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