  The paper is devoted to the consequences of blind random selection of items
from different item populations that might be based on completely uncorrelated
factors for item inter-correlations and corresponding factor loadings. Based on
the model of essentially parallel measurements, we explore the consequences of
presenting items from different populations across individuals and items from
identical populations within each individual for the factor model and item
inter-correlations in the total population of individuals. Moreover, we explore
the consequences of presenting items from different as well as identical item
populations across and within individuals. We show that correlations can be
substantial in the total population of individuals even when -- in
subpopulations of individuals -- items are drawn from populations with
uncorrelated factors. In order to address this challenge for the validity of a
scale, we propose a method that helps to detect whether item inter-correlations
result from different item populations in different subpopulations of
individuals and evaluate the method by means of a simulation study. Based on
the analytical results and on results from a simulation study, we provide
recommendations for the detection of subpopulations of individuals responding
to items from different item populations.
