qmboots {qmethod}

Q Methodology: Bootstrap

Description

Implementation of the bootstrap to Q methodology using Principal Components Analysis (PCA).

Usage

qmboots(dataset, nfactors, nsteps, load = "auto",
        rotation = "varimax", indet = "qindtest", fsi = TRUE, 
        forced = T, distribution = NULL, 
        cor.method="pearson", ...)

Arguments

dataset

a matrix or dataframe containing original data, with statements as rows, Q sorts as columns, and Q board column values in each cell.

nfactors

number of factors to extract using PCA.

load

a matrix of factor loadings to be used as target. If "auto", the target matrix is generated using the rotation indicated ("varimax" by default).

nsteps

number of steps (repetitions) for the bootstraping.

rotation

rotation method, set to "varimax" by default. Other possible rotations from psych principal function "none", "varimax", "quatimax", "promax", "oblimin", "simplimax", and "cluster" are possible.

indet

method to solve the double indeterminacy issue in PCA bootstrapping. "procrustes" for procrustes rotation, "qindtest" for simple solution valid for up to 3 factors extracted, "both" for a qindtest and a procrustes rotation, or "none" for no rotation. The latter is not recommended for it introduces inflated variability. If "none" is selected, each replication is rotated using varimax.

fsi

logical; Shall the Factor Stability index be calculated? (experimental index).

forced

logical; Is the ranking of the items forced to match the distributions? Set to TRUE if all respondents ranked the items strictly following the distribution scores, in which case the values of the distribution are calculated automatically. Set to FALSE if respondents had the possibility to rank the items without following the distribution, and the values of the distribution have to be provided as an array in the argument distribution.

distribution

logical; when forced = FALSE, the distribution has to be provided as a vector of numbers, such as c(-2, -1, -1, 0, 1, 1, 2, 2).

cor.method

character string indicating which correlation coefficient is to be computed, to be passed on to the function cor: "pearson" (default), "kendall", or "spearman".

...

Other arguments passed on to qmethod.

Value

zscore-stats

summary of the analysis. List of one object, plus as many objects as factors extracted: the bootstrapped factor scores, and the z-score statistics of the bootrstrap. The z-score statistics of interest are mean (the bootstrap estimate of the z-score), and sd (the bootstrap estimate of the SE).

full.bts.res

full bootstrap results. List with as many objects as factors extracted, each object containing three data frames: flagged, zsc and loa. These data frames have as many columns as bootstrap steps, and contain the results of the analysis of each iteration. See description of these three data frames in qmethod.

indet.tests

indeterminacy tests.

resamples

index of the Q-sorts selected for each step.

orig.res

original results. See details of all the objects in qmethod.

q.array

array of values in the distribution grid.

loa.stats

statistics of factor loadings. List with as many objects as factors extracted, each object containing one data frame with the factor loading statistics of the bootrstrap. The factor loading statistics of interest are mean (the bootstrap estimate of the factor loading), and sd (the bootstrap estimate of the SE). This table includes flag_freq, which indicates the frequency with which the given Q-sort was flagged for the given factor.

q.array

array of values in the distribution grid.

fsi

factor stability index (optional; experimental).

Author(s)

Aiora Zabala

References

Zabala, Pascual (2016) Bootstrapping Q Methodology to Improve the Understanding of Human Perspectives. PLoS ONE 11(2): e0148087.

See Also

qmethod

Examples

data(lipset)
boots <- qmboots(lipset[[1]], nfactors = 3, nsteps = 10, load = "auto",
           rotation = "varimax", indet = "qindtest",
           fsi = TRUE)
boots
boxplot(t(boots[[2]][[1]][[2]]), horizontal = TRUE, 
main = "Statement z-score boxplot for the first factor", las = 1)

#See the table summaries:
qms <- qmb.summary(boots)
round(qms$statements, digits=2) # statements
round(qms$qsorts, digits=2)     # Q-sorts

# A more synthetic visualisation:
# z-scores:
qmb.plot(qms, nfactors=3, type="zsc", sort="difference")
# factor loadings:
qmb.plot(qms, nfactors=3, type="loa", sort="difference")