Revisiting the evidence for cardinal treatment of ordinal variables

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in SOEPpapers on Multidisciplinary Panel Data Research at DIW BerlinThis series presents research findings based either directly on data from the German SocioEconomic Panel study (SOEP) or using SOEP data as part of an internationally comparable data set (e.g. CNEF, ECHP, LIS, LWS, CHER/PACO). SOEP is a truly multidisciplinary household panel study covering a wide range of social and behavioral sciences: economics, sociology, psychology, survey methodology, econometrics and applied statistics, educational science, political science, public health, behavioral genetics, demography, geography, and sport science.The decision to publish a submission in SOEPpapers is made by a board of editors chosen by the DIW Berlin to represent the wide range of disciplines covered by SOEP. There is no external referee process and papers are either accepted or rejected without revision. Papers appear in this series as works in progress and may also appear elsewhere. They often represent preliminary studies and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be requested from the author directly.Any opinions expressed in this series are those of the author(s) and not those of DIW Berlin.Research disseminated by DIW Berlin may include views on public policy issues, but the institute itself takes no institutional policy positions. The most common practice-comparing well-being by means of descriptive analysis or linear regressions-ignores that the underlying collected well-being information is ordinal. If the well-being function is ordinal, then monotonic transformations are allowed. We demonstrate that treating ordinal data by methods intended to be used for cardinal data may give an incorrect impression of a robust result. Particularly, we derive the conditions under which the use of cardinal method to an ordinal variable gives an illusionary sense of robustness, while in fact one can reverse the conclusion reached by using an alternative cardinal assumption. The paper provides empirical applications.

Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth About Happiness Scales

“…There are serious practical consequences when the ordinal nature of data is not respected. Schröder and Yitzhaki (2017) Without any rebuttal, much of the mean comparison results that form the basis of empirical studies in the happiness literature appear to have no empirical content. By exploiting the fact that the mean and median of symmetric distributions are identical, we show prior results from parametric ordered response models can still be useful if we focus on the median instead of the mean.…”

“…The results in Schröder and Yitzhaki (2017) and BL indicate that the stochastic order conditions needed to justify how SWB researchers currently go about analyzing SWB data are usually not…”

“…The third is to promote the use of median regression for categorical ordered data within economics and other social sciences. The last goal is important because the statistical reasonings behind the results in Schröder and Yitzhaki (2017) and BL apply to all categorical ordered data that can also be relevant to non-economists.…”

“…5The wide spread and growing use of OLS to analyze ordinal dependent variables have received some critical attentions recently. In economics of well-being,Schröder and Yitzhaki (2017) highlight that though results from linear regression and ordinal models may appear similar, many implications of SWB analysis using linear regression framework can be overturned by changing the ordinal scale.Liddell and Kruschke (2018) provide a similar conclusion for the research in psychology. Both papers suggest researchers to use ordered response models instead of the OLS to avoid arbitrariness of the ordinal scale.…”

Redefining Well-Being in Nations and Organizations

“…The person does not have to think whether a response of '4' is an absolute representation of satisfaction at a certain level compared to a 2. These kinds of ordinal measures (for example, satisfaction of '4' is higher than '3' but necessarily exactly 25% higher) cannot be used for many kinds of statistical analysis, particularly comparative analyses (Schröder & Yitzhaki 2015). If I give a score of 4 for my satisfaction and you give a 2, it does not mean that I am necessarily exactly twice as satisfied as you.…”