Quality & Quantity 34: 177–191, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Latent Class Analysis of Respondent Scalability
G. VAN DEN WITTENBOER
and E. D. DE LEEUW
Department of Education, University of Amsterdam;
Abstract. The psychometric literature contains many indices to detect aberrant respondents. A
different, promising approach is using ordered latent class analysis with the goal to distinguish latent
classes of respondents that are scalable, from latent classes of respondents that are not scalable (i.e.,
aberrant) according to the scaling model adopted. This article examines seven Latent Class models
for a cumulative scale. A simulation study was performed to study the efﬁcacy of different models
for data that follow the scale model perfectly. A second simulation study was performed to study
how well these models detect aberrant respondents.
Key words: latent class analysis, person ﬁt research, measurement error, respondent error.
Four well-known sources of measurement error in surveys are the questionnaire
(e.g., question wording), the data collection mode (e.g., face to face or telephone
interviews), the interviewer, and the respondent (Groves, 1989). Unlike the ﬁrst
three sources of measurement error (questionnaire, mode, interviewer), the fourth
error source (respondent) is difﬁcult to minimize. Respondents can be instructed
in what is expected from them (e.g., think carefully, use the answer categories pro-
vided) and they may be motivated to do their best. But it is difﬁcult to manipulate a
respondent to reduce the respondent error. Therefore, research on respondent errors
has concentrated on attempts to identify those respondents who produce errors and
search for their unique properties.
An important problem in this type of research is how to measure respondent er-
ror. Groves (1989: 445–446) summarizes this as follows: “Measurement errors are
generally viewed as speciﬁc to a particular measure, one question posed to the re-
spondent. Only by identifying response tendencies of respondents over many ques-
tions can inference about respondent inﬂuences on measurement error be made.
Then only by comparing different respondents on the same task can characteristics
of the respondents which produce measurement error be identiﬁed”.
One promising approach is the application of person ﬁt indices to detect incon-
sistent respondents (Meijer and De Leeuw, 1993; Meijer, 1994; De Leeuw and Hox,
Author for correspondence: Department of Education, University of Amsterdam, Wibautstraat
4, NL 1091 GM Amsterdam, The Netherlands, phone: + 31 20 5251529; fax: +31 20 5251200;