[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 16:55:02 CET 2013
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 example!
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
>
>
> _____________________________________________________________________
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