    .6135017
       female |   .5435942   .0815035     6.67   0.000     .3838503    .7033381
     cv       |
         male |   .3576463   .0548017     6.53   0.000     .2502369    .4650556
       female |   .3576463   .0548017     6.53   0.000     .2502369    .4650556
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |   .4513773   .0937037     4.82   0.000     .2677214    .6350331
       female |   .2101483   .0992473     2.12   0.034     .0156271    .4046694
     x        |
         male |   .5570378   .0914805     6.09   0.000     .3777393    .7363362
       female |   .5662498   .0857084     6.61   0.000     .3982643    .7342352
     cv       |
         male |    .209387   .0638934     3.28   0.001     .0841582    .3346158
       female |   .1231123   .0621467     1.98   0.048     .0013071    .2449176
 ------------------------------------------------------------------------------

The indirect effect of x on y for males is .2042854 while for females it is .1142354.

Next we will look at Model 2.

Model 2

Here is the diagram for Model 2.

Image model2s-1

For this model there is an interaction between w and x only in the mediator equation so we have to constrain the coefficient for the mediator to be equal in both equations in addition to the covariate and residuals.

sem (0: m <- x cv@c1)(0: y <- m@b1 x cv@c2) ///
     (1: m <- x cv@c1)(1: y <- m@b1 x cv@c2), group(w) ///
     variance(0: e.m@v1 e.y@v2) ///
     variance(1: e.m@v1 e.y@v2)**
 
 Endogenous variables 
 Observed:  m y
 
 Exogenous variables
 Observed:  x cv
 
 Fitting target model:
 Iteration 0:   log likelihood = -2880.2553  
 Iteration 1:   log likelihood = -2814.5984  
 Iteration 2:   log likelihood =  -2797.118  
 Iteration 3:   log likelihood = -2796.3599  
 Iteration 4:   log likelihood = -2796.3547  
 Iteration 5:   log likelihood = -2796.3547  
 
 Structural equation model                       Number of obs      =       200
 Grouping variable  = w                          Number of groups   =         2
 Estimation method  = ml
 Log likelihood     = -2796.3547
 
  ( 1)  [y]0bn.w#c.m - [y]1.w#c.m = 0
  ( 2)  [m]0bn.w#c.cv - [m]1.w#c.cv = 0
  ( 3)  [y]0bn.w#c.cv - [y]1.w#c.cv = 0
  ( 4)  [var(e.m)]0bn.w - [var(e.m)]1.w = 0
  ( 5)  [var(e.y)]0bn.w - [var(e.y)]1.w = 0
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4525824   .0821032     5.51   0.000      .291663    .6135017
       female |   .5435942   .0815035     6.67   0.000     .3838503    .7033381
     cv       |
          [*] |   .3576463   .0548017     6.53   0.000     .2502369    .4650557
     _cons    |
         male |   10.33924   4.225914     2.45   0.014     2.056604    18.62188
       female |   4.326879   4.000738     1.08   0.279    -3.514423    12.16818
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
          [*] |   .3384145   .0719076     4.71   0.000     .1974781    .4793508
     x        |
         male |   .4260495   .0896114     4.75   0.000     .2504144    .6016846
       female |   .3501396    .091638     3.82   0.000     .1705324    .5297469
     cv       |
          [*] |   .0503993   .0613771     0.82   0.412    -.0698976    .1706962
     _cons    |
         male |   10.18685   4.361284     2.34   0.020     1.638888    18.73481
       female |   12.17734   4.080339     2.98   0.003     4.180026    20.17466
 -------------+----------------------------------------------------------------
 Variance     |
   e.m        |
          [*] |   48.05346   4.805346                      39.50068    58.45812
   e.y        |
          [*] |   49.69406   4.969406                      40.84927    60.45394
 ------------------------------------------------------------------------------
 Note: [*] identifies parameter estimates constrained to be equal across
       groups.
 LR test of model vs. saturated: chi2(5)   =      7.16, Prob  chi2 = 0.2093

. estat teffects
 
 Direct effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4525824   .0821032     5.51   0.000      .291663    .6135017
       female |   .5435942   .0815035     6.67   0.000     .3838503    .7033381
     cv       |
         male |   .3576463   .0548017     6.53   0.000     .2502369    .4650557
       female |   .3576463   .0548017     6.53   0.000     .2502369    .4650557
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |   .3384145   .0719076     4.71   0.000     .1974781    .4793508
       female |   .3384145   .0719076     4.71   0.000     .1974781    .4793508
     x        |
         male |   .4260495   .0896114     4.75   0.000     .2504144    .6016846
       female |   .3501396    .091638     3.82   0.000     .1705324    .5297469
     cv       |
         male |   .0503993   .0613771     0.82   0.412    -.0698976    .1706962
       female |   .0503993   .0613771     0.82   0.412    -.0698976    .1706962
 ------------------------------------------------------------------------------
 
 Indirect effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
          [*] |          0  (no path)
     cv       |
          [*] |          0  (no path)
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
          [*] |          0  (no path)
     x        |
         male |   .1531604   .0427916     3.58   0.000     .0692904    .2370304
       female |   .1839601   .0478402     3.85   0.000     .0901952    .2777251
     cv       |
         male |   .1210327    .031707     3.82   0.000     .0588882    .1831772
       female |   .1210327    .031707     3.82   0.000     .0588882    .1831772
 ------------------------------------------------------------------------------
 Note: [*] identifies parameter estimates constrained to be equal across
       groups.
 
 Total effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .4525824   .0821032     5.51   0.000      .291663    .6135017
       female |   .5435942   .0815035     6.67   0.000     .3838503    .7033381
     cv       |
         male |   .3576463   .0548017     6.53   0.000     .2502369    .4650557
       female |   .3576463   .0548017     6.53   0.000     .2502369    .4650557
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |   .3384145   .0719076     4.71   0.000     .1974781    .4793508
       female |   .3384145   .0719076     4.71   0.000     .1974781    .4793508
     x        |
         male |     .57921   .0879948     6.58   0.000     .4067433    .7516766
       female |   .5340998    .087352     6.11   0.000     .3628929    .7053066
     cv       |
         male |    .171432   .0587342     2.92   0.004     .0563151    .2865488
       female |    .171432   .0587342     2.92   0.004     .0563151    .2865488
 ------------------------------------------------------------------------------

This time the indirect effect of x on y for males is .1531604 while for females it is .1839601.

Next up is Model 3.

Model 3

Here is the diagram for Model 3.

Image model3s-1

For Model 3 the interaction term is only in the equation for the dependent variable, y. To compute the indirect effect we will need to constrain the coefficient for x in both equations along with cv and the residuals. In addition we will need to constrain the constant, _cons to be equal in both groups for the first equation.

. sem (0: m <- x@b1 cv@c1 _cons@i1)(0: y <- m x@b2 cv@c2) ///
     (1: m <- x@b1 cv@c1 _cons@i1)(1: y <- m x@b2 cv@c2), group(w) ///
     variance(0: e.m@v1 e.y@v2) ///
     variance(1: e.m@v1 e.y@v2)**
 
 Endogenous variables
 Observed:  m y
 
 Exogenous variables
 Observed:  x cv
 
 Fitting target model:
 Iteration 0:   log likelihood = -2809.2798  
 Iteration 1:   log likelihood =  -2797.463  
 Iteration 2:   log likelihood = -2796.0327  
 Iteration 3:   log likelihood = -2796.0196  
 Iteration 4:   log likelihood = -2796.0196  
 
 Structural equation model                       Number of obs      =       200
 Grouping variable  = w                          Number of groups   =         2
 Estimation method  = ml
 Log likelihood     = -2796.0196
 
  ( 1)  [m]0bn.w#c.x - [m]1.w#c.x = 0
  ( 2)  [m]0bn.w#c.cv - [m]1.w#c.cv = 0
  ( 3)  [y]0bn.w#c.x - [y]1.w#c.x = 0
  ( 4)  [y]0bn.w#c.cv - [y]1.w#c.cv = 0
  ( 5)  [var(e.m)]0bn.w - [var(e.m)]1.w = 0
  ( 6)  [var(e.y)]0bn.w - [var(e.y)]1.w = 0
  ( 7)  [m]0bn.w - [m]1.w = 0
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
          [*] |   .5038419   .0628899     8.01   0.000     .3805799    .6271038
     cv       |
          [*] |     .35414     .05488     6.45   0.000     .2465771    .4617029
     _cons    |
          [*] |   7.146537   3.017773     2.37   0.018     1.231809    13.06126
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |    .425432   .0861437     4.94   0.000     .2565935    .5942706
       female |   .2444712   .0863545     2.83   0.005     .0752194    .4137229
     x        |
          [*] |   .3979248   .0727133     5.47   0.000     .2554093    .5404402
     cv       |
          [*] |   .0489704   .0609254     0.80   0.422    -.0704413     .168382
     _cons    |
         male |    7.15329   4.182562     1.71   0.087     -1.04438    15.35096
       female |   14.60934    3.86371     3.78   0.000     7.036603    22.18207
 -------------+----------------------------------------------------------------
 Variance     |
   e.m        |
          [*] |    48.6004    4.86004                      39.95027    59.12348
   e.y        |
          [*] |   48.97042   4.897041                      40.25443    59.57361
 ------------------------------------------------------------------------------
 Note: [*] identifies parameter estimates constrained to be equal across
       groups.
 LR test of model vs. saturated: chi2(7)   =      6.49, Prob  chi2 = 0.4843

. estat teffects

 Direct effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .5038419   .0628899     8.01   0.000     .3805799    .6271038
       female |   .5038419   .0628899     8.01   0.000     .3805799    .6271038
     cv       |
         male |     .35414     .05488     6.45   0.000     .2465771    .4617029
       female |     .35414     .05488     6.45   0.000     .2465771    .4617029
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |    .425432   .0861437     4.94   0.000     .2565935    .5942706
       female |   .2444712   .0863545     2.83   0.005     .0752194    .4137229
     x        |
         male |   .3979248   .0727133     5.47   0.000     .2554093    .5404402
       female |   .3979248   .0727133     5.47   0.000     .2554093    .5404402
     cv       |
         male |   .0489704   .0609254     0.80   0.422    -.0704413     .168382
       female |   .0489704   .0609254     0.80   0.422    -.0704413     .168382
 ------------------------------------------------------------------------------
 
 Indirect effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
          [*] |          0  (no path)
     cv       |
          [*] |          0  (no path)
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
          [*] |          0  (no path)
     x        |
         male |   .2143505   .0509868     4.20   0.000     .1144182    .3142827
       female |   .1231748   .0461456     2.67   0.008      .032731    .2136186
     cv       |
         male |   .1506625    .038416     3.92   0.000     .0753685    .2259565
       female |    .086577   .0333952     2.59   0.010     .0211236    .1520304
 ------------------------------------------------------------------------------
 Note: [*] identifies parameter estimates constrained to be equal across
       groups.
 
 Total effects
 ------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 Structural   |
   m <-       |
     x        |
         male |   .5038419   .0628899     8.01   0.000     .3805799    .6271038
       female |   .5038419   .0628899     8.01   0.000     .3805799    .6271038
     cv       |
         male |     .35414     .05488     6.45   0.000     .2465771    .4617029
       female |     .35414     .05488     6.45   0.000     .2465771    .4617029
   -----------+----------------------------------------------------------------
   y <-       |
     m        |
         male |    .425432   .0861437     4.94   0.000     .2565935    .5942706
       female |   .2444712   .0863545     2.83   0.005     .0752194    .4137229
     x        |
         male |   .6122752   .0745834     8.21   0.000     .4660944     .758456
       female |   .5210996   .0681111     7.65   0.000     .3876042     .654595
     cv       |
         male |   .1996329   .0622773     3.21   0.001     .0775716    .3216941
       female |   .1355474   .0595838     2.27   0.023     .0187652    .2523295
 ------------------------------------------------------------------------------

This time the indirect effect of x on y for males is .2143505 while for females it is .1231748.

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