\encoding{UTF-8}
\name{CCAI}
\docType{data}
\alias{CCAI}
\alias{CCAI_R}
\alias{CCAI_pattern}
\alias{CCAI_Phi}
\title{The CCAI Climate-Friendly Purchasing Choices Domain}

\description{
  Correlation matrix, factor pattern matrix, and factor intercorrelations
  for the Climate Change Action Inventory (CCAI) Climate-Friendly
  Purchasing Choices domain, from Bi and Barchard (2024). The scale
  measures the frequency with which individuals make purchasing
  choices aimed at reducing climate change. Data were collected from
  500 United States MTurk workers. After 15 climate change deniers
  and 24 multivariate outliers were removed, 461 participants remained.
  Climate change deniers were excluded because the scale measures
  behaviors intended to reduce climate change --- including individuals
  who do not believe climate change exists would be inconsistent with
  the measure's intent.
}
\usage{
  data(CCAI)
}
\format{
  Three objects are loaded by \code{data(CCAI)}:
  \itemize{
    \item \code{CCAI_R}: a \eqn{14 \times 14}{14 x 14} numeric
          correlation matrix. Row and column names are item labels
          \code{CCAI1} through \code{CCAI14}, ordered by factor
          to match \code{CCAI_pattern}.
    \item \code{CCAI_pattern}: a \eqn{14 \times 3}{14 x 3} numeric
          matrix of factor pattern coefficients. Row names are item
          labels \code{CCAI1} through \code{CCAI14}, ordered by
          factor to facilitate interpretation. Column names are factor
          labels \code{SustainableOptions}, \code{CollectiveAction},
          and \code{AvoidBuyingNew}.
    \item \code{CCAI_Phi}: a \eqn{3 \times 3}{3 x 3} numeric matrix
          of factor intercorrelations. Row and column names are the
          three factor labels.
  }
}

\details{
The CCAI Climate-Friendly Purchasing Choices domain consists 
of 14 items. Items used a nine-point frequency scale ranging
from 1 (less than once a year) to 9 (at least 14 times a week).
For full details on study design, data collection, analysis, and
interpretation see Bi and Barchard (2024). The Climate Change Action
Inventory contains eight domains; the Climate-Friendly Purchasing
Choices domain analyzed here is one of them.

\code{CCAI_R} is the observed \eqn{14 \times 14}{14 x 14} correlation
matrix for the 14 items of the Climate-Friendly Purchasing Choices
domain. The correlation matrix was kindly provided by 
the authors and has not been published separately.

\code{CCAI_pattern} is a \eqn{14 \times 3}{14 x 3} factor pattern
matrix from principal components extraction followed by direct
oblimin rotation, reported in Table 2 of Bi and Barchard (2024)
(the Table is labeled ``Factor Structure'' in the paper but contains
pattern coefficients). The three factors are:
Choosing Sustainable Options (F1), Supporting Collective Action
(F2), and Avoiding Buying New (F3).

\tabular{clrrr}{
Item \tab Description \tab F1 \tab F2 \tab F3 \cr
CCAI8  \tab Choose products with less impact on climate change    \tab  .95 \tab  .00 \tab -.02 \cr
CCAI6  \tab Choose products with less packaging                   \tab  .91 \tab -.04 \tab  .01 \cr
CCAI7  \tab Choose products made locally                          \tab  .89 \tab -.09 \tab  .07 \cr
CCAI11 \tab Encourage others to choose climate-friendly products  \tab  .56 \tab  .40 \tab  .05 \cr
CCAI12 \tab Problem solve to reduce impact of purchases           \tab  .52 \tab  .44 \tab  .04 \cr
CCAI10 \tab Encourage others to buy less                          \tab  .41 \tab  .44 \tab  .12 \cr
CCAI14 \tab Give time/money to orgs reducing purchase impact      \tab -.01 \tab  .97 \tab -.02 \cr
CCAI13 \tab Give time/money to orgs reducing purchases            \tab  .02 \tab  .93 \tab  .01 \cr
CCAI5  \tab Donate to charity rather than buying a gift           \tab -.02 \tab  .78 \tab  .20 \cr
CCAI2  \tab Use borrowed/rented/digital rather than buying        \tab -.02 \tab -.18 \tab  .90 \cr
CCAI4  \tab Buy used rather than new                              \tab  .00 \tab  .15 \tab  .76 \cr
CCAI1  \tab Repair rather than buying replacements                \tab  .03 \tab  .06 \tab  .76 \cr
CCAI3  \tab Use borrowed/rented tools rather than buying          \tab  .10 \tab  .21 \tab  .62 \cr
CCAI9  \tab Donate or sell old possessions                        \tab  .22 \tab  .27 \tab  .46 \cr
}

\code{CCAI_Phi} is a \eqn{3 \times 3}{3 x 3} factor intercorrelation
matrix. All three intercorrelations exceed 0.50. 

\tabular{lrrr}{
                             \tab F1   \tab F2   \tab F3   \cr
Choosing Sustainable Options \tab 1.00 \tab 0.59 \tab 0.59 \cr
Supporting Collective Action \tab 0.59 \tab 1.00 \tab 0.53 \cr
Avoiding Buying New          \tab 0.59 \tab 0.53 \tab 1.00 \cr
}

See \code{vignette("GPA3bifactor", package = "GPArotation")} for a
bifactor analysis of these data.
}

\note{
  The raw data are publicly available on the Open Science Framework.
  As the data are subject to a license, users should consult the
  OSF page for terms of use before using the raw data directly:
  \url{https://osf.io/h38yb/overview}.
}

\seealso{
  \code{\link{rotations}},
  \code{\link{bifactorT}},
  \code{\link[base]{eigen}}, 
  \code{\link[stats]{factanal}},
  \code{\link{Harman}},
  \code{\link{Thurstone}},
  \code{\link{WansbeekMeijer}}
}
\references{
  Barchard, K.A., Okagawa, K., Hoffman, C.K., and Odents, O. (2021).
  \emph{Climate Change Action Inventory.} Unpublished psychological
  test. Available from kim.barchard@unlv.edu.

  Bi, Y. and Barchard, K.A. (2024). Purchasing choices that reduce
  climate change: An exploratory factor analysis.
  \emph{Spectra Undergraduate Research Journal}, \bold{3}(2), 8--14.
  doi: 10.9741/2766-7227.1028.
}
\examples{
  data(CCAI, package = "GPArotation")

  # Observed correlation matrix
  round(CCAI_R, 2)

  # Published pattern matrix and factor intercorrelations
  round(CCAI_pattern, 2)
  round(CCAI_Phi, 2)

  # Reproduce published analysis: PCA extraction via eigendecomposition
  # followed by direct oblimin rotation --- no additional packages 
  # required. This gives the same result as psych:::principal used 
  # by Bi and Barchard (2024).
  ev          <- eigen(CCAI_R)
  k           <- 3
  L_unrotated <- ev$vectors[, 1:k] \%*\% diag(sqrt(ev$values[1:k]))
  rownames(L_unrotated) <- colnames(CCAI_R)
  res_oblimin <- oblimin(L_unrotated, randomStarts = 100)

  # print applies sorting --- capture the sorted result
  res_sorted  <- print(res_oblimin)
  L_repro <- loadings(res_sorted)

  # Compare reproduced vs published side by side, alternating by factor
  comparison <- cbind(round(L_repro[, 1], 2),      round(CCAI_pattern[, 1], 2),
                      round(L_repro[, 2], 2),      round(CCAI_pattern[, 2], 2),
                      round(L_repro[, 3], 2),      round(CCAI_pattern[, 3], 2))
  colnames(comparison) <- c("F1.repro", "F1.pub",
                             "F2.repro", "F2.pub",
                             "F3.repro", "F3.pub")
  print(comparison)

  # Orthogonal bifactor rotation on observed correlation matrix using MLE extraction
  fa_unrotated <- factanal(factors = 3, covmat = CCAI_R, n.obs = 461, 
                           rotation = "none")
  bif <- bifactorT(loadings(fa_unrotated))
  print(bif, sortLoadings = FALSE, digits = 3)
}
\keyword{datasets}