"I would like to analyze the underlying structure of a specific
outcome instrument. What should I do first, a Rasch analysis or a
factor analysis, or do I need to analyze my data both ways?"
Liliane Ryser
Rasch analysis constructs an interval variable from the dominant dimension (factor) in the data. This dominant dimension may be a hybrid, e.g., if a test has both reading and math items, then the dominant factor will reflect a composite reading-math competency. Lesser dimensions are reported as misfit. This off-dimensional behavior can be investigated by a factor analysis of residuals (Principal Components Analysis, PCA, of residuals) of those parts of the observations not explained by the Rasch dimension. That would separate reading and math items (RMT 10:3 p. 509).
Leaping first into a factor analysis of the original observations
is prone to misleading results.
(a) Since observations are non-linear,
they can generate illusory factors.
(b) Factor analysis
usually reports items clustering at different performance levels as
different factors (RMT 8:1 p. 347). There is no way of knowing
from factor analysis alone whether each factor is a dimension or a
slice of a shared dimension.
Linacre J.M. (1998) Rasch First or Factor First? Rasch Measurement Transactions 11:4 p. 603.
Rasch First or Factor First? Linacre J.M. … Rasch Measurement Transactions, 1998, 11:4 p. 603.
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