A Box-Cox normal model for response times
article
The log-transform has been a convenient choice in response time modelling on test
items. However, motivated by a dataset of the Medical College Admission Test where
the lognormal model violated the normality assumption, the possibilities of the broader
class of Box–Cox transformations for response time modelling are investigated. After
an introduction and an outline of a broader framework for analysing responses and
response times simultaneously, the performance of a Box–Cox normal model for
describing response times is investigated using simulation studies and a real data
example. A transformation-invariant implementation of the deviance information
criterium (DIC) is developed that allows for comparing model fit between models with
different transformation parameters. Showing an enhanced description of the shape of
the response time distributions, its application in an educational measurement context
is discussed at length.
items. However, motivated by a dataset of the Medical College Admission Test where
the lognormal model violated the normality assumption, the possibilities of the broader
class of Box–Cox transformations for response time modelling are investigated. After
an introduction and an outline of a broader framework for analysing responses and
response times simultaneously, the performance of a Box–Cox normal model for
describing response times is investigated using simulation studies and a real data
example. A transformation-invariant implementation of the deviance information
criterium (DIC) is developed that allows for comparing model fit between models with
different transformation parameters. Showing an enhanced description of the shape of
the response time distributions, its application in an educational measurement context
is discussed at length.
TNO Identifier
461989
Source
British Journal of Mathematical and Statistical Psychology, 62, pp. 621-640.
Pages
621-640
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