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A heteroscedastic generalized linear model with a non‐normal speed factor for responses and response times
Author(s) -
Molenaar Dylan,
Bolsinova Maria
Publication year - 2017
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12087
Subject(s) - homoscedasticity , heteroscedasticity , normality , mathematics , linear model , normal distribution , distribution (mathematics) , statistics , residual , econometrics , algorithm , mathematical analysis
In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non‐normality in the transformed response times. Most importantly, we distinguish between non‐normality due to heteroscedastic residual variances, and non‐normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set.