Much thanks to both for your advice. I'll take note to post relevant
questions going forward.

Regards,
Ruijie (RJ)

--------
He who has a why can endure any how.

~ Friedrich Nietzsche


On 15 February 2013 21:12, John Fox <jfox@mcmaster.ca> wrote:

> 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@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@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@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@r-project.org [mailto:
> r-help-bounces@r-project.org]
> > >> > On Behalf Of Ruijie
> > >> > Sent: Friday, February 08, 2013 9:56 PM
> > >> > To: R-help@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@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@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@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]]

