[R] Confirmatory factor analysis using the sem package. TLI CFI and RMSEA absent from model summary.
Kevin Cheung
K.Cheung at derby.ac.uk
Mon Mar 18 16:00:06 CET 2013
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 from 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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