[R] Confirmatory factor analysis using the sem package. TLI CFI and RMSEA absent from model summary.
John Fox
jfox at mcmaster.ca
Mon Mar 18 18:56:51 CET 2013
Dear Kevin,
In earlier versions of the sem package, the summary() method for model objects produced many (and from version to version, an increasing number of) fit indices by default. For various reasons, I decided to provide only the LR chisquare test for the model, the BIC, and the AIC by default, and to leave it up the user to decide what fit indices to show. This can be controlled with the fit.indices option as well as the fit.indices argument to the summary() method.
Best,
John
On Mon, 18 Mar 2013 16:46:03 +0000
Kevin Cheung <K.Cheung at derby.ac.uk> wrote:
> Dear John,
>
> Thank you for taking the time to help me with this, I have been able to obtain fit indices using the information that you provided.
>
> Note to users searching archived R-help posts about this issue: The instructional video I looked at (http://vimeo.com/38941937) gave fit indices using the default summary() command without any additional arguments. This may have been due to a different version of R (I noticed that the instructor was using a mac based OS).
>
> With regards,
> Kevin
>
> Kevin Yet Fong Cheung, Bsc., MRes., MBPsS.
> Postgraduate Researcher
> Centre for Psychological Research
> University of Derby
> Kedleston Road
> Derby DE22 1GB
> k.cheung at derby.ac.uk<mailto:k.cheung at derby.ac.uk>
> 01332592081
>
> http://derby.academia.edu/KevinCheung
>
>
> -----Original Message-----
> From: John Fox [mailto:jfox at mcmaster.ca]
> Sent: 18 March 2013 15:55
> To: Kevin Cheung
> Cc: r-help at r-project.org
> Subject: Re: [R] Confirmatory factor analysis using the sem package. TLI CFI and RMSEA absent from model summary.
>
> Dear Kevin,
>
> See ?summary.objectiveML, and in particular the description of the fit.indices argument. By default, the summary() method doesn't print many fit indices, but many are available optionally.
>
> I hope this helps,
> John
>
> ------------------------------------------------
> John Fox
> Sen. William McMaster Prof. of Social Statistics Department of Sociology McMaster University Hamilton, Ontario, Canada http://socserv.mcmaster.ca/jfox/
>
> On Mon, 18 Mar 2013 15:00:06 +0000
> Kevin Cheung <K.Cheung at derby.ac.uk> wrote:
> > Hi R-help,
> >
> > I am using the sem package to run confirmatory factor analysis (cfa) on some questionnaire data collected from 307 participants. I have been running R-2.15.3 in Windows in conjunction with R studio. The model I am using was developed from exploratory factor analysis of a separate dataset (n=439); it includes 18 items that load onto 3 factors. I have used the sem package documentation and this video (http://vimeo.com/38941937) to run the cfa and obtain a chi-square statistic for the model. However, when I use the summary() function, the model does not provide indices of fit; I need these as part of my analysis output. In particular, I am looking for the Tucker Lewis Index (TLI), Comparative Fit Index (CFI), & the Root Mean Square of Approximation (RMSEA). I have checked the documentation and cannot seem to find any reason for this; none of the arguments listed with the sem command indicate that I have to specify these as part of the output. In addition, the analysis examp!
le!
> f!
> > rom the video includes these indices as part of the output, but my analysis does not provide them. I have included my code with comments below:
> >
> > ________________________________________
> >
> > library(sem)
> >
> > validation.data <-
> > structure(list(V1 = c(5L, 4L, 2L, 4L, 5L, 6L, 6L, 4L, 5L, 3L, 6L, 5L,
> > 4L, 5L, 3L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 4L, 5L, 4L, 4L,
> > 5L, 4L, 4L, 5L, 5L, 5L, 5L, 2L, 6L, 5L, 6L, 4L, 5L, 6L, 5L, 5L, 4L,
> > 5L, 5L, 3L, 5L, 5L, 5L, 5L, 4L, 2L, 5L, 5L, 5L, 4L, 6L, 4L, 6L, 5L,
> > 5L, 5L, 4L, 5L, 5L, 4L, 5L, 6L, 4L, 5L, 4L, 5L, 5L, 5L, 3L, 5L, 5L,
> > 3L, 5L, 4L, 5L, 2L, 6L, 4L, 4L, 4L, 5L, 5L, 4L, 6L, 2L, 4L, 5L, 4L,
> > 5L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 2L, 4L, 4L, 5L, 5L, 4L,
> > 4L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 5L, 6L, 5L, 5L, 4L,
> > 4L, 5L, 4L, 4L, 5L, 4L, 4L, 4L, 5L, 5L, 6L, 5L, 5L, 5L, 4L, 4L, 3L,
> > 4L, 5L, 5L, 5L, 2L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 6L, 4L, 5L, 5L,
> > 6L, 5L, 5L, 5L, 5L, 4L, 5L, 4L, 5L, 5L, 4L, 4L, 4L, 4L, 5L, 2L, 4L,
> > 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 4L, 4L, 5L, 4L, 5L, 5L, 4L, 5L, 5L,
> > 4L, 4L, 5L, 5L, 5L, 5L, 4L, 4L, 2L, 6L, 5L, 5L, 5L, 6L, 4L, 3L, 5L,
> > 5L, 5L, 5L, 4L, 4L, 6L, 6L, 5L, 5L, 5L, 3L, 6L, 5L, 5L, 5L, 4L, 5L,
> > 5L, 4L, 5L, 4L, 6L, 5L, 4L, 4L, 5L, 4L, 3L, 4L, 5L, 4L, 5L, 6L, 2L,
> > 4L, 4L, 5L, 4L, 4L, 4L, 5L, 6L, 5L, 4L, 4L, 4L, 6L, 6L, 4L, 5L, 5L,
> > 5L, 2L, 4L, 4L, 5L, 4L, 5L, 5L, 4L, 5L, 3L, 5L, 6L, 5L, 4L, 4L, 3L,
> > 3L, 4L, 5L, 5L, 1L, 4L, 5L, 3L, 5L, 1L, 6L, 5L, 4L, 4L, 5L, 5L, 4L,
> > 5L, 5L, 6L, 5L, 5L, 5L), V2 = c(5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 5L,
> > 5L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 4L, 5L, 6L, 6L, 6L,
> > 6L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 6L,
> > 6L, 6L, 6L, 6L, 5L, 5L, 6L, 5L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L,
> > 4L, 6L, 5L, 6L, 5L, 5L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 6L, 5L,
> > 6L, 6L, 6L, 6L, 6L, 5L, 6L, 5L, 6L, 6L, 5L, 6L, 6L, 5L, 4L, 6L, 5L,
> > 6L, 5L, 5L, 6L, 5L, 6L, 6L, 5L, 6L, 6L, 6L, 5L, 5L, 6L, 6L, 5L, 4L,
> > 6L, 4L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 5L, 5L, 6L,
> > 6L, 5L, 6L, 5L, 6L, 6L, 5L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 5L, 6L, 5L,
> > 5L, 5L, 6L, 5L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 4L, 2L,
> > 5L, 6L, 4L, 5L, 5L, 6L, 6L, 5L, 6L, 4L, 6L, 5L, 5L, 6L, 5L, 6L, 6L,
> > 5L, 6L, 5L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 5L, 6L, 5L, 6L,
> > 6L, 5L, 6L, 5L, 6L, 5L, 6L, 6L, 5L, 5L, 6L, 6L, 6L, 5L, 5L, 6L, 6L,
> > 6L, 6L, 5L, 5L, 6L, 6L, 6L, 6L, 4L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
> > 6L, 5L, 6L, 6L, 3L, 5L, 6L, 6L, 6L, 5L, 6L, 5L, 5L, 6L, 6L, 6L, 5L,
> > 6L, 6L, 6L, 6L, 6L, 5L, 6L, 5L, 6L, 6L, 6L, 6L, 5L, 5L, 6L, 6L, 6L,
> > 6L, 6L, 5L, 5L, 6L, 4L, 5L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
> > 5L, 6L, 6L, 5L, 5L, 6L, 5L, 5L, 6L, 5L, 5L, 6L, 5L, 5L, 6L, 6L, 6L,
> > 6L, 6L, 6L, 5L, 6L, 6L, 5L, 6L, 6L), V3 = c(5L, 5L, 3L, 6L, 5L, 2L,
> > 4L, 4L, 4L, 4L, 6L, 5L, 5L, 4L, 4L, 4L, 4L, 5L, 4L, 4L, 1L, 3L, 4L,
> > 5L, 5L, 4L, 4L, 5L, 5L, 5L, 4L, 5L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
> > 5L, 4L, 1L, 5L, 5L, 4L, 5L, 4L, 5L, 5L, 4L, 5L, 4L, 3L, 2L, 5L, 6L,
> > 6L, 5L, 5L, 5L, 6L, 5L, 6L, 5L, 4L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 5L,
> > 3L, 5L, 4L, 5L, 5L, 5L, 3L, 5L, 5L, 5L, 3L, 5L, 4L, 5L, 4L, 5L, 4L,
> > 3L, 5L, 3L, 5L, 3L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
> > 5L, 5L, 5L, 5L, 2L, 5L, 4L, 5L, 4L, 6L, 4L, 5L, 5L, 4L, 5L, 4L, 5L,
> > 5L, 4L, 6L, 5L, 5L, 5L, 5L, 4L, 5L, 4L, 5L, 4L, 4L, 5L, 5L, 4L, 6L,
> > 4L, 6L, 5L, 4L, 4L, 5L, 5L, 5L, 4L, 4L, 1L, 5L, 4L, 4L, 5L, 5L, 4L,
> > 6L, 3L, 4L, 4L, 5L, 4L, 4L, 5L, 3L, 5L, 6L, 5L, 4L, 4L, 5L, 5L, 5L,
> > 5L, 3L, 5L, 4L, 6L, 5L, 4L, 6L, 3L, 4L, 2L, 4L, 4L, 5L, 4L, 4L, 5L,
> > 3L, 4L, 5L, 5L, 4L, 3L, 3L, 5L, 5L, 5L, 5L, 4L, 3L, 4L, 2L, 5L, 5L,
> > 6L, 4L, 5L, 4L, 4L, 5L, 4L, 6L, 6L, 4L, 4L, 4L, 5L, 5L, 6L, 5L, 4L,
> > 6L, 5L, 5L, 5L, 4L, 6L, 6L, 3L, 2L, 3L, 6L, 4L, 5L, 3L, 6L, 3L, 4L,
> > 4L, 5L, 4L, 6L, 4L, 5L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 4L, 5L,
> > 5L, 6L, 5L, 4L, 4L, 5L, 5L, 5L, 5L, 4L, 3L, 5L, 5L, 4L, 5L, 5L, 5L,
> > 5L, 6L, 5L, 4L, 4L, 3L, 4L, 5L, 5L, 4L, 1L, 6L, 4L, 4L, 4L, 2L, 6L,
> > 5L, 4L, 5L, 5L, 5L, 5L, 5L, 4L, 6L, 5L, 5L, 6L), V4 = c(5L, 3L, 4L,
> > 6L, 5L, 4L, 6L, 4L, 4L, 3L, 5L, 4L, 4L, 4L, 6L, 3L, 5L, 5L, 5L, 5L,
> > 2L, 4L, 5L, 5L, 5L, 4L, 6L, 5L, 4L, 5L, 4L, 6L, 5L, 5L, 4L, 5L, 5L,
> > 5L, 5L, 6L, 5L, 5L, 3L, 4L, 5L, 3L, 4L, 5L, 4L, 5L, 4L, 4L, 3L, 3L,
> > 3L, 5L, 5L, 6L, 4L, 5L, 5L, 6L, 5L, 4L, 5L, 4L, 4L, 5L, 4L, 5L, 5L,
> > 5L, 5L, 5L, 3L, 5L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 4L, 5L, 5L, 6L,
> > 5L, 5L, 4L, 5L, 5L, 5L, 4L, 4L, 4L, 6L, 5L, 5L, 5L, 6L, 4L, 5L, 5L,
> > 5L, 4L, 6L, 5L, 5L, 4L, 6L, 2L, 5L, 6L, 4L, 5L, 6L, 5L, 4L, 5L, 4L,
> > 5L, 4L, 5L, 5L, 6L, 6L, 4L, 4L, 5L, 4L, 4L, 5L, 4L, 6L, 4L, 4L, 5L,
> > 5L, 4L, 5L, 5L, 5L, 4L, 4L, 5L, 5L, 5L, 5L, 4L, 5L, 2L, 5L, 5L, 6L,
> > 5L, 2L, 3L, 6L, 4L, 1L, 4L, 5L, 4L, 5L, 5L, 3L, 4L, 5L, 5L, 4L, 4L,
> > 4L, 4L, 5L, 4L, 4L, 5L, 4L, 4L, 5L, 4L, 6L, 5L, 5L, 1L, 4L, 4L, 5L,
> > 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 4L, 3L, 5L, 5L, 5L, 5L, 4L, 3L, 5L,
> > 3L, 6L, 5L, 5L, 5L, 5L, 5L, 4L, 5L, 4L, 6L, 5L, 4L, 4L, 4L, 6L, 5L,
> > 5L, 4L, 4L, 6L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 3L, 4L, 6L, 5L, 5L, 5L,
> > 5L, 4L, 6L, 5L, 5L, 5L, 5L, 4L, 6L, 4L, 5L, 5L, 5L, 5L, 4L, 4L, 6L,
> > 5L, 4L, 5L, 5L, 6L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 6L, 5L, 5L,
> > 5L, 5L, 5L, 5L, 5L, 4L, 6L, 4L, 4L, 5L, 5L, 5L, 5L, 1L, 6L, 4L, 2L,
> > 5L, 5L, 5L, 5L, 4L, 4L, 5L, 5L, 5L, 6L, 5L, 5L, 5L, 4L, 6L), V5 =
> > c(6L, 6L, 5L, 6L, 6L, 6L, 6L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 5L,
> > 5L, 5L, 6L, 6L, 5L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 5L,
> > 5L, 6L, 6L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 4L, 5L, 6L, 5L, 5L, 6L, 5L,
> > 6L, 5L, 4L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 5L, 6L, 5L, 6L, 6L,
> > 5L, 5L, 6L, 5L, 5L, 6L, 5L, 6L, 5L, 6L, 5L, 6L, 5L, 6L, 5L, 6L, 5L,
> > 5L, 5L, 6L, 6L, 5L, 6L, 5L, 6L, 5L, 5L, 4L, 5L, 6L, 5L, 5L, 6L, 6L,
> > 5L, 5L, 6L, 6L, 5L, 6L, 5L, 5L, 5L, 6L, 5L, 5L, 6L, 6L, 6L, 6L, 6L,
> > 5L, 5L, 5L, 6L, 6L, 5L, 5L, 5L, 6L, 6L, 5L, 6L, 5L, 5L, 5L, 5L, 6L,
> > 6L, 5L, 6L, 6L, 6L, 6L, 5L, 6L, 5L, 5L, 5L, 6L, 6L, 4L, 5L, 6L, 5L,
> > 6L, 6L, 6L, 6L, 3L, 6L, 6L, 6L, 4L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 5L,
> > 5L, 5L, 6L, 5L, 5L, 6L, 5L, 5L, 6L, 5L, 6L, 4L, 6L, 6L, 6L, 6L, 5L,
> > 6L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 5L, 5L, 6L, 5L, 5L, 6L, 6L,
> > 5L, 5L, 6L, 5L, 5L, 6L, 6L, 6L, 5L, 5L, 5L, 5L, 3L, 6L, 5L, 6L, 6L,
> > 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 5L, 5L, 6L, 6L, 5L, 4L, 4L, 6L,
> > 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 6L, 5L,
> > 6L, 5L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 5L, 6L, 5L, 5L, 6L, 4L, 6L, 6L,
> > 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 1L,
> > 6L, 5L, 5L, 6L, 4L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
> > 6L), V6 = c(6L, 6L, 5L, 6L, 6L, 5L, 6L, 4L, 5L, 5L, 6L, 6L, 6L, 6L,
> > 6L, 6L, 5L, 6L, 5L, 6L, 6L, 2L, 4L, 5L, 5L, 5L, 4L, 5L, 5L, 6L, 5L,
> > 6L, 4L, 4L, 5L, 6L, 5L, 4L, 5L, 5L, 6L, 6L, 6L, 6L, 5L, 4L, 6L, 5L,
> > 5L, 5L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 5L, 6L, 5L, 6L, 6L,
> > 6L, 6L, 4L, 5L, 6L, 6L, 3L, 6L, 6L, 5L, 5L, 4L, 6L, 5L, 5L, 5L, 3L,
> > 4L, 5L, 5L, 5L, 2L, 5L, 5L, 4L, 5L, 6L, 3L, 6L, 4L, 4L, 5L, 5L, 3L,
> > 6L, 6L, 5L, 5L, 5L, 6L, 5L, 4L, 3L, 6L, 5L, 4L, 6L, 5L, 6L, 5L, 5L,
> > 4L, 6L, 4L, 6L, 5L, 4L, 5L, 5L, 5L, 6L, 6L, 6L, 5L, 6L, 5L, 4L, 4L,
> > 5L, 3L, 5L, 6L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 4L, 4L,
> > 5L, 6L, 2L, 4L, 4L, 6L, 4L, 6L, 6L, 5L, 5L, 4L, 5L, 5L, 6L, 6L, 4L,
> > 5L, 5L, 6L, 5L, 5L, 5L, 6L, 5L, 5L, 6L, 4L, 6L, 5L, 3L, 4L, 6L, 4L,
> > 4L, 5L, 4L, 4L, 5L, 6L, 4L, 3L, 6L, 5L, 5L, 4L, 4L, 5L, 6L, 4L, 5L,
> > 5L, 6L, 6L, 5L, 4L, 5L, 2L, 6L, 6L, 6L, 5L, 5L, 6L, 4L, 5L, 5L, 5L,
> > 6L, 6L, 4L, 3L, 6L, 6L, 6L, 5L, 4L, 6L, 5L, 6L, 5L, 4L, 6L, 6L, 3L,
> > 6L, 3L, 5L, 6L, 4L, 3L, 6L, 6L, 6L, 4L, 6L, 6L, 6L, 5L, 5L, 6L, 6L,
> > 5L, 5L, 4L, 4L, 2L, 6L, 6L, 3L, 4L, 6L, 6L, 6L, 5L, 6L, 5L, 4L, 5L,
> > 4L, 6L, 4L, 4L, 6L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 5L, 3L, 5L, 5L, 5L,
> > 6L, 5L, 1L, 5L, 4L, 5L, 6L, 4L, 5L, 6L, 5L, 5L, 6L, 5L, 5L, 6L, 5L,
> > 6L, 6L, 4L, 6L), V7 = c(4, 1, 1, 5, 3, 2, 6, 3, 3, 2, 6, 3, 3, 5, 5,
> > 1, 3, 3, 3, 5, 6, 1, 2, 3.5, 5, 2, 2, 3, 2, 4, 4, 2, 4, 4, 2, 5, 3, 4,
> > 4, 4, 4, 2, 5, 3, 2, 2, 4, 4, 2, 5, 3, 2, 4, 2, 4, 2, 4, 5, 5, 5, 2,
> > 6, 4, 2, 4, 2, 3, 1, 5, 4, 4, 2, 5, 5, 4, 4, 2, 5, 6, 4, 4, 1, 3, 2,
> > 2, 4, 2, 3, 4, 3, 3, 3, 2, 4, 2, 1, 4, 4, 3, 3, 5, 4, 4, 5, 5, 2, 2,
> > 3, 2, 4, 3, 5, 2, 1, 2, 3, 2, 6, 4, 2, 2, 3, 4, 4, 4, 3, 3, 5, 1, 5,
> > 3, 3, 1, 2, 3, 2, 6, 2, 4, 4, 5, 2, 5, 2, 5, 3, 1, 6, 3, 3, 2, 4, 1,
> > 1, 1, 6, 2, 2, 2, 4, 3, 1, 4, 4, 4, 4, 3, 2, 4, 3, 4, 4, 2, 2, 4, 4,
> > 4, 2, 1, 3, 2, 6, 2, 2.5, 3, 3, 2, 2, 4, 4, 1, 2, 2, 1, 3, 3, 2, 2, 4,
> > 2, 5, 3, 6, 4, 3, 2, 2, 1, 6, 5, 3, 2, 2, 5, 2, 3, 2, 4, 4, 2, 3, 1,
> > 4, 3, 6, 1, 3, 6, 4, 5, 3, 3, 4, 5, 1, 4, 3, 4, 3, 3, 3, 4, 1, 6, 3,
> > 4, 2, 5, 2, 3, 4, 5, 3, 2, 2, 3, 1, 4, 2, 4, 3, 4, 6, 5, 3, 4, 3, 2,
> > 2, 4, 3, 2, 4, 4, 6, 4, 5, 3, 4, 4, 4, 5, 2, 2, 3, 5, 4, 5, 1, 4, 3,
> > 4, 5, 2, 4, 2, 1, 4, 3, 2, 2, 5, 3, 4, 2, 2, 5), V8 = c(5, 5, 6, 6, 5,
> > 6, 6, 6, 5, 5, 6, 6, 5, 6, 6, 5, 6, 5, 6, 6, 5, 5, 5, 6, 6, 5, 6, 5,
> > 6, 6, 6, 6, 6, 5, 5, 6, 6, 4, 2, 6, 6, 4, 6, 6, 5, 6, 6, 5, 5, 5, 5,
> > 6, 6, 5, 6, 6, 5, 6, 6, 6, 5, 6, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6,
> > 5, 6, 6, 6, 6, 6, 5, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 5, 6, 5, 5,
> > 6, 5, 6, 5, 5, 6, 6, 6, 5, 6, 6, 6, 5, 5, 6, 2, 4, 6, 6, 6, 6, 6, 5,
> > 5, 5, 6, 6, 6, 5, 6, 6, 6, 5, 6, 5, 6, 4, 5, 6, 6, 5, 5, 6, 6, 6, 5,
> > 6, 5, 5, 5, 6, 5, 6, 4, 4, 6, 5, 6, 5, 6, 6, 6, 6, 6, 4, 6, 5, 4, 6,
> > 5, 6, 6, 5.5, 5, 5, 4, 5, 4, 6, 5, 5, 5, 5, 6, 4, 6, 4, 6, 6, 6, 4, 6,
> > 6, 6, 6, 5, 6, 5, 6, 5, 4, 5, 6, 6, 6, 6, 6, 5, 4, 5, 6, 5, 5, 5, 4,
> > 4, 5, 6, 5, 1, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 3,
> > 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 5, 6,
> > 5, 6, 5, 6, 6, 6, 6, 6, 6, 5, 6, 5, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 5,
> > 5, 5, 6, 5, 5, 6, 6, 5, 6, 4, 6, 6, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6,
> > 5, 6, 6), V9 = c(5, 4, 2, 6, 4, 6, 6, 4, 5, 2, 6, 5, 4, 5, 4, 5, 5, 5,
> > 6, 5, 6, 4, 3, 5, 5, 4, 5, 4, 6, 5, 4, 5, 5, 5, 5, 5, 2, 6, 5, 6, 5,
> > 5, 6, 5, 2, 4, 6, 5, 3, 5, 5, 5, 6, 4, 3, 5, 6, 5, 4, 6, 5, 6, 5, 5,
> > 4, 4, 5, 5, 5, 6, 6, 6, 4, 4, 4, 5, 5, 4, 4, 5, 3, 6, 5, 5, 3, 5, 4,
> > 5, 4, 4, 5, 4, 6, 5, 4, 5, 4, 4, 5, 5, 5, 5, 6, 5, 5, 5, 5, 4, 2, 5,
> > 4, 6, 5, 4, 4, 4.5, 5, 6, 5, 6, 5, 5, 5, 4, 6, 5, 5, 6, 4, 5, 4, 5, 6,
> > 4, 5, 5, 4, 5, 4, 5, 6, 5, 5, 5, 6, 5, 4, 5, 5, 5, 5, 6, 2, 5, 4, 5,
> > 5, 5, 6, 5, 4, 6, 4, 5, 4, 6, 4, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 3,
> > 5, 3, 4, 4, 4, 5, 5, 4, 4, 5, 6, 5, 4, 5, 4, 5, 4, 4, 5, 6, 4, 5, 4,
> > 6, 5, 5, 4, 5, 2, 5, 5, 5, 6, 5, 4, 4, 5, 5, 5, 5, 4, 5, 6, 6, 5, 5,
> > 5, 4, 5, 5, 5, 5, 4, 6, 6, 3, 5, 5, 6, 5, 4, 3, 4, 5, 3, 4, 5, 5, 5,
> > 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 6, 6, 4, 5, 5, 5, 2, 5, 4,
> > 5, 4, 5, 6, 5, 5, 4, 6, 6, 5, 5, 5, 5, 4, 4, 5, 5, 1, 5, 4, 5, 5, 4,
> > 4, 6, 4, 5, 5, 5, 4, 5, 6, 6, 6, 5, 6), V10 = c(5L, 5L, 3L, 6L, 5L,
> > 6L, 6L, 5L, 5L, 4L, 5L, 6L, 6L, 3L, 4L, 5L, 5L, 6L, 5L, 5L, 6L, 4L,
> > 5L, 6L, 6L, 5L, 5L, 5L, 5L, 6L, 5L, 6L, 6L, 5L, 6L, 5L, 5L, 6L, 5L,
> > 5L, 6L, 5L, 6L, 5L, 4L, 6L, 4L, 4L, 5L, 5L, 6L, 5L, 6L, 5L, 5L, 5L,
> > 6L, 6L, 6L, 6L, 5L, 6L, 6L, 4L, 6L, 5L, 5L, 6L, 4L, 6L, 6L, 4L, 4L,
> > 5L, 5L, 5L, 5L, 5L, 5L, 6L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 4L, 5L, 5L,
> > 5L, 5L, 6L, 5L, 5L, 5L, 4L, 5L, 4L, 6L, 5L, 6L, 6L, 6L, 6L, 5L, 6L,
> > 5L, 6L, 5L, 5L, 6L, 4L, 5L, 5L, 5L, 5L, 6L, 5L, 5L, 5L, 5L, 6L, 6L,
> > 5L, 5L, 6L, 6L, 2L, 6L, 5L, 6L, 5L, 5L, 5L, 6L, 4L, 5L, 6L, 6L, 6L,
> > 6L, 6L, 5L, 6L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 6L, 5L, 6L, 5L, 6L,
> > 5L, 5L, 1L, 4L, 5L, 5L, 5L, 6L, 4L, 2L, 6L, 5L, 5L, 6L, 5L, 5L, 6L,
> > 5L, 5L, 5L, 4L, 4L, 5L, 5L, 5L, 3L, 4L, 5L, 4L, 4L, 6L, 6L, 4L, 5L,
> > 4L, 2L, 5L, 3L, 4L, 5L, 5L, 5L, 5L, 6L, 6L, 5L, 5L, 4L, 5L, 5L, 6L,
> > 5L, 6L, 6L, 5L, 5L, 4L, 5L, 5L, 6L, 6L, 2L, 5L, 4L, 6L, 6L, 6L, 6L,
> > 5L, 6L, 4L, 5L, 5L, 4L, 6L, 6L, 4L, 5L, 5L, 6L, 5L, 5L, 5L, 5L, 4L,
> > 4L, 5L, 5L, 5L, 5L, 3L, 5L, 5L, 4L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 2L,
> > 5L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 5L, 5L, 5L, 6L, 6L, 5L,
> > 5L, 5L, 6L, 5L, 6L, 3L, 4L, 4L, 5L, 6L, 5L, 5L, 6L, 5L, 4L, 5L, 5L,
> > 6L, 6L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 6L, 6L, 6L), V11 = c(5, 6, 5,
> > 6, 5, 5, 6, 4, 4, 4, 6, 6, 6, 4, 6, 4, 5, 5, 4, 5, 6, 5, 2, 5, 6, 5,
> > 3, 5, 5, 6, 5, 6, 6, 5, 6, 5, 5, 5, 5, 6, 6, 4, 6, 5, 4, 5, 6, 5, 4,
> > 5, 6, 4, 4, 6, 5, 6, 4, 6, 5, 6, 5, 6, 6, 6, 3, 5, 6, 5, 5, 6, 5, 4,
> > 5, 6, 2, 5, 3, 6, 5, 6, 5, 2, 5, 5, 5, 6, 5, 4, 4, 4, 5, 6, 2, 5, 4,
> > 3, 4, 4, 4, 6, 6, 5, 6, 6, 6, 5, 4, 4.5, 5, 4, 5, 5, 4, 6, 5, 5, 5, 6,
> > 5, 5, 4, 4, 5, 5, 4, 5, 6, 5, 5, 6, 4, 4, 5, 5, 4, 2, 6, 4, 6, 6, 6,
> > 5, 6, 4, 4, 5, 5, 5, 4, 5, 5, 6, 2, 3, 3, 6, 5, 6, 5, 5, 1, 4, 4, 4,
> > 6, 6, 5, 2, 6, 5, 5, 6, 5, 5, 5, 4, 6, 3, 4, 5, 3, 5, 6, 3, 4, 3, 3,
> > 5, 5, 3, 6, 4, 3, 6, 5, 4, 4, 5, 6, 5, 5, 4, 6, 5, 4, 5, 5, 5, 6, 6,
> > 6, 4, 5, 6, 5, 4, 5, 6, 5, 5, 5, 6, 5, 6, 6, 5, 5, 5, 5, 6, 5, 4, 6,
> > 6, 3, 5, 3, 6, 5, 4, 5, 4, 5, 5, 4, 6, 5, 5, 4, 5, 6, 6, 5, 5, 5, 5,
> > 6, 6, 5, 4, 5, 5, 6, 5, 5, 6, 5, 3, 5, 4, 5, 4, 5, 5, 6, 5, 5, 5, 5,
> > 6, 5, 6, 2, 5, 5, 5, 5, 5, 1, 5, 3, 5, 5, 4, 6, 6, 5, 5, 5, 5, 5, 5,
> > 4, 6, 6, 6, 6), V12 = c(4L, 6L, 3L, 6L, 5L, 5L, 6L, 4L, 5L, 4L, 6L,
> > 5L, 5L, 5L, 5L, 5L, 4L, 5L, 4L, 5L, 6L, 5L, 4L, 5L, 5L, 4L, 4L, 5L,
> > 5L, 6L, 3L, 6L, 6L, 5L, 6L, 5L, 4L, 4L, 4L, 4L, 4L, 5L, 6L, 5L, 5L,
> > 4L, 4L, 5L, 5L, 3L, 5L, 4L, 4L, 6L, 4L, 4L, 5L, 6L, 6L, 6L, 4L, 6L,
> > 6L, 4L, 5L, 3L, 4L, 5L, 5L, 4L, 4L, 4L, 4L, 5L, 3L, 5L, 3L, 6L, 5L,
> > 6L, 4L, 3L, 5L, 2L, 4L, 5L, 5L, 4L, 5L, 4L, 5L, 2L, 2L, 5L, 4L, 4L,
> > 4L, 4L, 5L, 6L, 5L, 5L, 5L, 6L, 6L, 5L, 4L, 5L, 5L, 4L, 4L, 5L, 4L,
> > 5L, 5L, 5L, 5L, 6L, 5L, 5L, 5L, 4L, 5L, 6L, 6L, 6L, 6L, 6L, 3L, 6L,
> > 5L, 5L, 5L, 4L, 4L, 5L, 4L, 4L, 6L, 5L, 6L, 5L, 5L, 4L, 6L, 5L, 4L,
> > 6L, 4L, 5L, 5L, 3L, 2L, 4L, 4L, 5L, 5L, 2L, 3L, 5L, 4L, 6L, 5L, 5L,
> > 6L, 6L, 4L, 2L, 6L, 5L, 5L, 6L, 5L, 5L, 5L, 5L, 6L, 4L, 3L, 5L, 3L,
> > 4L, 2L, 3L, 4L, 3L, 4L, 4L, 5L, 2L, 5L, 4L, 5L, 5L, 5L, 4L, 4L, 5L,
> > 5L, 5L, 5L, 5L, 5L, 5L, 4L, 4L, 5L, 4L, 6L, 6L, 5L, 4L, 5L, 5L, 4L,
> > 5L, 5L, 6L, 5L, 5L, 5L, 6L, 5L, 5L, 6L, 6L, 4L, 6L, 5L, 2L, 5L, 3L,
> > 6L, 6L, 3L, 4L, 5L, 5L, 5L, 5L, 5L, 6L, 1L, 4L, 4L, 4L, 5L, 5L, 4L,
> > 5L, 4L, 5L, 4L, 4L, 4L, 3L, 5L, 5L, 5L, 4L, 4L, 5L, 6L, 5L, 5L, 6L,
> > 4L, 4L, 4L, 5L, 5L, 5L, 4L, 5L, 6L, 5L, 5L, 4L, 6L, 5L, 4L, 6L, 4L,
> > 4L, 4L, 5L, 6L, 5L, 5L, 5L, 4L, 4L, 5L, 3L, 5L, 6L, 5L, 5L, 5L, 3L,
> > 5L, 5L, 6L, 6L, 5L, 4L, 5L),
> > V13 = c(5L, 5L, 4L, 6L, 5L, 5L, 6L, 4L, 4L, 3L, 6L, 5L, 4L,
> > 5L, 4L, 3L, 4L, 5L, 4L, 4L, 4L, 4L, 3L, 4L, 6L, 5L, 5L, 5L,
> > 5L, 6L, 5L, 5L, 5L, 5L, 5L, 4L, 4L, 4L, 4L, 5L, 3L, 4L, 6L,
> > 5L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 3L, 2L, 5L, 5L, 5L, 6L,
> > 6L, 6L, 4L, 6L, 6L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 4L, 5L, 6L,
> > 6L, 3L, 4L, 2L, 6L, 6L, 5L, 4L, 3L, 5L, 5L, 5L, 5L, 4L, 4L,
> > 3L, 4L, 3L, 5L, 4L, 4L, 4L, 3L, 4L, 5L, 5L, 5L, 4L, 6L, 5L,
> > 4L, 5L, 5L, 4L, 5L, 5L, 4L, 4L, 5L, 4L, 4L, 4L, 5L, 4L, 5L,
> > 5L, 4L, 5L, 4L, 5L, 4L, 5L, 5L, 5L, 6L, 4L, 6L, 5L, 5L, 4L,
> > 4L, 3L, 5L, 4L, 3L, 5L, 4L, 5L, 4L, 4L, 5L, 4L, 5L, 5L, 5L,
> > 4L, 4L, 6L, 4L, 2L, 4L, 2L, 5L, 4L, 5L, 3L, 4L, 4L, 3L, 4L,
> > 5L, 3L, 6L, 4L, 2L, 5L, 6L, 5L, 5L, 5L, 5L, 4L, 6L, 5L, 4L,
> > 5L, 4L, 3L, 4L, 5L, 3L, 5L, 5L, 2L, 4L, 5L, 5L, 3L, 4L, 6L,
> > 5L, 5L, 4L, 4L, 4L, 4L, 3L, 5L, 5L, 5L, 5L, 4L, 3L, 4L, 3L,
> > 5L, 5L, 4L, 5L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 3L, 6L, 5L,
> > 5L, 5L, 4L, 4L, 4L, 6L, 2L, 5L, 5L, 6L, 5L, 3L, 5L, 2L, 5L,
> > 5L, 4L, 5L, 6L, 5L, 4L, 4L, 4L, 4L, 5L, 3L, 4L, 4L, 5L, 4L,
> > 2L, 4L, 3L, 3L, 6L, 5L, 4L, 5L, 5L, 6L, 4L, 4L, 4L, 5L, 5L,
> > 5L, 5L, 5L, 3L, 4L, 5L, 5L, 4L, 5L, 5L, 4L, 5L, 5L, 6L, 3L,
> > 3L, 4L, 5L, 5L, 5L, 1L, 5L, 3L, 4L, 4L, 1L, 6L, 4L, 5L, 5L,
> > 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L), V14 = c(4L, 5L, 4L,
> > 6L, 5L, 5L, 6L, 5L, 4L, 4L, 6L, 4L, 4L, 5L, 5L, 5L, 5L, 5L,
> > 5L, 4L, 6L, 4L, 4L, 5L, 5L, 5L, 4L, 5L, 5L, 6L, 5L, 5L, 5L,
> > 5L, 5L, 5L, 5L, 4L, 5L, 6L, 4L, 4L, 6L, 5L, 5L, 4L, 4L, 5L,
> > 5L, 4L, 5L, 4L, 4L, 4L, 5L, 5L, 5L, 6L, 6L, 5L, 5L, 6L, 5L,
> > 4L, 5L, 4L, 4L, 5L, 4L, 5L, 6L, 5L, 5L, 5L, 4L, 5L, 3L, 6L,
> > 5L, 5L, 4L, 4L, 5L, 5L, 2L, 4L, 5L, 4L, 4L, 5L, 3L, 5L, 5L,
> > 4L, 5L, 2L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 5L, 5L, 5L,
> > 5L, 5L, 4L, 5L, 4L, 5L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 4L, 6L,
> > 4L, 5L, 5L, 5L, 6L, 4L, 5L, 5L, 5L, 4L, 5L, 2L, 5L, 4L, 4L,
> > 5L, 6L, 6L, 5L, 4L, 5L, 4L, 4L, 2L, 5L, 4L, 5L, 4L, 5L, 1L,
> > 5L, 3L, 5L, 5L, 5L, 3L, 5L, 5L, 4L, 4L, 5L, 4L, 5L, 4L, 5L,
> > 6L, 6L, 5L, 4L, 6L, 5L, 5L, 5L, 5L, 3L, 5L, 4L, 4L, 4L, 5L,
> > 3L, 4L, 5L, 4L, 4L, 5L, 5L, 5L, 4L, 6L, 3L, 5L, 4L, 5L, 5L,
> > 5L, 4L, 5L, 5L, 5L, 5L, 4L, 4L, 4L, 4L, 6L, 5L, 4L, 6L, 5L,
> > 4L, 4L, 5L, 5L, 6L, 5L, 5L, 4L, 5L, 5L, 5L, 6L, 5L, 4L, 6L,
> > 4L, 4L, 5L, 4L, 6L, 6L, 2L, 5L, 4L, 6L, 5L, 4L, 4L, 5L, 4L,
> > 4L, 4L, 5L, 4L, 5L, 5L, 5L, 4L, 4L, 5L, 4L, 5L, 3L, 5L, 5L,
> > 5L, 4L, 5L, 5L, 6L, 4L, 5L, 4L, 5L, 5L, 5L, 4L, 4L, 4L, 4L,
> > 5L, 6L, 5L, 5L, 5L, 4L, 5L, 4L, 2L, 4L, 4L, 4L, 5L, 5L, 5L,
> > 5L, 5L, 4L, 4L, 4L, 1L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 5L, 5L,
> > 5L, 5L, 6L, 5L), V15 = c(5, 4, 4, 6, 5, 2, 6, 4, 5, 4, 5,
> > 4, 4, 5, 4, 5, 4, 4, 3, 3, 2, 4, 5, 5, 5, 5, 4, 5, 5, 5,
> > 4, 5, 5, 5, 5, 5, 4, 3, 2, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5,
> > 4, 5, 5, 4, 4, 2, 5, 5, 6, 6, 5, 5, 6, 5, 4, 4, 4, 5, 5,
> > 4, 4, 6, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 3, 5, 5, 4, 5, 5,
> > 4, 5, 5, 4, 4, 6, 4, 4, 3, 4, 6, 3, 5, 5, 5, 4, 5, 6, 5,
> > 4, 5, 5, 4, 4, 5, 4, 5, 5, 4.5, 4, 5, 5, 5, 5, 4, 5, 5, 5,
> > 5, 6, 6, 3, 6, 5, 4, 3, 5, 3, 6, 4, 4, 5, 5, 4, 5, 4, 4,
> > 4, 4, 4, 5, 4, 6, 5, 5, 3, 4, 4, 5, 5, 5, 4, 5, 3, 4, 5,
> > 6, 4, 6, 5, 2, 6, 4, 5, 4, 5, 5, 4, 6, 5, 5, 3, 4, 4, 4,
> > 4, 3, 4, 4, 2, 4, 5, 5, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5,
> > 5, 3, 4, 4, 3, 4, 4, 6, 5, 4, 5, 5, 4, 3, 4, 3, 5, 5, 5,
> > 4, 6, 4, 5, 6, 5, 4, 6, 5, 2, 5, 4, 3, 6, 5, 5, 3, 6, 5,
> > 4, 5, 5, 5, 4, 4, 5, 3, 5, 3, 5, 6, 4, 4, 5, 4, 3, 5, 5,
> > 5, 4, 5, 5, 6, 5, 4, 4, 3, 5, 4, 5, 4, 2, 5, 5, 5, 5, 5,
> > 5, 3, 5, 4, 5, 4, 4, 4, 4, 5, 5, 1, 5, 4, 4, 5, 3, 6, 2,
> > 4, 5, 5, 5, 5, 6, 5, 5, 5, 5, 4), V16 = c(5L, 6L, 4L, 6L,
> > 5L, 5L, 6L, 4L, 3L, 3L, 6L, 4L, 6L, 5L, 6L, 4L, 5L, 4L, 4L,
> > 5L, 6L, 3L, 4L, 5L, 5L, 5L, 3L, 5L, 4L, 5L, 5L, 5L, 4L, 4L,
> > 5L, 5L, 5L, 4L, 5L, 6L, 5L, 2L, 6L, 5L, 4L, 4L, 5L, 5L, 5L,
> > 5L, 5L, 4L, 4L, 4L, 4L, 2L, 5L, 6L, 5L, 6L, 4L, 6L, 6L, 5L,
> > 4L, 3L, 3L, 4L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 5L, 3L, 6L, 6L,
> > 4L, 4L, 1L, 4L, 5L, 4L, 4L, 4L, 3L, 5L, 4L, 2L, 6L, 2L, 5L,
> > 4L, 2L, 4L, 5L, 3L, 5L, 6L, 5L, 4L, 6L, 6L, 5L, 3L, 3L, 2L,
> > 4L, 4L, 5L, 4L, 6L, 5L, 4L, 2L, 6L, 5L, 6L, 5L, 4L, 5L, 5L,
> > 5L, 6L, 5L, 5L, 5L, 6L, 4L, 4L, 4L, 4L, 2L, 4L, 6L, 5L, 6L,
> > 6L, 6L, 6L, 5L, 5L, 5L, 5L, 6L, 4L, 3L, 5L, 5L, 5L, 1L, 4L,
> > 4L, 6L, 4L, 6L, 5L, 5L, 4L, 4L, 5L, 5L, 5L, 6L, 4L, 5L, 5L,
> > 6L, 5L, 5L, 4L, 5L, 5L, 4L, 6L, 2L, 3L, 5L, 3L, 5L, 6L, 3L,
> > 4L, 4L, 4L, 4L, 5L, 5L, 4L, 4L, 6L, 5L, 3L, 3L, 4L, 5L, 6L,
> > 4L, 5L, 4L, 5L, 5L, 4L, 4L, 5L, 4L, 6L, 5L, 5L, 4L, 5L, 5L,
> > 3L, 5L, 5L, 5L, 5L, 6L, 4L, 2L, 5L, 6L, 6L, 5L, 4L, 5L, 5L,
> > 6L, 5L, 4L, 4L, 6L, 2L, 6L, 3L, 6L, 5L, 4L, 4L, 4L, 5L, 6L,
> > 3L, 5L, 4L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 3L, 4L, 1L, 5L, 5L,
> > 4L, 4L, 5L, 6L, 5L, 5L, 6L, 4L, 3L, 5L, 4L, 4L, 4L, 5L, 4L,
> > 4L, 5L, 5L, 4L, 5L, 5L, 5L, 5L, 2L, 4L, 5L, 4L, 5L, 5L, 1L,
> > 5L, 3L, 4L, 6L, 4L, 5L, 2L, 4L, 5L, 5L, 4L, 5L, 5L, 5L, 5L,
> > 6L, 4L, 6L), V17 = c(5, 5, 6, 6, 5, 6, 6, 5, 4, 6, 6, 6,
> > 6, 6, 6, 4, 6, 1, 5, 6, 5, 4, 5, 5, 6, 5, 4, 5, 6, 6, 6,
> > 5, 6, 5, 5, 6, 6, 4, 2, 6, 6, 2, 5, 6, 4, 5, 6, 5, 5, 6,
> > 5, 5, 5, 5, 6, 4, 5, 6, 6, 6, 4, 6, 6, 5, 6, 4, 6, 6, 5,
> > 5, 6, 6, 6, 6, 4, 6, 5, 5, 5, 5, 5, 6, 5, 6, 3, 4, 5, 6,
> > 6, 5, 6, 6, 5, 5, 5, 4, 5, 6, 5, 6, 6, 5, 6, 5, 6, 5, 3,
> > 6, 4, 4, 4, 5, 4, 4, 6, 6, 4, 6, 5, 5, 5, 5, 5, 6, 5, 5,
> > 6, 6, 5, 5, 6, 5, 5, 5, 4, 6, 6, 5, 6, 6, 6, 6, 6, 6, 5,
> > 5, 4, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 3, 6, 5, 4, 4, 5, 5,
> > 6, 6, 5, 5, 6, 5, 5, 3, 5, 4, 4, 6, 5, 5, 5, 5, 6, 5, 6,
> > 5.5, 5, 6, 5, 5, 5, 6, 5, 6, 5, 6, 5, 5, 6, 4, 5, 6, 6, 6,
> > 6, 5, 5, 5, 6, 6, 6, 5, 5, 4, 4, 5, 4, 5, 1, 5, 5, 5, 5,
> > 5, 6, 5, 6, 4, 6, 4, 6, 6, 5, 6, 5, 6, 5, 5, 4, 6, 5, 5,
> > 6, 6, 6, 6, 5, 6, 6, 6, 5, 4, 6, 5, 5, 6, 5, 5, 5, 5, 5,
> > 3, 5, 6, 6, 5, 6, 6, 6, 5, 5, 4, 6, 5, 5, 5, 5, 6, 6, 6,
> > 5, 6, 5, 5, 6, 6, 5, 5, 6, 5, 5, 6, 4, 6, 6, 6, 6, 4, 5,
> > 6, 6, 5, 5, 6, 5, 6, 5, 5, 6), V18 = c(5L, 6L, 6L, 6L, 5L,
> > 5L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 5L, 5L, 6L, 3L, 5L, 6L,
> > 6L, 1L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 5L, 6L,
> > 6L, 5L, 4L, 2L, 5L, 6L, 2L, 5L, 6L, 4L, 6L, 6L, 4L, 6L, 5L,
> > 4L, 4L, 5L, 5L, 6L, 4L, 4L, 6L, 6L, 6L, 4L, 6L, 5L, 6L, 5L,
> > 4L, 6L, 6L, 5L, 5L, 6L, 6L, 5L, 6L, 3L, 6L, 4L, 5L, 6L, 5L,
> > 5L, 4L, 5L, 6L, 3L, 4L, 6L, 5L, 6L, 5L, 6L, 6L, 5L, 5L, 5L,
> > 4L, 4L, 6L, 5L, 5L, 5L, 6L, 6L, 5L, 6L, 5L, 3L, 6L, 4L, 5L,
> > 5L, 5L, 4L, 4L, 6L, 6L, 6L, 6L, 5L, 6L, 4L, 4L, 5L, 6L, 5L,
> > 4L, 5L, 6L, 6L, 5L, 6L, 5L, 4L, 6L, 5L, 6L, 6L, 5L, 6L, 6L,
> > 6L, 6L, 6L, 5L, 5L, 4L, 3L, 4L, 5L, 6L, 6L, 6L, 6L, 5L, 6L,
> > 4L, 6L, 5L, 6L, 5L, 4L, 4L, 5L, 6L, 6L, 5L, 5L, 5L, 6L, 5L,
> > 5L, 4L, 6L, 4L, 3L, 6L, 6L, 6L, 5L, 4L, 6L, 4L, 6L, 5L, 5L,
> > 6L, 6L, 5L, 6L, 6L, 6L, 6L, 5L, 6L, 5L, 6L, 6L, 5L, 4L, 6L,
> > 6L, 6L, 6L, 6L, 4L, 6L, 5L, 6L, 6L, 5L, 2L, 6L, 4L, 6L, 5L,
> > 5L, 1L, 4L, 5L, 4L, 4L, 5L, 6L, 5L, 6L, 3L, 6L, 4L, 6L, 6L,
> > 6L, 6L, 5L, 6L, 4L, 5L, 5L, 6L, 5L, 5L, 6L, 5L, 6L, 6L, 5L,
> > 6L, 6L, 6L, 4L, 3L, 6L, 6L, 5L, 5L, 5L, 4L, 5L, 5L, 5L, 6L,
> > 4L, 6L, 6L, 5L, 6L, 6L, 6L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L,
> > 6L, 6L, 6L, 5L, 6L, 5L, 2L, 6L, 6L, 5L, 5L, 6L, 5L, 1L, 6L,
> > 5L, 6L, 6L, 6L, 6L, 6L, 5L, 5L, 5L, 5L, 6L, 6L, 5L, 6L, 5L,
> > 5L, 5L)), .Names = c("V1", "V2", "V3", "V4", "V5", "V6", "V7",
> > "V8", "V9", "V10", "V11", "V12", "V13", "V14", "V15", "V16", "V17",
> > "V18"), class = "data.frame", row.names = c(NA, -307L))
> >
> > ## data set included using dump() command. Note that there is no missing data here as small amounts of na data have been replaced using linear interpolation.
> >
> >
> > cov.validation <- cov(validation.data) ## covariance matrix to be
> > used as the S argument in sem function
> >
> > cfa.validation <- specifyModel() ## copy and paste this command separately into R before copying the model
> > ABILITY -> V12, ability0
> > ABILITY -> V9, ability1
> > ABILITY -> V14, ability2
> > ABILITY -> V13, ability3
> > ABILITY -> V3, ability4
> > ABILITY -> V1, ability5
> > ABILITY -> V15, ability6
> > ABILITY -> V10, ability7
> > VALUES -> V17, values0
> > VALUES ->V18, values1
> > VALUES -> V8, values2
> > VALUES -> V2, values3
> > VALUES -> V5, values4
> > IDENTITY -> V16, identity0
> > IDENTITY -> V6, identity1
> > IDENTITY -> V11, identity2
> > IDENTITY -> V7, identity3
> > ABILITY <-> ABILITY, NA, 1
> > VALUES <-> VALUES, NA, 1
> > IDENTITY <-> IDENTITY, NA, 1
> > V1 <-> V1, error1
> > V2 <-> V2, error2
> > V3 <-> V3, error3
> > V4 <-> V4, error4
> > V5 <-> V5, error5
> > V6 <-> V6, error6
> > V7 <-> V7, error7
> > V8 <-> V8, error8
> > V9 <-> V9, error9
> > V10 <-> V10, error10
> > V11 <-> V11, error11
> > V12 <-> V12, error12
> > V13 <-> V13, error13
> > V14 <-> V14, error14
> > V15 <-> V15, error15
> > V16 <-> V16, error16
> > V17 <-> V17, error17
> > V18 <-> V18, error18
> > ABILITY <-> VALUES, cov1
> > ABILITY <-> IDENTITY, cov2
> > VALUES <-> IDENTITY, cov3
> >
> > ## model specified using standardised factor variances. Analysis has
> > also been run after setting the first item score for each factor to 1,
> > with no difference ## line numbers for the model have been omitted for
> > ease of copying and pasting into R
> >
> > cfa.validation.output <- sem(cfa.validation, cov.validation, nrow( validation.data)) ## nrow() function used to specify the number of observations.
> >
> > summary(cfa.validation.output)
> >
> > ______________________________________________________________
> >
> >
> > The summary that I obtain reads as follows:
> >
> > Model Chisquare = 561.2528 Df = 133 Pr(>Chisq) = 5.854301e-54
> > AIC = 637.2528
> > BIC = -200.418
> >
> > Normalized Residuals
> > Min. 1st Qu. Median Mean 3rd Qu. Max.
> > -2.51200 -0.43180 0.02767 0.66300 1.47200 9.78700
> >
> > R-square for Endogenous Variables
> > V12 V9 V14 V13 V3 V1 V15 V10 V17 V18 V8
> > 0.3193 0.2699 0.4813 0.4904 0.3310 0.3021 0.3544 0.2525 0.6333 0.5825 0.4169
> > V2 V5 V16 V6 V11 V7
> > 0.2248 0.3106 0.6653 0.5932 0.4485 0.3899
> >
> > Parameter Estimates
> > Estimate Std Error z value Pr(>|z|)
> > ability0 0.5454256 0.05495730 9.924534 3.256189e-23 V12 <--- ABILITY
> > ability1 0.4648402 0.05171841 8.987906 2.519863e-19 V9 <--- ABILITY
> > ability2 0.5751229 0.04485033 12.823158 1.216427e-37 V14 <--- ABILITY
> > ability3 0.6667419 0.05135888 12.982018 1.547491e-38 V13 <--- ABILITY
> > ability4 0.5430359 0.05354916 10.140887 3.637813e-24 V3 <--- ABILITY
> > ability5 0.4946864 0.05151662 9.602464 7.805609e-22 V1 <--- ABILITY
> > ability6 0.5364778 0.05075407 10.570143 4.098707e-26 V15 <--- ABILITY
> > ability7 0.4247777 0.04912394 8.647061 5.284253e-18 V10 <--- ABILITY
> > values0 0.6726096 0.04487096 14.989865 8.552626e-51 V17 <--- VALUES
> > values1 0.7427623 0.05225037 14.215445 7.348274e-46 V18 <--- VALUES
> > values2 0.4703353 0.04077475 11.534966 8.792193e-31 V8 <--- VALUES
> > values3 0.2867428 0.03579227 8.011306 1.134969e-15 V2 <--- VALUES
> > values4 0.3602499 0.03731974 9.653065 4.770800e-22 V5 <--- VALUES
> > identity0 0.8873503 0.05543298 16.007622 1.130485e-57 V16 <---
> > IDENTITY
> > identity1 0.7475428 0.05048877 14.806122 1.337368e-49 V6 <--- IDENTITY
> > identity2 0.6753142 0.05482191 12.318327 7.217620e-35 V11 <---
> > IDENTITY
> > identity3 0.8376139 0.07429317 11.274439 1.754934e-29 V7 <--- IDENTITY
> > error1 0.5652955 0.04986735 11.335985 8.704746e-30 V1 <--> V1
> > error2 0.2835150 0.02444977 11.595816 4.327216e-31 V2 <--> V2
> > error3 0.5960018 0.05327544 11.187177 4.711963e-29 V3 <--> V3
> > error4 0.7766920 0.06279183 12.369317 3.830654e-35 V4 <--> V4
> > error5 0.2880738 0.02581887 11.157491 6.582297e-29 V5 <--> V5
> > error6 0.3832292 0.04263115 8.989418 2.485441e-19 V6 <--> V6
> > error7 1.0980209 0.10041134 10.935227 7.820970e-28 V7 <--> V7
> > error8 0.3094475 0.02970430 10.417601 2.060859e-25 V8 <--> V8
> > error9 0.5844651 0.05087751 11.487691 1.521236e-30 V9 <--> V9
> > error10 0.5342599 0.04619898 11.564324 6.248167e-31 V10 <--> V10
> > error11 0.5607651 0.05324925 10.530948 6.220486e-26 V11 <--> V11
> > error12 0.6341278 0.05637253 11.248880 2.345511e-29 V12 <--> V12
> > error13 0.4619288 0.04592463 10.058410 8.434950e-24 V13 <--> V13
> > error14 0.3564872 0.03515096 10.141605 3.611160e-24 V14 <--> V14
> > error15 0.5242402 0.04741430 11.056583 2.037115e-28 V15 <--> V15
> > error16 0.3961271 0.05073686 7.807481 5.834244e-15 V16 <--> V16
> > error17 0.2619686 0.03471455 7.546364 4.475775e-14 V17 <--> V17
> > error18 0.3954005 0.04696524 8.419004 3.796997e-17 V18 <--> V18
> > cov1 0.2758005 0.06547343 4.212403 2.526678e-05 VALUES <--> ABILITY
> > cov2 0.6920402 0.04301632 16.087854 3.104127e-58 IDENTITY <--> ABILITY
> > cov3 0.3573852 0.06216556 5.748926 8.981225e-09 IDENTITY <--> VALUES
> >
> > Iterations = 30
> > _________________________________________________________
> > As far as I can tell, the analysis has estimated parameters in the model, but I cannot obtain the fit indices. I have also used the stdCoef() command to obtain standardised coefficients. I have searched for similar issues on the R-help archive and on a number of forums, but haven't found anything useful. I have also examined the documentation for these packages and cannot find the problem. I am starting to think that I have missed something very simple, but I have gone over every step very closely and carefully. Any help with this issue would be greatly appreciated.
> >
> > With regards,
> > Kevin Yet Fong Cheung
> >
> > Kevin Yet Fong Cheung, Bsc., MRes., MBPsS.
> > Postgraduate Researcher
> > Centre for Psychological Research
> > University of Derby
> > Kedleston Road
> > Derby DE22 1GB
> > k.cheung at derby.ac.uk<mailto:k.cheung at derby.ac.uk>
> > 01332592081
> >
> > http://derby.academia.edu/KevinCheung
> >
> >
> > _____________________________________________________________________
> > The University of Derby has a published policy regarding email and reserves the right to monitor email traffic. If you believe this email was sent to you in error, please notify the sender and delete this email. Please direct any concerns to Infosec at derby.ac.uk.
> >
> > ______________________________________________
> > 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.
>
>
>
> _____________________________________________________________________
> The University of Derby has a published policy regarding email and reserves the right to monitor email traffic. If you believe this email was sent to you in error, please notify the sender and delete this email. Please direct any concerns to Infosec at derby.ac.uk.
>
> ______________________________________________
> 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.
------------------------------------------------
John Fox
Sen. William McMaster Prof. of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox/
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