[R] Error messages when attempting to calculate polychoric correlation matrices

Tue Oct 2 00:46:40 CEST 2012

Dear Kevin,

>From ?polychor (in the polycor package):

"polychor(x, y, ML = FALSE, control = list(), std.err = FALSE, maxcor=.9999)

Arguments

x	
a contingency table of counts or an ordered categorical variable; the latter
can be numeric, logical, a factor, or an ordered factor, but if a factor,
its levels should be in proper order.

y	
if x is a variable, a second ordered categorical variable."

So polychor doesn't take a data frame as its argument, and computes only one
polychoric correlation at a time. (It generally helps in R, and even more
generally, to read the documentation.)

Thus, e.g.,

> with(data.matrix18, polychor(SABAS02, SABAS06))
[1] 0.1811532

> with(data.matrix18, polychor(SABAS02, SABAS06, ML=TRUE))
[1] 0.1817071

If you want to compute a matrix of polychoric correlations using the polycor
package, then you can use the hetcor function -- see ?hetcor -- but you'll
then have to change your variables from numeric to factors or ordered
factors, or hetcor will compute Pearson pairwise correlations among them.
You could use, for example

	for (j in 1:ncol(data.matrix18)) data.matrix18[, j] <-
as.factor(data.matrix18[, j])

I hope this helps,
 John

-----------------------------------------------
John Fox
Senator McMaster Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Kevin Cheung
> Sent: Monday, October 01, 2012 12:19 PM
> To: 'r-help at r-project.org'
> Subject: [R] Error messages when attempting to calculate polychoric
> correlation matrices
> 
> Dear R users,
> 
> I am a psychology postgraduate student who is relatively new to using R.
> I am currently developing a psychometric scale and have run into a few
> problems when using R to calculate a polychoric correlation matrix for
> my dataset. I am trying to produce a polychoric correlation matrix for
> calculating ordinal reliability estimates (eg. Alpha, omega).The set
> consists of 439 observations of 18 variables. Each of the 18 variables
> was measured using a 6 point Likert scale but some variables only
> feature responses across 5 ordinal steps because there were no observed
> responses for one extreme of the item. The dataset has no missing data
> following multiple imputation and preliminary analyses were conducted
> using SPSS. I have included a command that will reproduce the dataset
> below, apologies for the size of the command:
> 
> data.matrix18 <-
> structure(list(SABAS02 = structure(c(6, 2, 5, 6, 4, 6, 5, 3,
> 5, 1, 4, 4, 6, 5, 5, 5, 4, 4, 4, 3, 4, 6, 5, 2, 5, 4, 5, 4, 4,
> 5, 5, 5, 2, 5, 4, 5, 5, 5, 6, 3, 6, 4, 5, 5, 5, 5, 4, 4, 5, 5,
> 5, 4, 5, 5, 4, 6, 6, 5, 6, 4, 4, 5, 4, 5, 5, 5, 6, 4, 4, 5, 4,
> 6, 5, 6, 5, 6, 6, 5, 4, 6, 6, 5, 3, 4, 2, 4, 5, 5, 6, 2, 6, 5,
> 4, 6, 2, 5, 3, 5, 4, 4, 5, 4, 4, 3, 4, 4, 6, 5, 6, 6, 4, 4, 5,
> 5, 5, 6, 5, 5, 5, 5, 4, 5, 5, 5, 4, 4, 5, 6, 4, 5, 5, 4, 5, 5,
> 4, 5, 5, 4, 5, 5, 5, 4, 2, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 4, 4,
> 5, 4, 6, 2, 4, 6, 4, 4, 5, 4, 4, 6, 6, 5, 3, 3, 2, 4, 5, 5, 5,
> 5, 6, 2, 5, 5, 4, 6, 4, 5, 6, 5, 4, 5, 5, 4, 4, 5, 4, 5, 5, 3,
> 5, 4, 3, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 4, 4, 5, 5, 6,
> 4, 3, 5, 6, 5, 4, 5, 5, 2, 5, 5, 4, 2, 4, 5, 5, 5, 5, 5, 3, 4,
> 5, 2, 4, 3, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 4, 5, 6, 4, 5, 3,
> 5, 6, 5, 4, 5, 5, 5, 5, 5, 4, 4, 5, 6, 5, 4, 5, 5, 6, 6, 6, 4,
> 3, 4, 4, 5, 6, 4, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 4, 4, 5, 3, 5,
> 5, 4, 3, 4, 5, 4, 4, 5, 4, 5, 5, 3, 5, 6, 5, 5, 5, 5, 5, 4, 3,
> 5, 4, 4, 5, 5, 6, 4, 5, 4, 2, 6, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5,
> 5, 5, 4, 5, 5, 6, 5, 4, 4, 5, 4, 4, 5, 5, 4, 6, 4, 4, 5, 6, 5,
> 5, 4, 5, 4, 5, 4, 6, 5, 5, 5, 4, 5, 6, 5, 5, 5, 5, 5, 4, 3, 4,
> 5, 4, 4, 6, 4, 4, 4, 2, 5, 4, 4, 6, 2, 6, 4, 5, 5, 6, 5, 6, 4,
> 4, 3, 4, 5, 5, 6, 5, 5, 5, 5, 4, 5, 3, 5, 5, 5, 5, 6, 3, 5, 6,
> 5, 6, 4, 5, 4, 4, 5, 6, 2, 5, 6), value.labels = structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS06 =
> structure(c(6,
> 6, 6, 6, 6, 6, 5, 5, 6, 3, 6, 6, 6, 5, 5, 6, 5, 6, 6, 5, 5, 6,
> 6, 6, 6, 5, 6, 3, 6, 5, 5, 5, 5, 6, 6, 6, 3, 6, 6, 5, 5, 4, 5,
> 6, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6,
> 6, 6, 6, 6, 4, 6, 5, 5, 6, 6, 6, 6, 6, 6, 3, 5, 6, 6, 6, 6, 6,
> 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 6, 6, 6, 5, 5, 5, 6, 5, 6,
> 5, 6, 6, 6, 6, 5, 5, 6, 5, 5, 6, 2, 5, 5, 6, 5, 5, 5, 6, 5, 6,
> 5, 5, 6, 6, 6, 5, 5, 5, 6, 6, 5, 6, 6, 6, 4, 6, 6, 5, 4, 6, 5,
> 5, 6, 5, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 5, 6, 4, 6, 6, 6, 6, 5,
> 5, 6, 4, 5, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5,
> 6, 6, 5, 5, 6, 6, 5, 6, 5, 6, 5, 4, 6, 5, 6, 6, 5, 6, 5, 6, 5,
> 5, 5, 5, 6, 6, 5, 6, 5, 4, 6, 5, 6, 6, 5, 5, 6, 5, 5, 6, 6, 6,
> 6, 5, 5, 6, 6, 5, 5, 6, 6, 4, 5, 5, 6, 6, 6, 6, 4, 6, 6, 6, 6,
> 6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 5, 5, 6, 5, 6, 6, 6, 5, 2, 6, 6,
> 5, 5, 6, 5, 6, 6, 5, 6, 5, 6, 5, 6, 6, 6, 5, 5, 4, 5, 6, 6, 5,
> 5, 4, 4, 6, 6, 5, 4, 5, 5, 6, 6, 6, 5, 4, 5, 5, 3, 5, 5, 6, 6,
> 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 4, 5, 5, 6,
> 5, 6, 6, 6, 5, 6, 5, 6, 6, 6, 5, 5, 6, 5, 6, 6, 6, 6, 5, 6, 6,
> 5, 6, 5, 6, 6, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 6, 6, 5, 5, 6, 5,
> 5, 6, 6, 4, 3, 3, 4, 3, 5, 4, 5, 5, 6, 6, 6, 6, 6, 6, 2, 5, 6,
> 5, 6, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 6, 6, 5, 6, 5, 5, 5, 6, 6,
> 6, 6, 5, 6, 5, 6, 5, 6, 6, 6, 5, 4, 6, 6, 6, 6, 6, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS09 =
> structure(c(5,
> 3, 5, 5, 4, 5, 4, 2, 5, 1, 4, 5, 5, 5, 3, 5, 4, 4, 6, 4, 4, 6,
> 5, 6, 4, 4, 4, 4, 4, 4, 5, 5, 3, 4, 5, 5, 2, 2, 5, 4, 5, 4, 6,
> 5, 6, 4, 3, 6, 5, 5, 5, 5, 6, 5, 4, 5, 6, 6, 5, 5, 5, 5, 5, 5,
> 4, 5, 6, 5, 5, 4, 4, 2, 5, 5, 5, 5, 6, 1, 4, 5, 5, 5, 4, 4, 5,
> 5, 5, 5, 5, 5, 6, 5, 4, 5, 6, 4, 5, 5, 5, 5, 5, 4, 4, 5, 2, 4,
> 5, 6, 4, 6, 5, 5, 5, 5, 4, 4, 4, 3, 5, 3, 1, 4, 4, 4, 4, 5, 5,
> 5, 4, 5, 4, 4, 5, 3, 5, 6, 5, 3, 4, 5, 5, 3, 3, 5, 5, 5, 5, 5,
> 5, 5, 5, 2, 5, 4, 4, 4, 5, 5, 4, 5, 5, 2, 5, 3, 2, 5, 4, 5, 4,
> 3, 4, 2, 4, 5, 5, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4,
> 4, 4, 6, 4, 5, 5, 2, 4, 3, 4, 5, 4, 5, 5, 5, 5, 4, 3, 5, 3, 5,
> 5, 5, 4, 5, 4, 4, 6, 4, 5, 3, 5, 5, 5, 5, 2, 5, 3, 4, 4, 3, 5,
> 6, 5, 4, 5, 4, 4, 4, 4, 5, 2, 3, 5, 5, 5, 5, 4, 3, 5, 5, 5, 6,
> 5, 4, 4, 5, 4, 5, 4, 5, 6, 5, 3, 3, 5, 5, 4, 4, 4, 3, 4, 6, 5,
> 5, 4, 5, 5, 5, 6, 5, 4, 6, 4, 4, 4, 4, 5, 5, 2, 4, 6, 6, 6, 4,
> 3, 3, 5, 4, 6, 3, 5, 5, 3, 3, 6, 5, 3, 4, 5, 4, 4, 4, 4, 4, 5,
> 5, 4, 5, 4, 6, 4, 4, 5, 5, 5, 4, 5, 2, 5, 2, 3, 2, 5, 5, 4, 5,
> 5, 5, 5, 5, 5, 5, 4, 5, 5, 6, 3, 4, 5, 4, 5, 4, 4, 3, 4, 5, 4,
> 4, 5, 3, 5, 6, 1, 5, 4, 5, 5, 3, 4, 4, 5, 2, 4, 5, 5, 5, 6, 5,
> 5, 6, 5, 5, 4, 3, 3, 4, 5, 6, 1, 4, 4, 3, 2, 6, 5, 2, 4, 5, 6,
> 5, 5, 5, 6, 5, 6, 3, 4, 4, 5, 5, 5, 6, 4, 4, 5, 3, 5, 5, 4, 5,
> 6, 5, 5, 5, 3, 6, 5, 5, 4, 4, 5, 4, 6, 4, 5, 3, 5, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS10 =
> structure(c(6,
> 5, 4, 5, 6, 5, 5, 5, 5, 1, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 6,
> 5, 5, 5, 4, 5, 3, 4, 4, 5, 4, 4, 5, 5, 5, 2, 4, 5, 4, 5, 4, 5,
> 5, 5, 4, 4, 5, 5, 5, 5, 5, 6, 5, 4, 6, 6, 5, 5, 6, 6, 6, 5, 5,
> 4, 5, 6, 5, 5, 6, 2, 2, 5, 6, 5, 4, 6, 3, 3, 6, 5, 5, 5, 4, 5,
> 5, 6, 6, 5, 5, 6, 6, 5, 3, 6, 5, 4, 6, 5, 4, 5, 3, 4, 6, 3, 4,
> 5, 5, 5, 5, 5, 4, 5, 5, 4, 4, 5, 3, 4, 4, 1, 4, 5, 5, 3, 4, 5,
> 6, 6, 5, 5, 3, 4, 2, 4, 6, 5, 4, 4, 5, 3, 5, 4, 5, 5, 5, 4, 4,
> 5, 5, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 6, 3, 1, 4, 4, 5, 4, 5, 6,
> 4, 5, 3, 4, 5, 4, 5, 4, 5, 2, 5, 5, 5, 6, 5, 4, 5, 6, 5, 5, 5,
> 5, 4, 5, 2, 5, 5, 2, 4, 3, 5, 4, 4, 5, 5, 5, 4, 5, 3, 5, 1, 5,
> 4, 5, 5, 6, 4, 3, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 6, 5,
> 5, 5, 4, 5, 4, 4, 4, 4, 5, 1, 3, 5, 4, 5, 5, 5, 5, 5, 6, 6, 5,
> 5, 4, 4, 6, 5, 5, 4, 5, 6, 5, 4, 3, 4, 4, 4, 5, 4, 4, 5, 4, 6,
> 5, 5, 5, 6, 5, 6, 4, 5, 5, 4, 5, 5, 4, 6, 5, 4, 4, 6, 5, 4, 5,
> 4, 4, 5, 5, 5, 4, 5, 5, 5, 3, 5, 4, 5, 4, 4, 5, 5, 2, 5, 5, 5,
> 5, 4, 4, 4, 5, 5, 4, 6, 4, 6, 3, 4, 4, 5, 1, 3, 3, 2, 5, 5, 5,
> 6, 5, 5, 6, 5, 5, 4, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 5, 4, 6, 4,
> 4, 5, 4, 6, 6, 3, 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 6, 4,
> 5, 6, 5, 5, 4, 3, 3, 4, 5, 4, 4, 4, 5, 4, 6, 6, 5, 3, 2, 5, 6,
> 5, 5, 5, 6, 3, 1, 5, 4, 3, 4, 4, 5, 6, 5, 4, 5, 4, 5, 5, 4, 6,
> 6, 6, 5, 5, 4, 6, 5, 5, 4, 4, 5, 4, 6, 4, 6, 5, 4, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS12 =
> structure(c(6,
> 6, 6, 6, 6, 6, 5, 6, 6, 4, 5, 6, 6, 5, 6, 6, 6, 5, 6, 5, 5, 6,
> 4, 5, 5, 4, 5, 3, 5, 5, 5, 5, 4, 6, 5, 6, 3, 6, 6, 6, 4, 4, 6,
> 6, 6, 6, 5, 6, 6, 6, 5, 6, 6, 6, 5, 6, 6, 5, 5, 6, 5, 6, 5, 6,
> 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 2, 4, 5, 5, 6, 5, 6, 6,
> 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 6, 5, 6, 6, 5, 6, 6, 5, 6, 6, 6,
> 6, 6, 5, 6, 6, 5, 6, 6, 5, 6, 5, 4, 6, 6, 6, 5, 5, 4, 2, 5, 5,
> 6, 4, 5, 5, 5, 6, 6, 5, 6, 6, 4, 5, 6, 5, 5, 4, 6, 5, 6, 4, 5,
> 5, 5, 6, 4, 6, 6, 5, 5, 5, 5, 5, 5, 6, 4, 6, 4, 4, 6, 6, 6, 6,
> 4, 6, 5, 5, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 5, 5, 6, 6, 5, 5, 4,
> 5, 6, 6, 5, 6, 6, 3, 6, 4, 4, 5, 5, 6, 6, 6, 5, 5, 6, 5, 4, 5,
> 5, 5, 5, 6, 5, 5, 6, 5, 5, 5, 6, 6, 6, 5, 6, 5, 5, 6, 5, 5, 6,
> 6, 5, 5, 6, 5, 5, 4, 5, 6, 4, 5, 6, 5, 6, 5, 4, 3, 5, 6, 6, 5,
> 6, 4, 5, 5, 6, 4, 4, 6, 6, 5, 5, 5, 6, 6, 6, 5, 4, 5, 3, 6, 6,
> 5, 5, 6, 6, 6, 6, 5, 6, 5, 5, 5, 6, 5, 6, 6, 3, 4, 5, 6, 5, 5,
> 4, 4, 5, 6, 6, 4, 5, 6, 3, 5, 5, 5, 5, 4, 5, 4, 4, 6, 5, 4, 6,
> 5, 5, 4, 5, 6, 6, 5, 5, 5, 6, 5, 6, 3, 5, 6, 4, 5, 6, 5, 6, 5,
> 6, 6, 5, 6, 6, 5, 6, 6, 6, 6, 5, 6, 6, 5, 6, 5, 6, 5, 5, 6, 4,
> 5, 6, 5, 6, 6, 5, 6, 5, 6, 5, 5, 4, 5, 5, 6, 6, 5, 5, 6, 6, 6,
> 6, 6, 5, 5, 4, 4, 4, 3, 5, 5, 3, 5, 6, 5, 6, 6, 6, 6, 6, 5, 6,
> 5, 6, 6, 6, 6, 6, 6, 5, 6, 5, 5, 6, 6, 6, 5, 6, 4, 6, 5, 6, 6,
> 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS18 =
> structure(c(5,
> 3, 6, 5, 4, 6, 5, 5, 5, 1, 5, 3, 5, 5, 3, 5, 6, 5, 4, 2, 6, 6,
> 2, 5, 4, 4, 4, 1, 4, 3, 5, 5, 5, 4, 2, 5, 5, 3, 4, 1, 6, 4, 4,
> 3, 5, 5, 3, 4, 3, 5, 3, 6, 6, 4, 4, 6, 4, 4, 5, 4, 4, 3, 2, 6,
> 6, 4, 6, 5, 5, 4, 2, 6, 3, 3, 5, 3, 5, 4, 3, 5, 5, 5, 5, 4, 5,
> 5, 5, 5, 6, 6, 6, 6, 4, 5, 6, 5, 3, 6, 5, 4, 5, 1, 5, 6, 5, 5,
> 4, 6, 6, 5, 6, 5, 4, 5, 4, 5, 5, 4, 6, 5, 2, 3, 4, 4, 5, 5, 5,
> 6, 4, 4, 5, 5, 5, 3, 4, 6, 5, 3, 6, 4, 5, 5, 5, 4, 3, 5, 6, 4,
> 2, 5, 5, 5, 5, 3, 5, 2, 5, 5, 4, 5, 3, 5, 5, 4, 6, 3, 2, 5, 4,
> 3, 5, 3, 4, 6, 5, 6, 4, 5, 5, 6, 5, 5, 6, 4, 6, 5, 6, 5, 6, 4,
> 4, 4, 6, 3, 4, 5, 1, 4, 5, 6, 4, 4, 5, 6, 6, 5, 5, 4, 5, 4, 5,
> 4, 4, 5, 4, 3, 4, 5, 3, 5, 5, 5, 5, 6, 4, 5, 4, 3, 4, 4, 3, 5,
> 3, 2, 4, 5, 6, 4, 5, 6, 6, 6, 5, 4, 6, 5, 6, 5, 5, 6, 6, 6, 5,
> 5, 4, 5, 6, 5, 5, 3, 6, 6, 5, 3, 5, 6, 6, 5, 4, 5, 5, 5, 6, 6,
> 4, 5, 6, 6, 6, 1, 4, 3, 1, 6, 5, 5, 2, 4, 3, 4, 3, 5, 2, 6, 5,
> 3, 3, 4, 6, 4, 4, 4, 5, 4, 4, 6, 5, 3, 4, 2, 5, 3, 1, 5, 4, 6,
> 4, 4, 5, 5, 6, 5, 4, 6, 4, 6, 1, 6, 5, 6, 1, 4, 6, 6, 5, 5, 5,
> 5, 5, 5, 5, 6, 5, 5, 4, 5, 3, 5, 5, 2, 5, 5, 6, 5, 5, 3, 5, 2,
> 4, 6, 4, 4, 6, 4, 4, 4, 4, 5, 4, 5, 4, 5, 6, 4, 6, 5, 4, 2, 5,
> 1, 5, 5, 5, 6, 4, 4, 4, 5, 6, 5, 5, 5, 4, 1, 5, 6, 4, 5, 5, 1,
> 4, 5, 5, 6, 5, 5, 2, 4, 5, 4, 5, 5, 4, 6, 3, 2, 5, 4, 5, 6, 5,
> 5, 5, 5, 5, 4, 4, 4, 5, 5, 4, 6, 3, 6, 5, 5, 3, 6, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS26 =
> structure(c(4,
> 2, 6, 3, 4, 5, 4, 5, 5, 1, 2, 4, 4, 4, 3, 5, 5, 5, 2, 3, 4, 6,
> 5, 4, 5, 3, 3, 2, 4, 4, 4, 3, 2, 4, 1, 4, 3, 2, 2, 5, 3, 4, 2,
> 2, 2, 5, 3, 4, 5, 3, 3, 4, 6, 4, 3, 2, 3, 4, 2, 4, 4, 2, 2, 5,
> 2, 5, 5, 5, 4, 4, 3, 5, 2, 4, 4, 4, 6, 2, 2, 3, 4, 4, 1, 2, 3,
> 4, 5, 5, 4, 5, 2, 5, 2, 4, 1, 6, 3, 4, 5, 4, 4, 1, 4, 4, 4, 4,
> 2, 3, 5, 5, 5, 4, 3, 4, 4, 5, 4, 4, 5, 3, 2, 3, 4, 4, 2, 2, 5,
> 4, 3, 4, 3, 4, 5, 2, 4, 5, 3, 3, 3, 5, 2, 2, 3, 4, 4, 4, 3, 4,
> 2, 4, 4, 3, 4, 3, 4, 2, 4, 5, 4, 4, 4, 5, 4, 2, 4, 4, 2, 4, 3,
> 3, 4, 3, 4, 5, 4, 6, 4, 5, 2, 1, 5, 5, 5, 5, 4, 4, 4, 4, 5, 3,
> 4, 3, 5, 2, 4, 4, 1, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 3, 3, 2, 3,
> 4, 4, 4, 4, 2, 2, 4, 3, 3, 3, 5, 5, 4, 5, 5, 3, 3, 4, 3, 4, 5,
> 5, 2, 3, 5, 4, 4, 4, 4, 5, 1, 3, 2, 3, 4, 4, 5, 4, 4, 6, 6, 4,
> 5, 4, 4, 4, 6, 3, 3, 4, 6, 5, 3, 3, 4, 4, 3, 4, 4, 4, 5, 5, 2,
> 5, 5, 4, 5, 5, 4, 5, 4, 3, 3, 2, 3, 4, 4, 4, 3, 1, 5, 4, 5, 4,
> 3, 4, 4, 3, 3, 3, 3, 4, 3, 2, 5, 4, 4, 5, 4, 3, 1, 1, 3, 4, 5,
> 3, 4, 4, 4, 5, 4, 4, 6, 2, 1, 2, 5, 4, 1, 4, 4, 3, 5, 4, 2, 4,
> 3, 4, 3, 4, 6, 2, 4, 5, 3, 4, 4, 4, 3, 5, 4, 1, 5, 3, 3, 3, 2,
> 4, 6, 5, 5, 2, 3, 5, 3, 5, 4, 3, 1, 4, 5, 5, 4, 4, 5, 3, 6, 4,
> 3, 5, 5, 5, 5, 4, 3, 2, 5, 6, 3, 2, 3, 3, 3, 5, 4, 4, 4, 5, 1,
> 4, 4, 4, 5, 4, 4, 2, 4, 2, 4, 4, 4, 3, 6, 3, 2, 4, 5, 5, 6, 5,
> 5, 5, 2, 4, 5, 3, 3, 5, 4, 4, 5, 3, 4, 4, 4, 2, 6, 4), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS27 =
> structure(c(6,
> 6, 6, 5, 6, 6, 5, 5, 6, 3, 6, 6, 6, 5, 5, 5, 6, 6, 6, 5, 6, 6,
> 5, 4, 6, 4, 5, 1, 3, 5, 5, 4, 5, 6, 5, 5, 5, 6, 5, 4, 5, 4, 6,
> 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 4, 5, 6, 6, 5, 6, 6, 6, 5, 6,
> 5, 4, 6, 6, 4, 6, 5, 6, 6, 6, 5, 6, 6, 5, 4, 5, 6, 6, 6, 6, 5,
> 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6,
> 5, 6, 5, 6, 6, 5, 5, 5, 1, 6, 6, 5, 5, 6, 6, 5, 5, 6, 4, 6, 6,
> 6, 5, 6, 6, 4, 5, 5, 5, 6, 6, 5, 6, 6, 5, 4, 6, 6, 6, 5, 6, 5,
> 5, 5, 5, 6, 5, 6, 5, 5, 6, 5, 5, 6, 6, 5, 5, 4, 6, 6, 6, 6, 6,
> 4, 6, 4, 5, 6, 5, 6, 6, 6, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6,
> 5, 6, 6, 5, 6, 6, 5, 4, 5, 5, 6, 5, 6, 6, 6, 5, 6, 5, 5, 5, 5,
> 6, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 5, 6, 5, 6, 6, 6,
> 6, 5, 5, 6, 6, 6, 5, 5, 6, 3, 5, 5, 6, 5, 6, 6, 5, 6, 6, 6, 6,
> 5, 5, 6, 6, 6, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 4, 5, 4, 6, 6,
> 4, 5, 6, 6, 6, 6, 5, 5, 6, 4, 5, 5, 6, 6, 5, 5, 4, 5, 6, 5, 5,
> 5, 4, 5, 6, 6, 5, 5, 6, 6, 5, 5, 5, 5, 5, 4, 5, 6, 6, 6, 6, 6,
> 5, 5, 5, 5, 6, 6, 5, 5, 6, 6, 5, 6, 5, 6, 6, 4, 4, 6, 5, 6, 6,
> 6, 6, 5, 6, 6, 5, 6, 5, 5, 6, 5, 6, 6, 5, 6, 6, 6, 6, 5, 6, 5,
> 5, 6, 6, 6, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 6, 5, 5, 5, 6, 4,
> 6, 6, 6, 5, 4, 4, 4, 3, 5, 3, 5, 5, 6, 6, 6, 6, 6, 5, 4, 5, 6,
> 5, 5, 5, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 5, 5, 6, 4, 5, 5, 6, 4,
> 5, 6, 4, 5, 6, 6, 5, 6, 6, 6, 5, 4, 6, 6, 6, 6, 6, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS33 =
> structure(c(6,
> 2, 5, 6, 5, 6, 4, 2, 5, 1, 3, 4, 5, 5, 5, 5, 4, 4, 4, 3, 4, 6,
> 4, 2, 5, 4, 4, 5, 5, 4, 5, 5, 3, 4, 5, 4, 2, 5, 5, 2, 5, 5, 4,
> 5, 5, 4, 3, 4, 5, 5, 6, 4, 6, 5, 4, 5, 6, 6, 5, 5, 4, 4, 4, 5,
> 5, 5, 6, 5, 4, 4, 4, 5, 5, 5, 5, 6, 6, 5, 5, 5, 6, 5, 3, 4, 5,
> 4, 6, 5, 6, 4, 5, 5, 4, 4, 5, 5, 4, 4, 5, 4, 5, 1, 4, 4, 3, 4,
> 5, 5, 4, 6, 5, 4, 5, 5, 4, 5, 4, 5, 6, 5, 1, 5, 5, 6, 5, 3, 5,
> 6, 5, 5, 6, 5, 5, 3, 4, 6, 4, 4, 5, 5, 5, 3, 4, 5, 4, 4, 5, 4,
> 5, 5, 5, 5, 4, 5, 3, 5, 5, 5, 4, 5, 5, 5, 4, 4, 4, 4, 3, 5, 5,
> 5, 4, 2, 4, 5, 5, 6, 6, 5, 2, 5, 5, 4, 6, 4, 5, 5, 5, 4, 5, 5,
> 4, 4, 6, 5, 5, 5, 3, 4, 4, 4, 5, 3, 4, 5, 6, 5, 5, 5, 5, 4, 5,
> 5, 5, 4, 6, 4, 4, 6, 3, 4, 4, 5, 6, 4, 5, 6, 5, 5, 4, 4, 2, 5,
> 6, 5, 5, 5, 4, 5, 4, 4, 4, 4, 5, 3, 5, 5, 6, 4, 5, 5, 5, 6, 5,
> 5, 4, 5, 6, 4, 5, 3, 5, 6, 5, 3, 6, 5, 4, 5, 5, 5, 4, 5, 6, 5,
> 5, 5, 6, 5, 6, 6, 5, 3, 6, 3, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5,
> 4, 4, 5, 4, 6, 3, 5, 5, 3, 3, 4, 4, 3, 1, 4, 5, 5, 6, 4, 5, 6,
> 4, 5, 5, 5, 5, 4, 5, 5, 6, 4, 6, 5, 6, 4, 4, 4, 3, 6, 4, 5, 5,
> 6, 5, 5, 5, 6, 5, 4, 5, 5, 4, 4, 6, 6, 5, 4, 5, 4, 5, 4, 6, 4,
> 4, 6, 4, 4, 6, 5, 5, 5, 4, 4, 4, 5, 5, 6, 5, 6, 6, 5, 6, 6, 5,
> 5, 5, 5, 5, 4, 2, 4, 4, 5, 5, 6, 5, 5, 4, 3, 5, 5, 4, 6, 5, 6,
> 4, 5, 4, 5, 5, 5, 4, 4, 3, 4, 4, 4, 3, 6, 4, 2, 4, 4, 5, 4, 4,
> 4, 5, 5, 6, 6, 5, 5, 5, 6, 4, 5, 4, 5, 5, 6, 2, 5, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS34 =
> structure(c(3,
> 5, 6, 5, 5, 5, 5, 6, 6, 4, 5, 5, 6, 5, 5, 5, 6, 5, 5, 4, 6, 5,
> 5, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 5, 6, 5, 3, 6, 5, 4, 6, 4, 6,
> 5, 5, 5, 5, 5, 6, 6, 5, 4, 6, 5, 4, 6, 6, 6, 3, 4, 4, 5, 2, 6,
> 5, 4, 5, 4, 5, 5, 3, 5, 5, 5, 4, 6, 6, 5, 5, 5, 5, 5, 5, 4, 4,
> 5, 5, 5, 6, 5, 6, 6, 5, 5, 5, 5, 5, 5, 4, 3, 5, 5, 4, 5, 4, 5,
> 5, 5, 5, 6, 6, 5, 4, 5, 3, 4, 5, 4, 5, 6, 1, 5, 5, 5, 4, 5, 5,
> 6, 6, 5, 5, 6, 5, 2, 4, 6, 5, 3, 5, 6, 6, 6, 5, 6, 6, 4, 4, 5,
> 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 4, 6, 5, 6, 5, 5,
> 4, 4, 3, 5, 6, 5, 6, 6, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 4, 5, 5,
> 5, 4, 6, 2, 5, 6, 6, 4, 4, 5, 5, 5, 5, 5, 6, 5, 5, 4, 5, 5, 4,
> 5, 5, 5, 6, 4, 4, 6, 4, 3, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 4, 5,
> 6, 5, 5, 5, 5, 4, 5, 5, 6, 5, 4, 6, 5, 5, 6, 5, 5, 6, 6, 6, 6,
> 5, 4, 4, 6, 4, 5, 4, 5, 6, 5, 5, 4, 5, 4, 6, 4, 5, 4, 5, 6, 6,
> 4, 5, 6, 5, 6, 6, 5, 5, 6, 3, 4, 6, 5, 5, 4, 4, 5, 5, 6, 6, 5,
> 5, 5, 5, 6, 5, 4, 5, 4, 4, 4, 6, 5, 5, 2, 4, 5, 6, 6, 4, 3, 5,
> 4, 5, 6, 5, 6, 5, 5, 6, 6, 5, 5, 5, 5, 6, 5, 5, 4, 6, 5, 5, 5,
> 6, 5, 5, 5, 6, 5, 6, 6, 5, 5, 4, 6, 6, 5, 4, 5, 5, 5, 3, 6, 3,
> 5, 5, 4, 5, 6, 4, 5, 5, 5, 4, 4, 5, 5, 6, 6, 4, 6, 5, 6, 6, 5,
> 3, 5, 5, 4, 4, 3, 4, 4, 6, 6, 6, 4, 5, 3, 4, 5, 4, 4, 6, 5, 6,
> 5, 5, 5, 6, 6, 6, 5, 5, 5, 4, 5, 5, 6, 4, 5, 4, 5, 5, 5, 4, 2,
> 6, 5, 4, 5, 3, 6, 5, 5, 5, 4, 6, 5, 6, 5, 3, 5, 6, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS35 =
> structure(c(6,
> 3, 5, 5, 5, 6, 4, 6, 5, 1, 5, 4, 4, 5, 3, 5, 6, 5, 5, 5, 5, 6,
> 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 3, 4, 4, 5, 3, 6, 6, 4, 6, 4, 3,
> 4, 6, 5, 3, 5, 5, 5, 4, 5, 6, 5, 5, 6, 6, 6, 5, 6, 5, 6, 4, 6,
> 6, 4, 6, 4, 5, 4, 4, 6, 4, 5, 6, 6, 6, 3, 4, 5, 4, 5, 2, 3, 5,
> 5, 5, 5, 6, 6, 6, 6, 5, 4, 4, 4, 5, 5, 4, 5, 5, 1, 4, 6, 4, 4,
> 4, 6, 6, 6, 6, 5, 4, 6, 4, 6, 6, 4, 6, 5, 4, 5, 5, 4, 5, 5, 5,
> 6, 5, 5, 5, 5, 6, 3, 5, 6, 5, 5, 6, 6, 4, 6, 3, 6, 6, 5, 6, 5,
> 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 4, 6, 6, 5, 5, 4, 6, 3, 2, 5, 5,
> 4, 6, 4, 5, 6, 6, 6, 5, 6, 5, 3, 5, 6, 6, 4, 6, 4, 5, 5, 5, 5,
> 4, 3, 5, 3, 5, 6, 1, 3, 4, 5, 4, 3, 4, 6, 6, 5, 5, 5, 5, 4, 6,
> 5, 5, 5, 4, 6, 6, 6, 4, 6, 4, 5, 5, 6, 6, 5, 3, 5, 4, 4, 4, 5,
> 6, 5, 5, 6, 5, 4, 4, 5, 6, 6, 5, 4, 5, 4, 6, 5, 5, 6, 5, 6, 5,
> 5, 4, 5, 4, 6, 6, 4, 6, 6, 6, 4, 5, 6, 5, 6, 6, 6, 5, 5, 6, 4,
> 4, 5, 6, 5, 6, 6, 4, 5, 3, 5, 5, 6, 6, 6, 4, 3, 4, 5, 5, 6, 5,
> 4, 3, 4, 5, 5, 4, 5, 5, 3, 4, 6, 5, 4, 6, 4, 5, 2, 5, 5, 4, 5,
> 5, 6, 5, 5, 6, 4, 4, 6, 3, 5, 5, 6, 5, 5, 4, 4, 5, 6, 5, 4, 5,
> 6, 5, 4, 5, 6, 5, 5, 6, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 3, 4, 3,
> 4, 5, 4, 5, 6, 4, 5, 5, 5, 5, 4, 5, 4, 6, 6, 5, 6, 5, 5, 6, 5,
> 6, 5, 4, 6, 5, 4, 4, 4, 5, 6, 6, 5, 4, 5, 3, 5, 5, 3, 6, 5, 6,
> 4, 5, 5, 6, 5, 5, 3, 4, 4, 5, 5, 4, 6, 5, 4, 5, 5, 4, 5, 6, 5,
> 5, 6, 5, 5, 4, 2, 5, 5, 5, 5, 4, 3, 4, 6, 6, 3, 5, 6), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS36 =
> structure(c(6,
> 3, 4, 4, 5, 6, 5, 4, 5, 1, 4, 5, 5, 5, 5, 4, 5, 5, 5, 3, 5, 6,
> 5, 5, 4, 2, 3, 4, 5, 3, 5, 5, 4, 4, 4, 4, 3, 5, 6, 4, 6, 5, 4,
> 4, 5, 5, 4, 5, 5, 5, 6, 4, 6, 5, 3, 5, 6, 6, 5, 5, 5, 5, 4, 6,
> 3, 5, 6, 5, 4, 4, 4, 5, 4, 4, 4, 4, 6, 5, 3, 5, 5, 5, 5, 4, 3,
> 5, 5, 5, 6, 5, 5, 6, 4, 4, 3, 5, 4, 5, 5, 4, 5, 1, 4, 4, 2, 4,
> 6, 3, 6, 5, 6, 5, 4, 5, 4, 5, 5, 4, 6, 5, 2, 4, 5, 4, 6, 4, 5,
> 5, 3, 5, 4, 4, 5, 4, 4, 6, 4, 3, 6, 6, 5, 4, 4, 6, 6, 4, 5, 4,
> 5, 5, 5, 4, 5, 5, 3, 6, 6, 5, 3, 5, 5, 2, 5, 4, 5, 4, 2, 5, 4,
> 4, 5, 2, 5, 5, 5, 5, 5, 5, 2, 4, 5, 4, 5, 4, 4, 5, 5, 4, 5, 6,
> 4, 4, 5, 4, 5, 6, 2, 3, 4, 5, 4, 3, 4, 5, 5, 5, 5, 5, 4, 3, 5,
> 5, 5, 5, 3, 5, 2, 6, 4, 4, 5, 5, 5, 4, 4, 6, 5, 4, 4, 3, 2, 5,
> 6, 5, 4, 6, 4, 4, 4, 5, 5, 4, 5, 4, 4, 4, 6, 6, 4, 5, 5, 6, 5,
> 5, 4, 4, 6, 5, 6, 3, 5, 6, 4, 5, 5, 5, 4, 6, 3, 6, 5, 5, 6, 5,
> 5, 5, 6, 5, 6, 6, 4, 5, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 6, 5,
> 3, 5, 3, 4, 4, 5, 5, 5, 3, 3, 4, 4, 3, 5, 4, 5, 6, 2, 4, 3, 6,
> 3, 4, 5, 5, 6, 4, 3, 5, 4, 5, 6, 5, 5, 4, 4, 4, 4, 6, 5, 3, 6,
> 6, 4, 5, 5, 6, 5, 5, 5, 5, 5, 4, 4, 3, 5, 5, 4, 4, 5, 4, 4, 3,
> 4, 5, 4, 4, 6, 2, 5, 4, 4, 5, 3, 5, 4, 6, 6, 4, 6, 5, 5, 6, 5,
> 6, 5, 4, 6, 4, 3, 3, 4, 5, 6, 6, 5, 5, 4, 3, 5, 4, 4, 6, 5, 6,
> 5, 5, 4, 4, 5, 5, 4, 4, 3, 3, 4, 4, 4, 6, 4, 4, 5, 5, 5, 5, 4,
> 5, 5, 5, 6, 5, 5, 5, 5, 5, 4, 5, 3, 5, 5, 6, 3, 4, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS37 =
> structure(c(6,
> 4, 5, 4, 2, 6, 4, 2, 5, 1, 5, 5, 6, 5, 3, 4, 4, 4, 3, 3, 4, 6,
> 5, 5, 4, 4, 3, 3, 4, 5, 5, 4, 2, 4, 1, 4, 3, 3, 5, 5, 5, 4, 5,
> 2, 6, 4, 3, 4, 5, 5, 5, 4, 6, 5, 3, 5, 6, 6, 4, 4, 3, 4, 4, 5,
> 4, 5, 6, 5, 4, 4, 2, 4, 4, 4, 3, 6, 4, 3, 3, 4, 4, 5, 5, 3, 4,
> 5, 5, 5, 6, 5, 6, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 1, 3, 5, 4, 3,
> 6, 5, 4, 5, 5, 5, 4, 5, 4, 4, 4, 3, 5, 4, 1, 3, 5, 4, 4, 4, 4,
> 5, 3, 4, 6, 4, 5, 4, 4, 5, 4, 3, 5, 5, 3, 2, 5, 5, 5, 5, 4, 4,
> 5, 5, 5, 3, 5, 5, 5, 6, 4, 5, 4, 5, 5, 2, 5, 4, 4, 5, 4, 5, 4,
> 3, 5, 2, 4, 6, 6, 6, 5, 4, 2, 4, 4, 4, 5, 4, 4, 6, 5, 4, 5, 5,
> 5, 5, 5, 1, 4, 6, 3, 3, 5, 5, 5, 5, 5, 5, 5, 4, 4, 3, 5, 3, 5,
> 5, 4, 5, 3, 5, 3, 5, 4, 2, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 2, 5,
> 5, 5, 4, 5, 3, 5, 4, 5, 5, 3, 4, 5, 3, 4, 5, 4, 4, 5, 6, 4, 4,
> 5, 4, 4, 5, 4, 6, 3, 5, 6, 5, 3, 4, 6, 5, 4, 4, 5, 3, 4, 4, 5,
> 4, 5, 5, 5, 6, 5, 4, 4, 5, 5, 5, 4, 5, 6, 5, 1, 4, 5, 5, 6, 5,
> 2, 2, 3, 5, 4, 4, 5, 5, 3, 2, 5, 4, 5, 5, 3, 4, 5, 1, 3, 3, 5,
> 2, 5, 5, 5, 6, 4, 3, 5, 4, 4, 4, 5, 3, 5, 1, 5, 2, 4, 5, 1, 5,
> 6, 5, 5, 5, 6, 5, 5, 5, 5, 5, 4, 2, 4, 4, 5, 5, 5, 4, 4, 3, 1,
> 5, 4, 4, 5, 6, 3, 5, 4, 4, 5, 3, 2, 5, 5, 5, 5, 5, 5, 5, 6, 5,
> 5, 5, 4, 5, 3, 3, 3, 1, 4, 2, 6, 4, 5, 4, 3, 4, 4, 4, 6, 5, 6,
> 5, 5, 4, 6, 6, 4, 1, 2, 4, 4, 5, 4, 5, 3, 4, 5, 4, 4, 5, 5, 5,
> 4, 5, 4, 5, 4, 6, 4, 5, 2, 3, 5, 2, 6, 5, 6, 4, 5, 4), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS38 =
> structure(c(6,
> 5, 4, 5, 3, 5, 4, 2, 5, 1, 5, 5, 6, 5, 5, 5, 5, 5, 3, 4, 5, 6,
> 5, 5, 5, 4, 3, 3, 4, 3, 5, 4, 4, 4, 3, 6, 3, 5, 5, 5, 4, 3, 6,
> 3, 6, 4, 4, 6, 5, 5, 5, 4, 6, 5, 4, 5, 6, 5, 4, 4, 4, 5, 5, 4,
> 3, 4, 5, 5, 5, 4, 3, 4, 5, 5, 4, 4, 6, 5, 3, 4, 5, 5, 5, 4, 3,
> 5, 5, 5, 5, 4, 6, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 4, 4, 6, 4, 5,
> 4, 6, 5, 6, 5, 5, 4, 5, 4, 5, 4, 4, 5, 5, 1, 3, 5, 5, 5, 4, 4,
> 6, 4, 4, 4, 5, 5, 3, 4, 5, 4, 3, 5, 6, 3, 3, 5, 5, 4, 4, 4, 4,
> 5, 5, 4, 4, 5, 4, 4, 5, 5, 5, 4, 5, 6, 2, 5, 4, 4, 4, 4, 4, 4,
> 3, 5, 2, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5, 5,
> 5, 4, 6, 5, 5, 6, 4, 3, 5, 5, 5, 4, 5, 5, 5, 5, 4, 3, 5, 4, 5,
> 5, 5, 4, 4, 5, 3, 4, 3, 3, 5, 5, 5, 5, 4, 5, 5, 5, 4, 4, 3, 5,
> 5, 5, 4, 5, 4, 4, 5, 5, 6, 1, 4, 5, 4, 4, 6, 5, 5, 5, 6, 6, 5,
> 5, 4, 4, 5, 5, 6, 3, 5, 6, 5, 3, 4, 6, 5, 5, 5, 5, 4, 4, 6, 5,
> 5, 5, 5, 5, 6, 5, 5, 5, 6, 3, 5, 4, 5, 5, 5, 3, 5, 5, 5, 6, 5,
> 4, 3, 4, 5, 4, 3, 5, 5, 3, 4, 6, 5, 3, 5, 4, 4, 4, 4, 4, 3, 5,
> 3, 5, 4, 5, 6, 4, 4, 6, 5, 5, 4, 5, 2, 5, 4, 4, 4, 5, 5, 4, 5,
> 5, 4, 5, 5, 6, 5, 5, 5, 5, 4, 4, 1, 4, 4, 5, 4, 4, 5, 3, 6, 1,
> 4, 5, 4, 5, 6, 4, 5, 5, 5, 5, 4, 4, 5, 6, 5, 4, 6, 4, 5, 6, 5,
> 3, 5, 5, 5, 3, 3, 2, 2, 5, 3, 1, 4, 5, 4, 3, 5, 4, 3, 6, 4, 6,
> 5, 5, 6, 6, 5, 5, 1, 4, 3, 4, 5, 4, 6, 4, 5, 3, 4, 5, 5, 5, 6,
> 5, 5, 5, 5, 3, 5, 4, 5, 4, 4, 6, 1, 6, 5, 6, 5, 4, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS40 =
> structure(c(6,
> 5, 6, 5, 5, 5, 4, 4, 5, 1, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 2, 6,
> 5, 5, 5, 3, 5, 1, 4, 4, 4, 4, 5, 4, 4, 5, 2, 5, 5, 4, 6, 4, 6,
> 5, 6, 4, 4, 5, 5, 5, 5, 5, 6, 5, 4, 5, 6, 5, 4, 6, 5, 5, 5, 5,
> 2, 4, 6, 5, 5, 4, 4, 5, 5, 6, 4, 4, 6, 3, 2, 4, 5, 5, 4, 4, 4,
> 5, 4, 5, 5, 4, 4, 5, 5, 5, 3, 5, 4, 4, 5, 5, 4, 3, 4, 5, 5, 4,
> 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 4, 3, 5, 5, 1, 3, 5, 5, 4, 4, 5,
> 6, 4, 4, 4, 4, 5, 4, 4, 5, 5, 4, 5, 6, 4, 5, 5, 6, 5, 4, 4, 5,
> 5, 5, 5, 4, 5, 4, 5, 6, 4, 5, 4, 5, 5, 5, 5, 4, 5, 4, 6, 6, 5,
> 4, 5, 3, 4, 5, 4, 5, 6, 5, 2, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5,
> 4, 3, 5, 3, 5, 6, 5, 2, 5, 5, 5, 4, 6, 5, 5, 5, 5, 3, 5, 3, 3,
> 4, 5, 3, 4, 5, 3, 6, 4, 4, 5, 5, 6, 5, 5, 5, 5, 4, 5, 4, 2, 4,
> 6, 5, 4, 5, 5, 4, 5, 5, 6, 4, 5, 5, 4, 5, 5, 4, 5, 6, 6, 6, 4,
> 5, 4, 6, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 3, 5, 4, 4, 5, 4, 6, 5,
> 5, 5, 6, 5, 6, 5, 4, 4, 6, 4, 5, 4, 5, 6, 5, 4, 5, 5, 5, 6, 5,
> 4, 4, 4, 5, 5, 3, 4, 5, 4, 4, 5, 5, 4, 4, 3, 4, 5, 3, 4, 3, 5,
> 4, 4, 5, 5, 6, 4, 4, 5, 4, 6, 5, 5, 1, 6, 4, 4, 3, 5, 5, 5, 5,
> 5, 5, 5, 5, 6, 4, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 6, 4,
> 4, 5, 5, 5, 6, 4, 5, 4, 4, 4, 4, 6, 5, 6, 5, 4, 6, 5, 5, 6, 5,
> 6, 5, 5, 5, 3, 3, 4, 4, 5, 5, 5, 5, 6, 5, 4, 5, 4, 1, 3, 5, 6,
> 5, 4, 5, 5, 6, 5, 4, 5, 4, 4, 3, 5, 6, 5, 5, 5, 5, 5, 4, 6, 6,
> 5, 5, 4, 5, 5, 6, 5, 6, 3, 5, 6, 3, 5, 5, 6, 5, 6, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS41 =
> structure(c(5,
> 3, 5, 6, 4, 6, 5, 5, 5, 1, 4, 3, 5, 4, 3, 5, 5, 5, 4, 3, 5, 6,
> 3, 5, 3, 4, 4, 2, 4, 3, 5, 5, 4, 3, 1, 5, 3, 4, 5, 3, 6, 4, 2,
> 4, 6, 5, 3, 4, 5, 4, 3, 5, 6, 5, 3, 5, 4, 6, 5, 5, 4, 4, 2, 5,
> 6, 4, 6, 5, 4, 4, 2, 6, 3, 3, 5, 3, 6, 3, 4, 5, 5, 5, 3, 2, 5,
> 4, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 4, 5, 5, 5, 6, 1, 4, 4, 5, 4,
> 4, 6, 6, 6, 6, 5, 4, 5, 4, 6, 6, 5, 6, 4, 1, 4, 4, 4, 5, 4, 5,
> 6, 6, 4, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 5, 6, 3, 6, 4, 4, 5, 4,
> 2, 5, 3, 3, 5, 4, 5, 6, 5, 5, 4, 5, 5, 5, 6, 4, 6, 3, 3, 4, 5,
> 3, 5, 3, 4, 6, 5, 6, 4, 6, 2, 4, 5, 5, 6, 5, 5, 5, 5, 5, 5, 3,
> 4, 5, 5, 4, 5, 5, 1, 1, 4, 6, 5, 4, 5, 5, 6, 5, 5, 5, 4, 2, 2,
> 4, 4, 4, 3, 2, 4, 6, 3, 6, 4, 5, 5, 6, 5, 5, 3, 2, 4, 4, 3, 5,
> 4, 3, 3, 6, 5, 4, 5, 5, 4, 5, 4, 3, 4, 3, 5, 5, 6, 6, 6, 6, 5,
> 5, 3, 5, 5, 5, 6, 3, 6, 6, 5, 3, 5, 6, 6, 5, 5, 6, 5, 3, 6, 5,
> 4, 5, 5, 5, 6, 5, 4, 4, 1, 5, 5, 2, 4, 6, 4, 4, 2, 5, 4, 6, 5,
> 3, 3, 6, 6, 5, 4, 4, 5, 3, 3, 6, 5, 3, 4, 4, 5, 2, 1, 4, 3, 6,
> 4, 3, 5, 5, 6, 4, 3, 6, 3, 4, 1, 5, 4, 6, 4, 3, 5, 6, 5, 5, 4,
> 5, 5, 2, 6, 6, 5, 5, 6, 5, 5, 5, 6, 4, 5, 5, 6, 4, 5, 3, 6, 2,
> 4, 6, 4, 4, 5, 4, 5, 3, 5, 3, 3, 3, 4, 4, 1, 4, 4, 5, 4, 3, 5,
> 2, 5, 3, 5, 4, 4, 2, 4, 5, 6, 5, 5, 4, 4, 3, 5, 4, 2, 3, 5, 1,
> 4, 5, 5, 6, 6, 5, 4, 5, 3, 4, 5, 5, 2, 6, 3, 2, 5, 5, 5, 6, 5,
> 5, 5, 3, 5, 4, 2, 4, 5, 4, 4, 5, 3, 4, 5, 5, 3, 5, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS43 =
> structure(c(6,
> 5, 6, 6, 6, 6, 5, 6, 5, 4, 5, 4, 5, 5, 6, 5, 6, 6, 6, 5, 6, 6,
> 4, 5, 5, 6, 4, 1, 3, 3, 5, 4, 5, 5, 5, 5, 4, 6, 3, 5, 5, 4, 6,
> 6, 6, 5, 5, 5, 6, 6, 5, 5, 6, 5, 4, 5, 6, 5, 5, 6, 6, 6, 5, 6,
> 6, 5, 6, 6, 5, 6, 4, 6, 6, 5, 4, 5, 6, 3, 2, 4, 5, 5, 6, 5, 5,
> 6, 5, 6, 5, 6, 6, 6, 5, 6, 5, 5, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6,
> 5, 6, 4, 6, 6, 5, 5, 6, 5, 5, 6, 4, 5, 5, 6, 5, 5, 6, 6, 5, 5,
> 6, 4, 5, 6, 4, 5, 5, 4, 6, 6, 4, 6, 6, 5, 4, 4, 6, 6, 5, 6, 5,
> 5, 5, 4, 5, 5, 4, 6, 5, 4, 5, 5, 5, 6, 5, 5, 4, 5, 5, 5, 6, 6,
> 4, 6, 4, 5, 6, 5, 6, 5, 6, 4, 5, 5, 6, 6, 6, 5, 6, 6, 5, 5, 6,
> 5, 6, 6, 4, 4, 6, 4, 6, 5, 6, 6, 3, 6, 5, 6, 5, 5, 5, 5, 4, 4,
> 6, 5, 4, 3, 5, 5, 6, 4, 4, 5, 5, 6, 6, 5, 5, 4, 5, 4, 3, 5, 5,
> 6, 3, 5, 6, 6, 5, 5, 5, 6, 2, 5, 5, 5, 6, 5, 5, 3, 6, 6, 6, 6,
> 5, 4, 6, 6, 6, 6, 5, 6, 6, 6, 5, 5, 6, 5, 4, 5, 4, 4, 4, 6, 6,
> 5, 5, 6, 6, 6, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 3, 2, 5, 6, 6, 4,
> 4, 4, 6, 6, 6, 5, 4, 5, 3, 5, 5, 5, 4, 4, 3, 5, 5, 5, 6, 4, 6,
> 5, 5, 5, 5, 6, 6, 4, 5, 4, 4, 5, 6, 4, 6, 6, 4, 4, 6, 5, 6, 5,
> 5, 6, 5, 6, 6, 5, 6, 6, 5, 6, 5, 6, 6, 5, 5, 5, 5, 6, 5, 5, 5,
> 5, 6, 5, 6, 6, 4, 5, 4, 6, 4, 5, 4, 5, 6, 5, 6, 6, 5, 5, 6, 5,
> 6, 6, 5, 5, 4, 4, 2, 3, 5, 4, 4, 4, 6, 5, 6, 5, 6, 6, 3, 5, 6,
> 5, 6, 5, 6, 6, 6, 6, 5, 6, 4, 4, 6, 6, 5, 5, 6, 4, 5, 3, 6, 5,
> 5, 6, 4, 5, 6, 6, 5, 6, 6, 6, 5, 3, 6, 6, 6, 5, 6, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree"))), SABAS47 =
> structure(c(6,
> 5, 5, 6, 6, 6, 5, 6, 6, 4, 6, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 6,
> 4, 4, 5, 5, 5, 1, 5, 4, 4, 4, 3, 6, 5, 5, 2, 6, 3, 5, 6, 4, 6,
> 6, 6, 5, 5, 5, 6, 5, 5, 5, 6, 4, 3, 5, 6, 6, 5, 6, 6, 6, 4, 6,
> 6, 5, 6, 6, 5, 6, 3, 6, 4, 6, 5, 5, 6, 5, 4, 4, 6, 5, 5, 5, 5,
> 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6,
> 5, 6, 4, 5, 6, 5, 5, 6, 5, 6, 5, 4, 5, 4, 5, 5, 5, 6, 5, 6, 5,
> 6, 6, 5, 5, 5, 5, 6, 5, 6, 6, 5, 6, 6, 4, 4, 6, 6, 6, 5, 4, 6,
> 5, 5, 6, 5, 5, 4, 6, 5, 6, 5, 5, 5, 6, 5, 6, 4, 6, 6, 5, 6, 5,
> 5, 6, 4, 5, 6, 5, 6, 6, 6, 4, 5, 6, 6, 6, 5, 5, 5, 6, 4, 5, 5,
> 6, 6, 6, 4, 5, 6, 4, 6, 5, 6, 6, 4, 6, 6, 6, 4, 5, 6, 5, 5, 4,
> 6, 5, 4, 6, 5, 4, 6, 4, 4, 6, 5, 6, 6, 6, 6, 5, 5, 5, 5, 4, 6,
> 6, 3, 6, 6, 6, 6, 6, 5, 6, 3, 5, 5, 6, 6, 5, 4, 5, 4, 5, 6, 5,
> 5, 4, 6, 6, 6, 6, 5, 4, 6, 6, 5, 6, 6, 6, 5, 5, 5, 5, 4, 6, 6,
> 4, 5, 6, 6, 6, 5, 5, 5, 5, 6, 5, 4, 5, 6, 5, 3, 4, 5, 6, 6, 5,
> 5, 4, 6, 6, 6, 5, 4, 5, 3, 4, 5, 5, 4, 4, 3, 5, 5, 6, 5, 6, 6,
> 5, 4, 5, 5, 6, 6, 5, 5, 4, 4, 5, 6, 4, 6, 6, 4, 3, 6, 5, 6, 6,
> 6, 5, 6, 6, 5, 5, 5, 6, 5, 6, 6, 6, 6, 5, 5, 6, 5, 6, 5, 6, 6,
> 5, 6, 6, 6, 6, 6, 5, 5, 6, 4, 5, 4, 4, 6, 6, 6, 5, 5, 5, 6, 5,
> 6, 5, 5, 4, 4, 4, 2, 3, 5, 5, 3, 5, 6, 6, 6, 6, 5, 6, 3, 5, 6,
> 5, 6, 5, 6, 6, 6, 5, 6, 6, 5, 5, 6, 6, 5, 5, 5, 3, 5, 4, 6, 6,
> 4, 6, 4, 5, 5, 6, 5, 5, 6, 5, 5, 2, 6, 6, 6, 5, 5, 5), value.labels =
> structure(c(6,
> 5, 4, 3, 2, 1), .Names = c("Strongly Agree", "Agree", "Slightly Agree",
> "Slightly Disagree", "Disagree", "Strongly Disagree")))), .Names =
> c("SABAS02",
> "SABAS06", "SABAS09", "SABAS10", "SABAS12", "SABAS18", "SABAS26",
> "SABAS27", "SABAS33", "SABAS34", "SABAS35", "SABAS36", "SABAS37",
> "SABAS38", "SABAS40", "SABAS41", "SABAS43", "SABAS47"), row.names =
> c(NA,
> -439L), class = "data.frame", codepage = 1252L)
> 
> 
> I have attempted to use the polychoric command from the psych package
> (Revelle, 2005)
> 
> > polychoric(data.matrix18)
> 
> which returns the following error message at 20%: "Error in tab * log(P)
> : non-conformable arrays".
> 
> 
> 
> I have also used the polychor command from the polycor package (Fox,
> 2010),
> 
> polychor(data.matrix18, ML=TRUE)
> 
>  which returns the error message: "Error in checkmvArgs(lower = lower,
> upper = upper, mean = mean, corr = corr,  :
> 
>   at least one element of 'lower' is larger than 'upper'"
> 
> 
> 
> When using the two step estimation method, R has output a single
> coefficient rather than a correlation matrix, this could be due to a
> misunderstanding of the command on my part.
> 
> > polychor(data.matrix18, ML=FALSE)
> 
> [1] -0.0002762387
> 
> 
> In addition, I have used the dataset with the random.polchor.pa package
> (Presaghi & Desimoni, 2011) to conduct parallel analysis with randomly
> generated polychoric correlation matrices and this was successful. I
> conducted these analyses on a larger dataset with 33 variables and also
> with the 18 variable version.
> Any advice about how I can calculate a polychorric correlation matrix
> from this dataset and use it to look at ordinal reliability estimates
> would be much appreciated. I have one other query that does not relate
> to R specifically but is likely to be a subject familiar to someone
> reading this post. I have recently read a number of technical papers
> relating to the use of different reliability estimates in scale
> development (Sjimtsa, 2009; Cronbach & Shavelson, 2004; Revelle &
> Zinbarg, 2009; Gadermann, Guhn & Zumbo, 2012). These have been helpful
> for me, but I am wondering if there are any less technical articles that
> advise on which estimates to report from an applied research context. I
> don't fully understand the mathematical subtleties of each statistic and
> am hoping that someone from an applied psychology background would be
> able to point me in the right direction.
> 
> 
> References
> Cronbach, L. J., & Shavelson, R. J. (2004). My current thoughts on
> coefficientalpha and successor procedures. Educational and Psychological
> Measurement, 64, 391-418. doi:10.1177/0013164404266386
> 
> Gadermann, A. J., Guhn, M., & Zumbo, B.D. (2012). Estimating ordinal
> reliability for Likert-type and ordinal item response data: A
> conceptual, empirical, and practical guide. Practical Assessment,
> Research & Evaluation, 17(3), 1-13.
> 
> Revelle, W., & Zinbarg, R. E. (2009). Coefficients alpha, beta, omega,
> and the glb: Comments on Sijtsma. Psychometrika, 74, 145-154. doi:
> 10.1007/s11336-008-9102-z
> 
> Sijtsma, K. (2009). On the use, the misuse, and the very limited
> usefulness of Cronbach's alpha. Psychometrika, 74, 107-120. doi:
> 10.1007/s11336-008-9101-0
> 
> 
> 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<mailto:k.cheung at derby.a
> c.uk%3cmailto:k.cheung at derby.ac.uk>>
> 01332592081
> 
> 
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