Quality & Quantity 33: 203–213, 1999.
© 1999 Kluwer Academic Publishers. Printed in the Netherlands.
Modeling Item Nonresponse in Questionnaires
PHILIP HANS FRANSES
, IRMA GELUK
and PAUL VAN HOMELEN
Econometric Institute, Erasmus University Rotterdam, PO Box 1738, NL-3000 DR Rotterdam, The
Institute for Research and Investment Services, ROBECO–RaboBank
Abstract. The statistical analysis of empirical questionnaire data can be hampered by the fact that
not all questions are answered by all individuals. In this paper we propose a simple practical method
to deal with such item nonresponse in case of ordinal questionnaire data, where we assume that item
nonresponse is caused by an incomplete set of answers between which the individuals are supposed to
choose. Our statistical method is based on extending the ordinal regression model with an additional
category for nonresponse, and on investigating whether this extended model describes and forecasts
the data well. We illustrate our approach for two questions from a questionnaire held amongst a
sample of clients of a ﬁnancial investment company.
Key words: ordered regression, item nonresponse.
1. Introduction and Motivation
Attitude questionnaires often concern a set of Q questions, which can be answered
by A answers. Frequently, Q can be as large as 25, and A often takes the value
of 3, 4, 5 or 7. For each question, N individuals are asked to mark one of the A
possible answers. Sometimes these answers correspond with degrees of agreement,
that is, for example, when A = 5, answer 1 corresponds with “strongly agree” and
answer 5 with “strongly disagree’ In other cases the answers can correspond with
explicitly stated attitudes, that is, for example, when A = 3, answer 1 corresponds
with “I invest in those products which are advised to me by a ﬁnancial consultant”
and answer 3 with “I actively follow international ﬁnancial developments and I
make my own choices”. Our application in Section 4 deals with questionnaire data
of the latter type, but our statistical method can also be applied to data of the ﬁrst
type. The answers are often measured on an ordinal scale, that is, one can rank
the answers from 1 to A with A having a higher rank. For example, in the A =
3 example above, answer 3 corresponds with an active investor, while answer 1
matches with an inactive investor.
When Q becomes large, it is frequently encountered in practice that not all
N individuals give answers to all Q questions. Hence, one encounters missing
data. Additionally, it is often observed that there is item nonresponse, see Little
Author for correspondence. This paper was mainly written while the ﬁrst author was enjoying
the kind hospitality of ROBECO, Rotterdam.