[R] Troubleshooting underidentification issues in structural equation modelling (SEM)
John Fox
jfox at mcmaster.ca
Fri Feb 15 14:12:48 CET 2013
Dear Ruijie and Bert,
I agree with Bert that it's very difficult to do effective statistical consulting long-distance by email. I think that you'd be much better served by getting competent statistical help locally, as I've already suggested.
On the other hand, I'm surprised that your reading didn't suggest that a CFA model with latent variables that have just one observed indicator each, and in which both the factor loadings and error variances for these variables are free parameters, is underidentified. If you haven't already read it, I recommend Bollen's Structural Equations with Latent Variables (Wiley, 1989), despite its age.
Best,
John
On Fri, 15 Feb 2013 02:11:01 -0800
Bert Gunter <gunter.berton at gene.com> wrote:
> These are statistical, not R issues, so please do not post further
> here. You are clearly out of your depth statistically. You need to get
> local statistical help, or you can try posting on a statistical list
> like stats.stackexchange.com if you care to take advice from unknown
> sources who don't understand the details of your situation.
>
> -- Bert
>
> On Fri, Feb 15, 2013 at 1:11 AM, Ruijie <breakaway8 at gmail.com> wrote:
> > Thanks Prof Fox for your guidance. My purpose in fitting this model is to
> > contrast it with another model that I am proposing which I believe will be
> > a better fit.
> >
> > On the point of some of the items being close to invariant, I had a close
> > look at my data and indeed that is the case I am aware of it. However, I am
> > not sure what to do with these items. Do I remove them? If I do, what
> > threshold of variance do I set for removal? How do I decide on that
> > threshold?
> >
> > I've combed a number of textbooks for answers but sadly have not found
> > much. Hope you could offer some advice, thanks!
> >
> > Regards,
> > Ruijie (RJ)
> >
> > --------
> > He who has a why can endure any how.
> >
> > ~ Friedrich Nietzsche
> >
> >
> > On 10 February 2013 00:38, John Fox <jfox at mcmaster.ca> wrote:
> >
> >> 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.
> >>
> >>
> >
> > [[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.
>
>
>
> --
>
> Bert Gunter
> Genentech Nonclinical Biostatistics
>
> Internal Contact Info:
> Phone: 467-7374
> Website:
> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>
> ______________________________________________
> 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.
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