Re: [R] Confirmatory factor analysis problems using sem package (works in Amos)
Thanks John. Can I ask under what function you call optim/nlm? I cannot see how this is done by examining sem. Thanks, -Solomon -Original Message- From: John Fox [mailto:j...@mcmaster.ca] Sent: Monday, July 27, 2009 6:23 PM To: 'Solomon Messing' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear Solomon, When I originally programmed the sem() function, I used optim() and experimented with the different methods provided, settling on BFGS as the default. Shortly after that, I compared optim() to nlm() for a range of problems and found that the latter performed better. It would not be hard to replace nlm() with optim() in sem(), if you wish to do it. Regards, John -Original Message- From: Solomon Messing [mailto:mess...@stanford.edu] Sent: July-27-09 8:01 PM To: 'John Fox' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear John, Would it possible to use a different optimizer with the sem package? Perhaps optim(..., method = c(Nelder-Mead, BFGS, CG, L-BFGS-B, SANN),...) for example? Thank you very much, -Solomon -Original Message- From: John Fox [mailto:j...@mcmaster.ca] Sent: Friday, May 22, 2009 6:25 AM To: 'S. Messing' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear Solomon, -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of S. Messing Sent: May-22-09 1:27 AM To: r-help@r-project.org Subject: [R] Confirmatory factor analysis problems using sem package (works in Amos) Hello all, I'm trying to replicate a confirmatory factor analysis done in Amos. Occasionally in an ill-conditioned problem, one program will produce a solution and another won't. As a general matter, I'd expect Amos to be more robust than sem() since Amos is written specifically for SEMs, while sem() uses nlm(), a general-purpose optimizer. The idea is to compare a one-factor and a two-factor model. I get the following warning message when I run either model: Could not compute QR decomposition of Hessian. Optimization probably did not converge. I have no idea what to do here. A general strategy is to set debug=TRUE in the call to sem() and see what happens in the optimization. Then there are several things that you can do to try to get the optimization to converge; see ?sem. In this case, however, I wasn't able to get a solution. The one-factor model is equivalent to a one-factor exploratory FA, which can be fit by ML using factanal(): factanal(factors=1, covmat=correl, n.obs=1100) Call: factanal(factors = 1, covmat = correl, n.obs = 1100) Uniquenesses: pvote jmposaff jmnegaff boposaff bonegaff obama.therm mccain.thermoddcand.D evencand.D 0.1000.4960.4970.2770.397 0.1290.3120.4660.585 Loadings: Factor1 pvote-0.949 jmposaff 0.710 jmnegaff -0.709 boposaff -0.850 bonegaff 0.777 obama.therm -0.934 mccain.therm 0.830 oddcand.D 0.731 evencand.D0.645 Factor1 SS loadings 5.744 Proportion Var 0.638 Test of the hypothesis that 1 factor is sufficient. The chi square statistic is 1710.03 on 27 degrees of freedom. The p-value is 0 As you can see, the one-factor model fits the data very poorly (as does a two-factor EFA); I suspect, but am not sure, that this is the source of the problem in sem(). I couldn't get a solution from sem() even when I used the factanal() solution as start values. I believe posters reported the same problem. In almost all cases, the models haven't been properly specified, which is not the case here. Here, the model just doesn't fit the data. It seems that the ability to invert the correlation matrix may have something to do with this error, but solve(correl) yields a solution. No, the input correlation matrix is positive-definite. sem() would have complained if it were not: eigen(correl, only.values=TRUE) $values [1] 6.12561630 0.82418329 0.71616585 0.51263750 0.24467315 0.18248909 0.17024374 [8] 0.13905585 0.08493524 I'll keep your problem as a test case to see whether I can produce a solution, possibly using a different optimizer -- as I mentioned, sem() uses nlm(). Regards, John Here are my correlation matrix and model specifications: --- R CODE BEGIN
Re: [R] Confirmatory factor analysis problems using sem package (works in Amos)
Dear Solomon, You should get a copy of the source package from CRAN. nlm() [not currently optim()] is called in sem:::sem.default. Regards, John -Original Message- From: Solomon Messing [mailto:mess...@stanford.edu] Sent: July-28-09 2:38 PM To: 'John Fox' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Thanks John. Can I ask under what function you call optim/nlm? I cannot see how this is done by examining sem. Thanks, -Solomon -Original Message- From: John Fox [mailto:j...@mcmaster.ca] Sent: Monday, July 27, 2009 6:23 PM To: 'Solomon Messing' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear Solomon, When I originally programmed the sem() function, I used optim() and experimented with the different methods provided, settling on BFGS as the default. Shortly after that, I compared optim() to nlm() for a range of problems and found that the latter performed better. It would not be hard to replace nlm() with optim() in sem(), if you wish to do it. Regards, John -Original Message- From: Solomon Messing [mailto:mess...@stanford.edu] Sent: July-27-09 8:01 PM To: 'John Fox' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear John, Would it possible to use a different optimizer with the sem package? Perhaps optim(..., method = c(Nelder-Mead, BFGS, CG, L-BFGS-B, SANN),...) for example? Thank you very much, -Solomon -Original Message- From: John Fox [mailto:j...@mcmaster.ca] Sent: Friday, May 22, 2009 6:25 AM To: 'S. Messing' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear Solomon, -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of S. Messing Sent: May-22-09 1:27 AM To: r-help@r-project.org Subject: [R] Confirmatory factor analysis problems using sem package (works in Amos) Hello all, I'm trying to replicate a confirmatory factor analysis done in Amos. Occasionally in an ill-conditioned problem, one program will produce a solution and another won't. As a general matter, I'd expect Amos to be more robust than sem() since Amos is written specifically for SEMs, while sem() uses nlm(), a general-purpose optimizer. The idea is to compare a one-factor and a two-factor model. I get the following warning message when I run either model: Could not compute QR decomposition of Hessian. Optimization probably did not converge. I have no idea what to do here. A general strategy is to set debug=TRUE in the call to sem() and see what happens in the optimization. Then there are several things that you can do to try to get the optimization to converge; see ?sem. In this case, however, I wasn't able to get a solution. The one-factor model is equivalent to a one-factor exploratory FA, which can be fit by ML using factanal(): factanal(factors=1, covmat=correl, n.obs=1100) Call: factanal(factors = 1, covmat = correl, n.obs = 1100) Uniquenesses: pvote jmposaff jmnegaff boposaff bonegaff obama.therm mccain.thermoddcand.D evencand.D 0.1000.4960.4970.2770.397 0.1290.3120.4660.585 Loadings: Factor1 pvote-0.949 jmposaff 0.710 jmnegaff -0.709 boposaff -0.850 bonegaff 0.777 obama.therm -0.934 mccain.therm 0.830 oddcand.D 0.731 evencand.D0.645 Factor1 SS loadings 5.744 Proportion Var 0.638 Test of the hypothesis that 1 factor is sufficient. The chi square statistic is 1710.03 on 27 degrees of freedom. The p-value is 0 As you can see, the one-factor model fits the data very poorly (as does a two-factor EFA); I suspect, but am not sure, that this is the source of the problem in sem(). I couldn't get a solution from sem() even when I used the factanal() solution as start values. I believe posters reported the same problem. In almost all cases, the models haven't been properly specified, which is not the case here. Here, the model just doesn't fit the data. It seems that the ability to invert the correlation matrix may have something to do with this error, but solve(correl) yields a solution. No, the input correlation matrix is positive-definite. sem() would have
Re: [R] Confirmatory factor analysis problems using sem package (works in Amos)
Dear John, Would it possible to use a different optimizer with the sem package? Perhaps optim(..., method = c(Nelder-Mead, BFGS, CG, L-BFGS-B, SANN),...) for example? Thank you very much, -Solomon -Original Message- From: John Fox [mailto:j...@mcmaster.ca] Sent: Friday, May 22, 2009 6:25 AM To: 'S. Messing' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear Solomon, -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of S. Messing Sent: May-22-09 1:27 AM To: r-help@r-project.org Subject: [R] Confirmatory factor analysis problems using sem package (works in Amos) Hello all, I'm trying to replicate a confirmatory factor analysis done in Amos. Occasionally in an ill-conditioned problem, one program will produce a solution and another won't. As a general matter, I'd expect Amos to be more robust than sem() since Amos is written specifically for SEMs, while sem() uses nlm(), a general-purpose optimizer. The idea is to compare a one-factor and a two-factor model. I get the following warning message when I run either model: Could not compute QR decomposition of Hessian. Optimization probably did not converge. I have no idea what to do here. A general strategy is to set debug=TRUE in the call to sem() and see what happens in the optimization. Then there are several things that you can do to try to get the optimization to converge; see ?sem. In this case, however, I wasn't able to get a solution. The one-factor model is equivalent to a one-factor exploratory FA, which can be fit by ML using factanal(): factanal(factors=1, covmat=correl, n.obs=1100) Call: factanal(factors = 1, covmat = correl, n.obs = 1100) Uniquenesses: pvote jmposaff jmnegaff boposaff bonegaff obama.therm mccain.thermoddcand.D evencand.D 0.1000.4960.4970.2770.397 0.1290.3120.4660.585 Loadings: Factor1 pvote-0.949 jmposaff 0.710 jmnegaff -0.709 boposaff -0.850 bonegaff 0.777 obama.therm -0.934 mccain.therm 0.830 oddcand.D 0.731 evencand.D0.645 Factor1 SS loadings 5.744 Proportion Var 0.638 Test of the hypothesis that 1 factor is sufficient. The chi square statistic is 1710.03 on 27 degrees of freedom. The p-value is 0 As you can see, the one-factor model fits the data very poorly (as does a two-factor EFA); I suspect, but am not sure, that this is the source of the problem in sem(). I couldn't get a solution from sem() even when I used the factanal() solution as start values. I believe posters reported the same problem. In almost all cases, the models haven't been properly specified, which is not the case here. Here, the model just doesn't fit the data. It seems that the ability to invert the correlation matrix may have something to do with this error, but solve(correl) yields a solution. No, the input correlation matrix is positive-definite. sem() would have complained if it were not: eigen(correl, only.values=TRUE) $values [1] 6.12561630 0.82418329 0.71616585 0.51263750 0.24467315 0.18248909 0.17024374 [8] 0.13905585 0.08493524 I'll keep your problem as a test case to see whether I can produce a solution, possibly using a different optimizer -- as I mentioned, sem() uses nlm(). Regards, John Here are my correlation matrix and model specifications: --- R CODE BEGIN library(sem) correl - matrix( c(1.000,-0.6657822,0.6702089,0.7997673,-0.7225454,0.8992372, -0.8026491,-0.6715168,-0.5781565,- 0.6657822,1.000,-0.5107568, -0.5030886,0.6971188,- 0.6306937,0.7200848,0.5121227,0.4496810, 0.6702089,-0.5107568,1.000,0.7276558,- 0.3893792,0.6043672, -0.7176532,-0.5247434,-0.4670362,0.7997673,- 0.5030886,0.7276558, 1.000,-0.6251056,0.8164190,-0.6728515,- 0.6371453,-0.5531964, -0.7225454,0.6971188,-0.3893792,- 0.6251056,1.000,-0.7760765, 0.6175124,0.5567924,0.4914176,0.8992372,- 0.6306937,0.6043672, 0.8164190,-0.7760765,1.000,-0.7315507,- 0.6625136,-0.5814590, -0.8026491,0.7200848,-0.7176532,- 0.6728515,0.6175124,-0.7315507, 1.000,0.5910688,0.5096898,-0.6715168,0.5121227,- 0.5247434, -0.6371453,0.5567924,- 0.6625136,0.5910688,1.000,0.8106496, -0.5781565,0.4496810,-0.4670362,- 0.5531964,0.4914176,-0.5814590
Re: [R] Confirmatory factor analysis problems using sem package (works in Amos)
Dear Solomon, When I originally programmed the sem() function, I used optim() and experimented with the different methods provided, settling on BFGS as the default. Shortly after that, I compared optim() to nlm() for a range of problems and found that the latter performed better. It would not be hard to replace nlm() with optim() in sem(), if you wish to do it. Regards, John -Original Message- From: Solomon Messing [mailto:mess...@stanford.edu] Sent: July-27-09 8:01 PM To: 'John Fox' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear John, Would it possible to use a different optimizer with the sem package? Perhaps optim(..., method = c(Nelder-Mead, BFGS, CG, L-BFGS-B, SANN),...) for example? Thank you very much, -Solomon -Original Message- From: John Fox [mailto:j...@mcmaster.ca] Sent: Friday, May 22, 2009 6:25 AM To: 'S. Messing' Cc: r-help@r-project.org Subject: RE: [R] Confirmatory factor analysis problems using sem package (works in Amos) Dear Solomon, -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of S. Messing Sent: May-22-09 1:27 AM To: r-help@r-project.org Subject: [R] Confirmatory factor analysis problems using sem package (works in Amos) Hello all, I'm trying to replicate a confirmatory factor analysis done in Amos. Occasionally in an ill-conditioned problem, one program will produce a solution and another won't. As a general matter, I'd expect Amos to be more robust than sem() since Amos is written specifically for SEMs, while sem() uses nlm(), a general-purpose optimizer. The idea is to compare a one-factor and a two-factor model. I get the following warning message when I run either model: Could not compute QR decomposition of Hessian. Optimization probably did not converge. I have no idea what to do here. A general strategy is to set debug=TRUE in the call to sem() and see what happens in the optimization. Then there are several things that you can do to try to get the optimization to converge; see ?sem. In this case, however, I wasn't able to get a solution. The one-factor model is equivalent to a one-factor exploratory FA, which can be fit by ML using factanal(): factanal(factors=1, covmat=correl, n.obs=1100) Call: factanal(factors = 1, covmat = correl, n.obs = 1100) Uniquenesses: pvote jmposaff jmnegaff boposaff bonegaff obama.therm mccain.thermoddcand.D evencand.D 0.1000.4960.4970.2770.397 0.1290.3120.4660.585 Loadings: Factor1 pvote-0.949 jmposaff 0.710 jmnegaff -0.709 boposaff -0.850 bonegaff 0.777 obama.therm -0.934 mccain.therm 0.830 oddcand.D 0.731 evencand.D0.645 Factor1 SS loadings 5.744 Proportion Var 0.638 Test of the hypothesis that 1 factor is sufficient. The chi square statistic is 1710.03 on 27 degrees of freedom. The p-value is 0 As you can see, the one-factor model fits the data very poorly (as does a two-factor EFA); I suspect, but am not sure, that this is the source of the problem in sem(). I couldn't get a solution from sem() even when I used the factanal() solution as start values. I believe posters reported the same problem. In almost all cases, the models haven't been properly specified, which is not the case here. Here, the model just doesn't fit the data. It seems that the ability to invert the correlation matrix may have something to do with this error, but solve(correl) yields a solution. No, the input correlation matrix is positive-definite. sem() would have complained if it were not: eigen(correl, only.values=TRUE) $values [1] 6.12561630 0.82418329 0.71616585 0.51263750 0.24467315 0.18248909 0.17024374 [8] 0.13905585 0.08493524 I'll keep your problem as a test case to see whether I can produce a solution, possibly using a different optimizer -- as I mentioned, sem() uses nlm(). Regards, John Here are my correlation matrix and model specifications: --- R CODE BEGIN library(sem) correl - matrix( c(1.000,-0.6657822,0.6702089,0.7997673,-0.7225454,0.8992372, -0.8026491,-0.6715168,-0.5781565,- 0.6657822,1.000,-0.5107568, -0.5030886,0.6971188,- 0.6306937,0.7200848,0.5121227,0.4496810, 0.6702089,-0.5107568,1.000,0.7276558,- 0.3893792,0.6043672, -0.7176532,-0.5247434,-0.4670362,0.7997673,- 0.5030886,0.7276558
[R] Confirmatory factor analysis problems using sem package (works in Amos)
Hello all, I'm trying to replicate a confirmatory factor analysis done in Amos. The idea is to compare a one-factor and a two-factor model. I get the following warning message when I run either model: Could not compute QR decomposition of Hessian. Optimization probably did not converge. I have no idea what to do here. I believe posters reported the same problem. It seems that the ability to invert the correlation matrix may have something to do with this error, but solve(correl) yields a solution. Here are my correlation matrix and model specifications: --- R CODE BEGIN correl - matrix( c(1.000,-0.6657822,0.6702089,0.7997673,-0.7225454,0.8992372, -0.8026491,-0.6715168,-0.5781565,-0.6657822,1.000,-0.5107568, -0.5030886,0.6971188,-0.6306937,0.7200848,0.5121227,0.4496810, 0.6702089,-0.5107568,1.000,0.7276558,-0.3893792,0.6043672, -0.7176532,-0.5247434,-0.4670362,0.7997673,-0.5030886,0.7276558, 1.000,-0.6251056,0.8164190,-0.6728515,-0.6371453,-0.5531964, -0.7225454,0.6971188,-0.3893792,-0.6251056,1.000,-0.7760765, 0.6175124,0.5567924,0.4914176,0.8992372,-0.6306937,0.6043672, 0.8164190,-0.7760765,1.000,-0.7315507,-0.6625136,-0.5814590, -0.8026491,0.7200848,-0.7176532,-0.6728515,0.6175124,-0.7315507, 1.000,0.5910688,0.5096898,-0.6715168,0.5121227,-0.5247434, -0.6371453,0.5567924,-0.6625136,0.5910688,1.000,0.8106496, -0.5781565,0.4496810,-0.4670362,-0.5531964,0.4914176,-0.5814590, 0.5096898,0.8106496,1.000), ,nrow=9,ncol=9) rownames(correl) = c(pvote, jmposaff, jmnegaff, boposaff,bonegaff, obama.therm, mccain.therm, oddcand.D, evencand.D ) colnames(correl) = c(pvote, jmposaff, jmnegaff, boposaff,bonegaff, obama.therm, mccain.therm, oddcand.D, evencand.D ) #One Factor Model: model.all - specify.model() allmeasures - pvote, b1, NA allmeasures - obama.therm, b2, NA allmeasures - mccain.therm,b3, NA allmeasures - jmposaff,b4, NA allmeasures - jmnegaff,b5, NA allmeasures - boposaff,b6, NA allmeasures - bonegaff,b7, NA allmeasures - oddcand.D, b8, NA allmeasures - evencand.D, b9, NA allmeasures - allmeasures,NA,1 pvote - pvote,v1, NA obama.therm - obama.therm,v2, NA mccain.therm - mccain.therm, v3, NA jmposaff - jmposaff, v4, NA jmnegaff - jmnegaff, v5, NA boposaff - boposaff, v6, NA bonegaff - bonegaff, v7, NA oddcand.D - oddcand.D,v8, NA evencand.D - evencand.D, v9, NA sem.all - sem(model.all, correl, 1100) summary(sem.all) #Two Factor Model: model.vi - specify.model() verbal - pvote,b1, NA verbal - obama.therm, b2, NA verbal - mccain.therm, b3, NA verbal - jmposaff, b4, NA verbal - jmnegaff, b5, NA verbal - boposaff, b6, NA verbal - bonegaff, b7, NA imp - oddcand.D, b8, NA imp - evencand.D, b9, NA imp - imp,NA, 1 verbal - verbal, NA, 1 pvote - pvote,v1, NA obama.therm - obama.therm,v2, NA mccain.therm - mccain.therm, v3, NA jmposaff - jmposaff, v4, NA jmnegaff - jmnegaff, v5, NA boposaff - boposaff, v6, NA bonegaff - bonegaff, v7, NA oddcand.D - oddcand.D,v8, NA evencand.D - evencand.D, v9, NA imp - verbal, civ, NA sem.vi - sem(model.vi, correl, 1100) summary(sem.vi) --- R CODE END Thanks very much. -Solomon -- View this message in context: http://www.nabble.com/Confirmatory-factor-analysis-problems-using-sem-package-%28works-in-Amos%29-tp23664618p23664618.html Sent
Re: [R] Confirmatory factor analysis problems using sem package (works in Amos)
Dear Solomon, -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of S. Messing Sent: May-22-09 1:27 AM To: r-help@r-project.org Subject: [R] Confirmatory factor analysis problems using sem package (works in Amos) Hello all, I'm trying to replicate a confirmatory factor analysis done in Amos. Occasionally in an ill-conditioned problem, one program will produce a solution and another won't. As a general matter, I'd expect Amos to be more robust than sem() since Amos is written specifically for SEMs, while sem() uses nlm(), a general-purpose optimizer. The idea is to compare a one-factor and a two-factor model. I get the following warning message when I run either model: Could not compute QR decomposition of Hessian. Optimization probably did not converge. I have no idea what to do here. A general strategy is to set debug=TRUE in the call to sem() and see what happens in the optimization. Then there are several things that you can do to try to get the optimization to converge; see ?sem. In this case, however, I wasn't able to get a solution. The one-factor model is equivalent to a one-factor exploratory FA, which can be fit by ML using factanal(): factanal(factors=1, covmat=correl, n.obs=1100) Call: factanal(factors = 1, covmat = correl, n.obs = 1100) Uniquenesses: pvote jmposaff jmnegaff boposaff bonegaff obama.therm mccain.thermoddcand.D evencand.D 0.1000.4960.4970.2770.397 0.1290.3120.4660.585 Loadings: Factor1 pvote-0.949 jmposaff 0.710 jmnegaff -0.709 boposaff -0.850 bonegaff 0.777 obama.therm -0.934 mccain.therm 0.830 oddcand.D 0.731 evencand.D0.645 Factor1 SS loadings 5.744 Proportion Var 0.638 Test of the hypothesis that 1 factor is sufficient. The chi square statistic is 1710.03 on 27 degrees of freedom. The p-value is 0 As you can see, the one-factor model fits the data very poorly (as does a two-factor EFA); I suspect, but am not sure, that this is the source of the problem in sem(). I couldn't get a solution from sem() even when I used the factanal() solution as start values. I believe posters reported the same problem. In almost all cases, the models haven't been properly specified, which is not the case here. Here, the model just doesn't fit the data. It seems that the ability to invert the correlation matrix may have something to do with this error, but solve(correl) yields a solution. No, the input correlation matrix is positive-definite. sem() would have complained if it were not: eigen(correl, only.values=TRUE) $values [1] 6.12561630 0.82418329 0.71616585 0.51263750 0.24467315 0.18248909 0.17024374 [8] 0.13905585 0.08493524 I'll keep your problem as a test case to see whether I can produce a solution, possibly using a different optimizer -- as I mentioned, sem() uses nlm(). Regards, John Here are my correlation matrix and model specifications: --- R CODE BEGIN library(sem) correl - matrix( c(1.000,-0.6657822,0.6702089,0.7997673,-0.7225454,0.8992372, -0.8026491,-0.6715168,-0.5781565,- 0.6657822,1.000,-0.5107568, -0.5030886,0.6971188,- 0.6306937,0.7200848,0.5121227,0.4496810, 0.6702089,-0.5107568,1.000,0.7276558,- 0.3893792,0.6043672, -0.7176532,-0.5247434,-0.4670362,0.7997673,- 0.5030886,0.7276558, 1.000,-0.6251056,0.8164190,-0.6728515,- 0.6371453,-0.5531964, -0.7225454,0.6971188,-0.3893792,- 0.6251056,1.000,-0.7760765, 0.6175124,0.5567924,0.4914176,0.8992372,- 0.6306937,0.6043672, 0.8164190,-0.7760765,1.000,-0.7315507,- 0.6625136,-0.5814590, -0.8026491,0.7200848,-0.7176532,- 0.6728515,0.6175124,-0.7315507, 1.000,0.5910688,0.5096898,-0.6715168,0.5121227,- 0.5247434, -0.6371453,0.5567924,- 0.6625136,0.5910688,1.000,0.8106496, -0.5781565,0.4496810,-0.4670362,- 0.5531964,0.4914176,-0.5814590, 0.5096898,0.8106496,1.000), ,nrow=9,ncol=9) rownames(correl) = c(pvote, jmposaff, jmnegaff, boposaff,bonegaff, obama.therm, mccain.therm, oddcand.D, evencand.D ) colnames(correl) = c(pvote, jmposaff, jmnegaff, boposaff,bonegaff, obama.therm, mccain.therm, oddcand.D, evencand.D ) #One Factor Model: model.all - specify.model() allmeasures - pvote, b1, NA allmeasures - obama.therm
