Ruijie
2013-Feb-09 02:55 UTC
[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 <-
as.matrix(read.table("http://dl.dropbox.com/u/1445171/cov.mat.csv",
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]]
John Fox
2013-Feb-09 16:38 UTC
[R] Troubleshooting underidentification issues in structural equation modelling (SEM)
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: Read 9 items 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 Hamilton, Ontario, Canada> -----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 <- > as.matrix(read.table("http://dl.dropbox.com/u/1445171/cov.mat.csv", > 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]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting- > guide.html > and provide commented, minimal, self-contained, reproducible code.