Constraining Variance Estimates

[Andrea Niles]

Hi There,

I'm having difficulty getting my latent growth model to converge. I am trying to estimate the intercept and linear slope of a variable collected at three timepoints (bias1 bias8 bias15). Using the trouble shooting section of the Stata manual, I was able to identify that the problem is that my variances of my latent variables and an exogenous observed variable are going to zero, and no modification of the starting values has seemed to resolve the problem. What did resolve the problem was constraining the problem variances to 1 (see below). What are the implications of constraining the model in this way? Can the parameter estimates still be valid?

      sem (I  -> bias1@1 bias8@1 bias15@1) (S -> bias1@0 bias8@1 bias15@2) ///
 (I S pcltot_1  -> pcltot_2) (cond3 pcltot_1 -> S I) if (status==1),  ///
 var(e.I@1 e.pcltot_2@1)

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(bias1 bias8 bias15 pcltot_1 pcltot_2) byte(status cond3)
  50.72662   46.35406  -74.31885  67  66 1 0
-16.848877   34.93335   51.38678  86  65 1 1
-18.862549 -30.511597          . 100 100 1 0
-17.005737   16.75708  -5.733887  83  66 1 1
  81.79395 -26.947693   21.27118  70  70 1 0
 -56.50024  -6.033813  -9.299438  60  66 1 1
         . -36.430542   31.56531  60  62 1 0
-14.743286  -62.68158    13.5589  65  34 1 0
  61.46094  -42.19403 -33.318176 100 100 1 0
-16.464478  12.968872   -9.50177  43  68 1 1
 -55.65192   15.67102 -4.5979004  78  43 1 1
 -32.79889 -20.813354   19.91559  64  68 1 0
-30.289917 -31.182556 -14.216492  73  60 1 0
   54.4599  15.295593   43.17926  59  49 1 0
  -38.3089   -1.64093    7.22876  58  61 1 0
-17.537598  -6.139343  18.042175  59  49 1 0
  85.21997  10.187256  12.340637  83  61 1 1
  -65.7027 -1.7076416  144.98267  72  86 1 0
 113.39447  31.173584   97.36334  71  77 1 0
         .  28.552185          .  75  85 1 1
  3.445007 -30.490845  -45.90674  77  79 1 0
 -7.616333  -.6096191 -18.210266  72  67 1 1
         .  -30.26892   43.51868  74  62 1 0
  50.09943  -43.37177  -2.722473  56  43 1 1
  48.41949  10.556763   31.38495  54  52 1 0
 10.750732  -5.559631   63.67004  85  70 1 1
  30.80481   4.149048          .  60  29 1 0
 30.829773   26.18823 -37.978577  86  75 1 0
  -11.0578    8.23877   11.26538  44  40 1 1
 -51.78711  14.556152   7.198608  59  48 1 1
-18.026855  2.0898438  -36.15735  61  43 1 1
 -50.66699   65.99982 -24.184143  85  20 1 1
 27.027405  -39.91675  -30.62897  87  92 1 1
-10.959229   9.856873  -5.990784  87  59 1 1
  .0947876 -13.710144          .  63  48 1 0
 -7.798706 -37.735107   19.96411  38  54 1 1
  91.47205 -26.766907  23.696167  45  72 1 0
  5.792786          .  136.65924  72  81 1 0
-32.124146   8.849426          .  55  57 1 1
  3.640991   4.642639  -11.20288  62  41 1 1
  47.20209   18.21106  -49.46057  62  58 1 1
  48.90637  -35.92627  -61.00037  81  59 1 1
-70.581116   14.91504  26.250366  64  65 1 0
 27.700867 -23.816895  -1.996521  78  44 1 0
  29.52368   39.00415   -81.7655  46  43 1 0
  39.10889  -.2027588   77.15845  42  26 1 0
-35.754333 -25.199707  -40.31506  68  68 1 1
    -24.81   .6847534 -16.282593  70  79 1 0
  1.385132   35.71039   23.19513  85  91 1 1
 -75.41724   17.45935  -68.57477  71  20 1 0
 1.0522461  -21.77301   24.35034  66  58 1 1
 -27.04651  1.5617065  -9.128357  74  55 1 1
 -37.85144  11.499756 -15.968018  66  24 1 0
 23.433105    1.71344  -22.17914  66  59 1 1
-18.992065 -13.257263  -62.21466  92  72 1 0
-4.7525635  -53.54388   54.69061  69  53 1 1
  5.111816  -13.55005   11.65869  77  66 1 0
 11.895752  34.177917 -1.5999146  72  57 1 0
  6.607056 -34.812317  21.727356  66  21 1 0
-1.3138428 -28.264404  -55.25183  83  77 1 0
  6.936768 -14.408508   42.30225  64  28 1 1
         .          .          .  54  42 1 0
   24.7204  4.3624268  18.204346  86  63 1 0
 33.307983 -32.409912  -18.72174  81  67 1 1
 -44.72766 -10.523193  -6.378723  47  52 1 0
-32.897583  19.213684   28.01233  64  70 1 1
  51.99274  17.490112   -59.8125  59  38 1 0
 -6.570435  13.099487  -.7216797  55  53 1 0
 17.139343  -2.972534 -11.387756  57  43 1 0
 30.321045  -39.47168          .  63  46 1 1
 -43.62738   53.53833   3.940796  65  49 1 0
-31.602234 -11.476501  -41.62286  49  49 1 0
 -58.50317  -97.23523   75.81476  81  65 1 1
 -12.88922   -41.6261   5.341431  83  85 1 1
  5.430359  -37.14032          .  59  64 1 1
 -6.488464  -14.42987    28.3526  69  59 1 1
 -54.85425  -45.43951 -114.44684  99  73 1 0
 -34.65039  -7.399658 -28.279724  51  41 1 1
 -72.52374   .1867676   39.56714  45  42 1 0
  6.427307   -45.1311    26.7077  56  40 1 1
         .    27.1322  -32.99536  59  76 1 1
 -45.72913  -2.757263 -37.852356  56  60 1 1
 16.995544  -16.69281  -67.17621  65  54 1 0
 17.650146  -27.74402          .  84  75 1 0
 17.913757  35.352905  -4.388733  32  20 1 0
 -55.60132   27.75061          .  74  57 1 0
  48.32593  -3.091553   24.66284  82  42 1 1
  29.70709 -32.517212   29.64197  52  50 1 0
 -57.65033   7.196594   .3500366  56  76 1 0
  -30.5025  12.665833  -86.94556  78  63 1 0
 29.442566  -7.301392  24.843506  43  47 1 1
         .  -19.76007          .  85  55 1 1
  36.68683          . -17.065613  54  69 1 0
  41.39307  34.438965  25.516113  40  24 1 0
 -24.58264   55.27649  -42.38269  76  88 1 1
-10.977905   14.54358   86.59998  59  42 1 1
 23.900146   44.76068  -40.16736  64  51 1 0
         .   2.989685    2.87146  61  56 1 1
 -20.45227   27.89612 -17.881104  62  44 1 0
 37.193115    21.5025  18.563599  52  48 1 0
end

[Phil Bromiley]

In SEM you have to constrain the variance of latent variables somehow. Usually this is done either by setting one of the parameters associating the latent to a observed variable to one or directly constraining the variance. If you don't constrain the variance of a latent variable, the model is not identified - I can always rescale the latent variable and get different parameters but with exactly the same fit. I cannot speak to whether the constraints you have imposed are the right ones - that is a matter of substance as much as statistics.

[Andrea Niles]

Hi Phil,

Thank you for your response. Have I not already set the parameters associating the latent to observed variables in the first part of this command?

sem (I -> bias1@1 bias8@1 bias15@1) (S -> bias1@0 bias8@1 bias15@2)

Can I also constrain the variance? If so, how would I determine what I would constrain it to? Andrea

[Joseph Coveney]

What are the implications of constraining the model in this way? Can the parameter estimates still be valid?

1. Have you confirmed that your model is identified?

2. Is this

(I S pcltot_1  -> pcltot_2) (cond3 pcltot_1 -> S I)

a cogent supposition?

[Andrea Niles]

Hi Joseph,

How do you confirm that the model is identified? Also, what is "cogent supposition"?

Andrea