# [R] Troubleshooting underidentification issues in structural equation modelling (SEM)

John Fox jfox at mcmaster.ca
Sat Feb 9 17:38:03 CET 2013

```Dear Ruijie,

Your model is underidentified by virtue of two of the factors having only
one observed indicator each. No SEM software can magically estimate this
model as it stands. Beyond that, I won't comment on the wisdom of what
you're doing, such as computing covariances between ordinal variables -- but
see what I discovered below.

Removing these two variables and the associated factors produces the
following model:

--------- snip ------------

> model <- cfa(reference.indicators=FALSE)
1: F01: I01, I02, I03
2: F02: I04, I05, I06, I07, I08, I09, I10, I11, I12, I13
3: F03: I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26
4: F04: I27, I28, I29, I30, I31, I32, I33, I34
5: F05: I35, I36, I37, I38, I39, I40, I41, I42, I43
6: F07: I46, I47, I48, I49, I50, I51
7: F08: I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64
8: F09: I65, I66, I67
9: F11: I69, I70, I71
10:
NOTE: adding 66 variances to the model
>
> cfa.output <- sem(model, cov.mat, N = 900)

--------- snip ------------

sem() ran out of iterations, but the summary output is revealing:

--------- snip ------------

> summary(cfa.output)

Model Chisquare =  5677.1   Df =  2043 Pr(>Chisq) = 0
AIC =  6013.1
BIC =  -8220.193

Normalized Residuals
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-3.9910 -0.5887 -0.1486  0.2588  0.8092 17.2900

R-square for Endogenous Variables
I01     I02     I03     I04     I05     I06     I07     I08     I09
I10
0.0953  0.1263  0.0000  0.1131  0.4039  0.2519  0.1168  0.0468  0.0005
0.0059
I11     I12     I13     I14     I15     I16     I17     I18     I19
I20
0.0479  0.0228  0.1150  0.2813  0.0001  0.0388  0.2106  0.0001  0.0913
0.0063
I21     I22     I23     I24     I25     I26     I27     I28     I29
I30
0.0041  0.0077  0.0022  0.0000  0.0299  0.0067  0.0019  0.0011  0.0010
0.0000
I31     I32     I33     I34     I35     I36     I37     I38     I39
I40
0.0005  0.0117  0.0270  0.0001  0.0084  0.0001  0.0256  0.4969  0.0613
0.0515
I41     I42     I43     I46     I47     I48     I49     I50     I51
I54
0.0005  0.0052  0.0307  0.0003  0.1131  0.0014  0.0000  0.1276  0.9728
0.0520
I55     I56     I57     I58     I59     I60     I61     I62     I63
I64
0.2930  0.0127  0.0543  0.0500  0.0378  0.0001  0.3048  0.0002  0.0304
0.0001
I65     I66     I67     I69     I70     I71
56.7264  0.0000  0.0002  0.2220  0.2342  0.2240

Parameter Estimates
Estimate      Std Error    z value      Pr(>|z|)

lam[I01:F01]  3.023074e-02 5.133785e-03  5.888586224  3.895133e-09 I01 <---
F01
lam[I02:F01]  3.283192e-02 5.291069e-03  6.205157975  5.464199e-10 I02 <---
F01
lam[I03:F01]  1.123398e-04 2.695713e-03  0.041673509  9.667590e-01 I03 <---
F01
lam[I04:F02]  1.365329e-01 1.555023e-02  8.780124358  1.632940e-18 I04 <---
F02
lam[I05:F02]  9.525580e-02 5.517838e-03 17.263245517  8.896692e-67 I05 <---
F02
lam[I06:F02]  1.720147e-01 1.277593e-02 13.463962882  2.548717e-41 I06 <---
F02
lam[I07:F02]  3.164280e-02 3.543421e-03  8.930015663  4.259485e-19 I07 <---
F02
lam[I08:F02]  5.685988e-02 1.021854e-02  5.564386503  2.630763e-08 I08 <---
F02
lam[I09:F02]  1.234516e-03 2.228298e-03  0.554017268  5.795670e-01 I09 <---
F02
lam[I10:F02]  1.656005e-02 8.458411e-03  1.957820181  5.025112e-02 I10 <---
F02
lam[I11:F02]  8.785114e-02 1.560646e-02  5.629151062  1.810987e-08 I11 <---
F02
lam[I12:F02]  3.022114e-02 7.815459e-03  3.866842129  1.102537e-04 I12 <---
F02
lam[I13:F02]  5.075487e-02 5.732307e-03  8.854177302  8.430329e-19 I13 <---
F02
lam[I14:F03]  2.587670e-01 2.308125e-02 11.211137448  3.595430e-29 I14 <---
F03
lam[I15:F03] -2.999816e-04 1.469667e-03 -0.204115351  8.382634e-01 I15 <---
F03
lam[I16:F03]  2.314973e-02 5.256310e-03  4.404179628  1.061849e-05 I16 <---
F03
lam[I17:F03]  9.333201e-02 9.301123e-03 10.034488472  1.075152e-23 I17 <---
F03
lam[I18:F03] -3.389770e-04 1.469665e-03 -0.230649144  8.175874e-01 I18 <---
F03
lam[I19:F03]  6.783532e-02 1.005099e-02  6.749117110  1.487475e-11 I19 <---
F03
lam[I20:F03]  3.916003e-02 2.208166e-02  1.773418523  7.615938e-02 I20 <---
F03
lam[I21:F03]  7.260062e-03 5.059696e-03  1.434881038  1.513210e-01 I21 <---
F03
lam[I22:F03]  4.556262e-02 2.322628e-02  1.961683814  4.979931e-02 I22 <---
F03
lam[I23:F03]  1.528270e-03 1.469492e-03  1.039998378  2.983407e-01 I23 <---
F03
lam[I24:F03] -8.635421e-04 7.794243e-03 -0.110792296  9.117811e-01 I24 <---
F03
lam[I25:F03]  3.625777e-02 9.391320e-03  3.860774500  1.130282e-04 I25 <---
F03
lam[I26:F03]  2.350350e-02 1.287924e-02  1.824913234  6.801412e-02 I26 <---
F03
lam[I27:F04]  8.013741e-03 7.100286e-03  1.128650332  2.590454e-01 I27 <---
F04
lam[I28:F04]  1.094008e-03 1.051268e-03  1.040655898  2.980353e-01 I28 <---
F04
lam[I29:F04]  3.712052e-03 3.647614e-03  1.017665748  3.088368e-01 I29 <---
F04
lam[I30:F04]  2.309796e-04 3.735193e-03  0.061838730  9.506913e-01 I30 <---
F04
lam[I31:F04]  9.905663e-03 1.152962e-02  0.859149344  3.902581e-01 I31 <---
F04
lam[I32:F04]  2.612580e-02 2.019934e-02  1.293398622  1.958732e-01 I32 <---
F04
lam[I33:F04]  8.299228e-02 6.192966e-02  1.340105491  1.802111e-01 I33 <---
F04
lam[I34:F04] -1.131056e-03 2.529220e-03 -0.447195412  6.547340e-01 I34 <---
F04
lam[I35:F05]  7.917586e-03 3.671643e-03  2.156414987  3.105128e-02 I35 <---
F05
lam[I36:F05] -1.122579e-03 6.021404e-03 -0.186431415  8.521065e-01 I36 <---
F05
lam[I37:F05]  5.245211e-03 1.392977e-03  3.765467592  1.662377e-04 I37 <---
F05
lam[I38:F05]  1.459603e-01 1.212396e-02 12.038999880  2.216262e-33 I38 <---
F05
lam[I39:F05]  9.091376e-02 1.563821e-02  5.813567281  6.115538e-09 I39 <---
F05
lam[I40:F05]  1.174920e-01 2.202669e-02  5.334074682  9.603300e-08 I40 <---
F05
lam[I41:F05] -6.674451e-03 1.240103e-02 -0.538217344  5.904270e-01 I41 <---
F05
lam[I42:F05]  2.074782e-02 1.220154e-02  1.700426338  8.905076e-02 I42 <---
F05
lam[I43:F05]  2.058762e-02 4.991076e-03  4.124885623  3.709190e-05 I43 <---
F05
lam[I46:F07] -7.270739e-03 1.477067e-02 -0.492241486  6.225486e-01 I46 <---
F07
lam[I47:F07]  3.294388e-02 3.596677e-03  9.159533769  5.212202e-20 I47 <---
F07
lam[I48:F07]  1.960841e-02 1.764661e-02  1.111171519  2.664945e-01 I48 <---
F07
lam[I49:F07] -3.231036e-06 1.918097e-03 -0.001684501  9.986560e-01 I49 <---
F07
lam[I50:F07]  3.300839e-02 3.426575e-03  9.633058172  5.797778e-22 I50 <---
F07
lam[I51:F07]  3.234144e-02 1.806978e-03 17.898079438  1.220591e-71 I51 <---
F07
lam[I54:F08]  1.003417e-01 1.711888e-02  5.861462155  4.588091e-09 I54 <---
F08
lam[I55:F08]  1.408049e-01 9.886797e-03 14.241707324  5.047855e-46 I55 <---
F08
lam[I56:F08]  4.096655e-02 1.425085e-02  2.874673321  4.044457e-03 I56 <---
F08
lam[I57:F08]  7.137153e-02 1.191379e-02  5.990663872  2.089862e-09 I57 <---
F08
lam[I58:F08]  1.206947e-01 2.100849e-02  5.745043255  9.189749e-09 I58 <---
F08
lam[I59:F08]  7.178104e-02 1.439758e-02  4.985632949  6.175929e-07 I59 <---
F08
lam[I60:F08]  2.027172e-03 6.627611e-03  0.305867676  7.597054e-01 I60 <---
F08
lam[I61:F08]  1.215272e-01 8.374503e-03 14.511567971  1.023539e-47 I61 <---
F08
lam[I62:F08]  1.072324e-03 3.404172e-03  0.315002895  7.527595e-01 I62 <---
F08
lam[I63:F08]  4.836428e-02 1.084696e-02  4.458785647  8.242530e-06 I63 <---
F08
lam[I64:F08] -7.221766e-04 2.879830e-03 -0.250770557  8.019915e-01 I64 <---
F08
lam[I65:F09]  3.983293e+00 9.711381e+01  0.041016748  9.672825e-01 I65 <---
F09
lam[I66:F09] -1.673556e-03 4.096286e-02 -0.040855450  9.674111e-01 I66 <---
F09
lam[I67:F09]  5.049621e-04 1.235197e-02  0.040881113  9.673907e-01 I67 <---
F09
lam[I69:F11]  1.586150e-01 1.373361e-02 11.549406592  7.433188e-31 I69 <---
F11
lam[I70:F11]  8.237619e-02 6.956861e-03 11.840999012  2.395820e-32 I70 <---
F11
lam[I71:F11]  9.448552e-02 8.147082e-03 11.597468367  4.244491e-31 I71 <---
F11
C[F01,F02]    3.728217e-02 9.597514e-02  0.388456537  6.976782e-01 F02 <-->
F01
C[F01,F03]    7.240582e-01 1.355959e-01  5.339824854  9.303642e-08 F03 <-->
F01
C[F01,F04]   -5.354253e-01 5.303413e-01 -1.009586227  3.126936e-01 F04 <-->
F01
C[F01,F05]    2.384885e-01 1.052432e-01  2.266070269  2.344708e-02 F05 <-->
F01
C[F01,F07]    1.040182e+00 1.489435e-01  6.983736644  2.874306e-12 F07 <-->
F01
C[F01,F08]   -1.013298e-01 1.035977e-01 -0.978107752  3.280210e-01 F08 <-->
F01
C[F01,F09]    1.171918e-02 2.860487e-01  0.040969189  9.673205e-01 F09 <-->
F01
C[F01,F11]    7.946394e-02 1.093765e-01  0.726517178  4.675218e-01 F11 <-->
F01
C[F02,F03]    2.272594e-01 6.201036e-02  3.664862498  2.474715e-04 F03 <-->
F02
C[F02,F04]    1.730434e-01 2.421846e-01  0.714510214  4.749117e-01 F04 <-->
F02
C[F02,F05]    5.724325e-02 5.826660e-02  0.982436740  3.258847e-01 F05 <-->
F02
C[F02,F07]    6.462176e-02 4.345441e-02  1.487116261  1.369841e-01 F07 <-->
F02
C[F02,F08]    9.751552e-01 4.152782e-02 23.481976829 6.233472e-122 F08 <-->
F02
C[F02,F09]   -6.044195e-04 1.578879e-02 -0.038281562  9.694632e-01 F09 <-->
F02
C[F02,F11]    1.026869e-01 6.243113e-02  1.644803751  1.000103e-01 F11 <-->
F02
C[F03,F04]    7.503546e-01 5.859127e-01  1.280659345  2.003133e-01 F04 <-->
F03
C[F03,F05]    2.162240e-01 6.673622e-02  3.239980149  1.195380e-03 F05 <-->
F03
C[F03,F07]    3.686512e-01 5.011777e-02  7.355697641  1.899325e-13 F07 <-->
F03
C[F03,F08]    2.308590e-01 6.677771e-02  3.457127167  5.459671e-04 F08 <-->
F03
C[F03,F09]    3.422314e-02 8.348605e-01  0.040992640  9.673018e-01 F09 <-->
F03
C[F03,F11]    2.699455e-01 7.051428e-02  3.828238253  1.290638e-04 F11 <-->
F03
C[F04,F05]    1.062305e+00 7.911158e-01  1.342793467  1.793389e-01 F05 <-->
F04
C[F04,F07]   -8.324317e-02 1.748320e-01 -0.476132285  6.339801e-01 F07 <-->
F04
C[F04,F08]    1.389356e-01 2.448826e-01  0.567356043  5.704723e-01 F08 <-->
F04
C[F04,F09]    5.856590e-02 1.429422e+00  0.040971726  9.673184e-01 F09 <-->
F04
C[F04,F11]    2.294948e+00 1.661805e+00  1.380997204  1.672798e-01 F11 <-->
F04
C[F05,F07]    2.099261e-01 4.716298e-02  4.451078015  8.544029e-06 F07 <-->
F05
C[F05,F08]    4.221026e-02 6.261302e-02  0.674145115  5.002191e-01 F08 <-->
F05
C[F05,F09]    3.165187e-02 7.721368e-01  0.040992561  9.673018e-01 F09 <-->
F05
C[F05,F11]    7.351754e-01 6.818771e-02 10.781639916  4.203245e-27 F11 <-->
F05
C[F07,F08]    3.180037e-03 4.670052e-02  0.068094253  9.457106e-01 F08 <-->
F07
C[F07,F09]    6.292195e-03 1.535561e-01  0.040976532  9.673146e-01 F09 <-->
F07
C[F07,F11]    1.049909e-01 4.942732e-02  2.124147077  3.365785e-02 F11 <-->
F07
C[F08,F09]    1.346105e-02 3.284233e-01  0.040986879  9.673064e-01 F09 <-->
F08
C[F08,F11]    1.383223e-01 6.694679e-02  2.066152656  3.881407e-02 F11 <-->
F08
C[F09,F11]    4.571695e-02 1.115233e+00  0.040993193  9.673013e-01 F11 <-->
F09
V[I01]        8.680184e-03 4.762484e-04 18.226169942  3.199593e-74 I01 <-->
I01
V[I02]        7.459398e-03 4.540213e-04 16.429621740  1.173889e-60 I02 <-->
I02
V[I03]        7.478254e-03 3.527242e-04 21.201419570 9.265904e-100 I03 <-->
I03
V[I04]        1.461376e-01 7.255861e-03 20.140635357  3.251385e-90 I04 <-->
I04
V[I05]        1.339123e-02 8.832859e-04 15.160696593  6.438285e-52 I05 <-->
I05
V[I06]        8.789764e-02 4.794460e-03 18.333167786  4.499223e-75 I06 <-->
I06
V[I07]        7.568474e-03 3.765280e-04 20.100692934  7.277043e-90 I07 <-->
I07
V[I08]        6.587699e-02 3.167671e-03 20.796666217  4.639577e-96 I08 <-->
I08
V[I09]        3.217338e-03 1.517789e-04 21.197527600  1.006468e-99 I09 <-->
I09
V[I10]        4.621928e-02 2.185030e-03 21.152695320  2.606174e-99 I10 <-->
I10
V[I11]        1.535621e-01 7.387455e-03 20.786870576  5.690287e-96 I11 <-->
I11
V[I12]        3.908344e-02 1.860301e-03 21.009196121  5.404186e-98 I12 <-->
I12
V[I13]        1.983328e-02 9.856998e-04 20.121018746  4.830497e-90 I13 <-->
I13
V[I14]        1.710572e-01 1.211810e-02 14.115839622  3.033809e-45 I14 <-->
I14
V[I15]        1.075179e-03 5.071602e-05 21.199985035 9.552682e-100 I15 <-->
I15
V[I16]        1.326202e-02 6.467196e-04 20.506601881  1.879773e-93 I16 <-->
I16
V[I17]        3.265749e-02 1.988078e-03 16.426667150  1.232493e-60 I17 <-->
I17
V[I18]        1.075154e-03 5.071579e-05 21.199589039 9.633394e-100 I18 <-->
I18
V[I19]        4.579942e-02 2.353962e-03 19.456315348  2.576564e-84 I19 <-->
I19
V[I20]        2.413742e-01 1.144346e-02 21.092761358  9.269013e-99 I20 <-->
I20
V[I21]        1.269773e-02 6.009212e-04 21.130448044  4.175664e-99 I21 <-->
I21
V[I22]        2.667065e-01 1.265916e-02 21.068268778  1.555139e-98 I22 <-->
I22
V[I23]        1.072933e-03 5.069564e-05 21.164210344  2.041534e-99 I23 <-->
I23
V[I24]        3.024220e-02 1.426452e-03 21.200993757 9.350120e-100 I24 <-->
I24
V[I25]        4.271005e-02 2.065984e-03 20.672986805  6.064466e-95 I25 <-->
I25
V[I26]        8.208471e-02 3.892796e-03 21.086314551  1.062215e-98 I26 <-->
I26
V[I27]        3.448443e-02 1.627464e-03 21.189053796  1.204944e-99 I27 <-->
I27
V[I28]        1.074072e-03 5.065613e-05 21.203199739 8.921947e-100 I28 <-->
I28
V[I29]        1.388601e-02 6.548663e-04 21.204342235 8.707941e-100 I29 <-->
I29
V[I30]        3.656256e-02 1.724532e-03 21.201435371 9.262794e-100 I30 <-->
I30
V[I31]        1.989840e-01 9.383562e-03 21.205594692 8.479218e-100 I31 <-->
I31
V[I32]        5.755557e-02 2.882318e-03 19.968499245  1.035172e-88 I32 <-->
I32
V[I33]        2.481455e-01 1.532786e-02 16.189179144  6.012530e-59 I33 <-->
I33
V[I34]        1.484183e-02 7.000026e-04 21.202534570 9.048952e-100 I34 <-->
I34
V[I35]        7.415580e-03 3.516263e-04 21.089380308  9.955712e-99 I35 <-->
I35
V[I36]        2.011634e-02 9.488573e-04 21.200591226 9.430434e-100 I36 <-->
I36
V[I37]        1.047757e-03 5.025784e-05 20.847625170  1.601775e-96 I37 <-->
I37
V[I38]        2.156861e-02 3.241426e-03  6.654050864  2.851341e-11 I38 <-->
I38
V[I39]        1.265785e-01 6.238795e-03 20.288931432  1.610577e-91 I39 <-->
I39
V[I40]        2.541968e-01 1.242997e-02 20.450322391  5.967951e-93 I40 <-->
I40
V[I41]        8.528364e-02 4.023849e-03 21.194542822  1.072350e-99 I41 <-->
I41
V[I42]        8.216499e-02 3.888144e-03 21.132187265  4.024656e-99 I42 <-->
I42
V[I43]        1.337408e-02 6.438437e-04 20.772251070  7.715629e-96 I43 <-->
I43
V[I46]        1.907454e-01 8.996895e-03 21.201249767 9.299396e-100 I46 <-->
I46
V[I47]        8.508783e-03 4.165525e-04 20.426677159  9.687421e-93 I47 <-->
I47
V[I48]        2.714640e-01 1.280461e-02 21.200497563 9.449220e-100 I48 <-->
I48
V[I49]        3.218862e-03 1.518230e-04 21.201415045 9.266795e-100 I49 <-->
I49
V[I50]        7.447779e-03 3.685477e-04 20.208454710  8.249036e-91 I50 <-->
I50
V[I51]        2.929982e-05 1.053218e-04  0.278193234  7.808640e-01 I51 <-->
I51
V[I54]        1.833931e-01 8.842196e-03 20.740673158  1.488283e-95 I54 <-->
I54
V[I55]        4.784306e-02 2.783744e-03 17.186584134  3.346789e-66 I55 <-->
I55
V[I56]        1.304849e-01 6.185550e-03 21.095115843  8.818929e-99 I56 <-->
I56
V[I57]        8.868251e-02 4.280267e-03 20.718917274  2.338858e-95 I57 <-->
I57
V[I58]        2.765876e-01 1.332324e-02 20.759777754  1.000282e-95 I58 <-->
I58
V[I59]        1.309969e-01 6.275841e-03 20.873197799  9.384143e-97 I59 <-->
I59
V[I60]        2.844711e-02 1.341830e-03 21.200226581 9.503782e-100 I60 <-->
I60
V[I61]        3.368300e-02 1.992102e-03 16.908270471  3.910162e-64 I61 <-->
I61
V[I62]        7.504898e-03 3.540020e-04 21.200154519 9.518345e-100 I62 <-->
I62
V[I63]        7.472838e-02 3.568523e-03 20.940981942  2.267379e-97 I63 <-->
I63
V[I64]        5.371193e-03 2.533508e-04 21.200616220 9.425427e-100 I64 <-->
I64
V[I65]       -1.558692e+01 7.736661e+02 -0.020146825  9.839262e-01 I65 <-->
I65
V[I66]        6.009302e-02 2.837570e-03 21.177638375  1.535393e-99 I66 <-->
I66
V[I67]        1.075013e-03 5.220505e-05 20.592119939  3.229259e-94 I67 <-->
I67
V[I69]        8.817859e-02 5.000004e-03 17.635704215  1.310532e-69 I69 <-->
I69
V[I70]        2.218392e-02 1.279170e-03 17.342438243  2.249872e-67 I70 <-->
I70
V[I71]        3.093500e-02 1.758727e-03 17.589432179  2.968370e-69 I71 <-->
I71

Iterations =  1000

--------- snip ------------

Several of the observed variables have R^2s that round to 0 and many more
are very small.

I don't have your original data, but I did look at the input covariance
matrix. Here are the standard deviations of the observed variables:

--------- snip ------------

> sqrt(diag(cov.mat))
I01        I02        I03        I04        I05        I06        I07

0.09794939 0.09239769 0.08647698 0.40592964 0.14988296 0.34276336 0.09257290

I08        I09        I10        I11        I12        I13        I14

0.26288788 0.05673501 0.21562354 0.40159670 0.19999190 0.14969750 0.48787040

I15        I16        I17        I18        I19        I20        I21

0.03279129 0.11746460 0.20339207 0.03279129 0.22450179 0.49285671 0.11291786

I22        I23        I24        I25        I26        I27        I28

0.51844236 0.03279129 0.17390500 0.20982058 0.28746674 0.18587268 0.03279129

I29        I30        I31        I32        I33        I34        I35

0.11789736 0.19121352 0.44618622 0.24132578 0.50500808 0.12183229 0.08647698

I36        I37        I38        I39        I40        I41        I42

0.14183651 0.03279129 0.20705800 0.36721084 0.51768833 0.29210990 0.28739426

I43        I45        I46        I47        I48        I49        I50

0.11746460 0.13454976 0.43680464 0.09794939 0.52139099 0.05673501 0.09239769

I51        I54        I55        I56        I57        I58        I59

0.03279129 0.43984267 0.26013269 0.36354251 0.30622933 0.53958761 0.36898429

I60        I61        I62        I63        I64        I65        I66

0.16867489 0.22011795 0.08663745 0.27761032 0.07329198 0.52861343 0.24514452

I67        I68        I69        I70        I71
0.03279129 0.16616880 0.33665601 0.17020504 0.19965594

--------- snip ------------

Some of the standard deviations are very small, suggesting that the
corresponding variables must have been close to invariant in your data set.

If you haven't already done so, I think that you might back up and look more
closely at your data, and perhaps seek some competent local help.

I hope that this helps,
John

-----------------------------------------------
John Fox
Senator McMaster Professor of Social Statistics
Department of Sociology
McMaster University

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Ruijie
> Sent: Friday, February 08, 2013 9:56 PM
> To: R-help at stat.math.ethz.ch
> Subject: [R] Troubleshooting underidentification issues in structural
> equation modelling (SEM)
>
> Hi all, hope someone can help me out with this.
> Background Introduction
>
> I have a data set consisting of data collected from a questionnaire that
> I
> wish to validate. I have chosen to use confirmatory factor analysis to
> analyse this data set.
> Instrument
>
> The instrument consists of 11 subscales. There is a total of 68 items in
> the 11 subscales. Each item is scored on an integer scale between 1 to
> 4.
> Confirmatory factor analysis (CFA) setup
>
> I use the sem package to conduct the CFA. My code is as below:
>
> cov.mat <-
> sep = ",", header = TRUE))
> rownames(cov.mat) <- colnames(cov.mat)
>
> model <- cfa(file = "http://dl.dropbox.com/u/1445171/cfa.model.txt",
> reference.indicators = FALSE)
> cfa.output <- sem(model, cov.mat, N = 900, maxiter = 80000, optimizer
> = optimizerOptim)
> Warning message:In eval(expr, envir, enclos) : Negative parameter
> variances.Model may be underidentified.
>
> Straight off you might notice a few anomalies, let me explain.
>
>    - Why is the optimizer chosen to be optimizerOptim?
>
> ANS: I originally stuck with the default optimizerSem but no matter how
> many iterations I run, either I run out of memory first (8GB RAM setup)
> or
> it would report no convergence Things "seemed" a little better when I
> switched to optimizerOptim where by it would conclude successfully but
> throws up the error that the model is underidentified. Upon closer
> inspection, I realise that the output shows convergence as TRUE but
> iterations is NA so I am not sure what is exactly happening.
>
>    - The maxiter is too high.
>
> ANS: If I set it to a lower value, it refuses to converge, although as
> mentioned above, I doubt real convergence actually occurred.
> Problem
>
> So by now I guess that the model is really underidentified so I looked
> for
> resources to resolve this problem and found:
>
>    - http://davidakenny.net/cm/identify_formal.htm
>    - http://faculty.ucr.edu/~hanneman/soc203b/lectures/identify.html
>
> I followed the 2nd link quite closely and applied the t-rule:
>
>    - I have 68 observed variables, providing me with 68 variances and
> 2278
>    covariances between variables = *2346 data points*.
>    - I also have 68 regression coefficients, 68 error variances of
>    variables, 11 factor variances and 55 factor covariances to estimate
> making
>    it a total of 191 parameters.
>    - Since I will be fixing the variances of the 11 latent factors to 1
> for
>    scaling, I would remove them from the parameters to estimate making
> it a
>    total of *180 parameters to estimate*.
>       - My degrees of freedom is therefore 2346 - 180 = 2166, making it
> an
>       over identified model by the t-rule.
>
> Questions
>
>    1. Is the low variance of some of my items a possible cause for the
>    underidentification? I was advised previously to remove items with
> zero
>    variance which led me to think about items which are very close to
> zero.
>    Should they be removed too?
>    2. After reading much, I think but am not sure that it might be a
> case
>    of empirical underidentification. Is there a systematic way of
> diagnosing
>    what kind of underidentification it is? And what are my options to
> proceed
>    with my analysis?
>
> I have more questions but let's take it at these 2 for now. Thanks for
> any
> help!
>
> Regards,
> Ruijie (RJ)
>
> --------
> He who has a why can endure any how.
>
> ~ Friedrich Nietzsche
>
> 	[[alternative HTML version deleted]]
>
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