Implement the polynomial method for computing conditional standard errors of
measurement for scale scores (CSSEM). A polynomial regression of scale scores
on raw scores is fit for degrees 1 through K; for each degree k,
the transformation derivative is used to map raw-score CSEM values to
scale-score CSSEM values.
cssem_polynomial(csemx, ct, K = 10, gra = TRUE)A list with two components:
A matrix with one column containing the R-squared values
from polynomial fits of degree k = 1, ..., K, where
K is the largest successfully fitted degree.
A data frame containing the merged data
(x, csem, ss) and, for each degree k,
the additional columns:
fx_k1, fx_k2, ...: transformation derivatives
\(f'_k(x)\) for each raw score,
ss_k1, ss_k2, ...: fitted (rounded) scale scores
from the polynomial of degree k,
cssem_k1, cssem_k2, ...: CSSEM values on
the scale-score metric, computed as \(f'_k(x)\,\mathrm{CSEM}_x\).
A data frame or matrix containing raw scores and their CSEM on the raw-score metric. It must have at least the following numeric columns:
x: raw scores,
csem: conditional standard errors of measurement on the
raw-score metric.
A data frame or matrix containing the score conversion table. It must have at least the following numeric columns:
x: raw scores (matching those in csemx),
ss: scale scores corresponding to each raw score.
Integer. Highest polynomial degree to fit. Defaults to 10.
Logical. If TRUE, a plot of the fitted polynomial curve
and the observed conversion points is produced for each degree k.
At the beginning of the function, csemx and ct are merged by
the x column (inner join) to create an internal data frame . Only
rows with x values present in both inputs are
used. The polynomial model is then fit to ss ~ poly(x, k, raw = TRUE)
for k = 1, ..., K.
data(ct.u)
cssem_polynomial(as.data.frame(csem_lord(40)), ct.u, K = 4, gra = TRUE)
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