Spurious Latent Classes in the
Mixture Rasch Model
7/12/2011
Introduction
• Mixture IRT models offer the information not
captured by traditional single class IRT models.
• When model assumptions are violated, more
complex models may be preferred.
• Overextraction of latent classes may occur
frequently and may lead to misinterpretation
of the results.
Mixture Rasch model
p(x | )    g p(x | , g )
g
I
exp( xi (  ig ))
i 1
1  exp( xi (  ig ))
p(x | , g )  
The BIC has been found to be more accurate than other
statistical indices.
Using a Mixture Rasch Model on 2PL Data
• Why do a two-class MRM fit the data better?
• Fixed or variant mixed proportion?
How Many Non-Rasch Items Would Be
needed to Cause a Spurious Class to Form
Do Two Classes in a Mixture Rasch Model
Always Collapse into One Class in 2PL?
• Two-class Rasch and 2PL models always had a
smaller BIC than one-class models.
An Example
• Grade 8 mathematics test with 30
dichotomous items
• Twenty samples of 3000 examinees were
randomly drawn from the original dataset.
• WINMIRA 2001
Discussion
• The findings of three simulation studies
• There is high potential of detecting spurious
latent classes if the wrong model is applied.
• Further studies