On a law of ordinal error

David Andrich, Pender Pedler

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

When no systematic factor disturbs replicated measurements of the same entity with the same instrument, the observed or inferred distribution is expected to satisfy the Gaussian law of measurement error. A characteristic of this distribution, which ensures it is unimodal with a smooth transition between adjacent probabilities, is that it is strictly log-concave. Many assessments in the social sciences begin by analogy to measurements in that an idealised linear continuum is partitioned by successive thresholds into contiguous, ordered categories. However, the distances between successive thresholds, generally finite, are not equal and assessments remain ordinal. The paper establishes that if the thresholds in the probabilistic Rasch measurement model used to transform ordinal assessments into measurements are in their natural order, then the distribution is also strictly log-concave. Therefore it is proposed that the Rasch model with ordered thresholds be referred to as the law of ordinal error. Accordingly, by analogy to the expectation that the distribution of replicated measurements satisfy the law of measurement error, it is proposed that the observed or inferred distribution of replicated ordinal assessments be expected to satisfy the proposed law of ordinal error.

Original languageEnglish
Article number012055
JournalJournal of Physics: Conference Series
Volume1044
Issue number1
DOIs
Publication statusPublished - 18 Jun 2018
Event2017 Joint IMEKO TC1-TC7-TC13 Symposium: Measurement Science Challenges in Natural and Social Sciences - Rio de Janeiro, Brazil
Duration: 31 Jul 20173 Aug 2017

Fingerprint

thresholds
continuums

Cite this

Andrich, David ; Pedler, Pender. / On a law of ordinal error. In: Journal of Physics: Conference Series. 2018 ; Vol. 1044, No. 1.
@article{b1c893e8422340babd0032618e9f8c65,
title = "On a law of ordinal error",
abstract = "When no systematic factor disturbs replicated measurements of the same entity with the same instrument, the observed or inferred distribution is expected to satisfy the Gaussian law of measurement error. A characteristic of this distribution, which ensures it is unimodal with a smooth transition between adjacent probabilities, is that it is strictly log-concave. Many assessments in the social sciences begin by analogy to measurements in that an idealised linear continuum is partitioned by successive thresholds into contiguous, ordered categories. However, the distances between successive thresholds, generally finite, are not equal and assessments remain ordinal. The paper establishes that if the thresholds in the probabilistic Rasch measurement model used to transform ordinal assessments into measurements are in their natural order, then the distribution is also strictly log-concave. Therefore it is proposed that the Rasch model with ordered thresholds be referred to as the law of ordinal error. Accordingly, by analogy to the expectation that the distribution of replicated measurements satisfy the law of measurement error, it is proposed that the observed or inferred distribution of replicated ordinal assessments be expected to satisfy the proposed law of ordinal error.",
author = "David Andrich and Pender Pedler",
year = "2018",
month = "6",
day = "18",
doi = "10.1088/1742-6596/1044/1/012055",
language = "English",
volume = "1044",
journal = "Journal of Physics: Conference Series (Print)",
issn = "1742-6588",
publisher = "IOP Publishing",
number = "1",

}

On a law of ordinal error. / Andrich, David; Pedler, Pender.

In: Journal of Physics: Conference Series, Vol. 1044, No. 1, 012055, 18.06.2018.

Research output: Contribution to journalConference article

TY - JOUR

T1 - On a law of ordinal error

AU - Andrich, David

AU - Pedler, Pender

PY - 2018/6/18

Y1 - 2018/6/18

N2 - When no systematic factor disturbs replicated measurements of the same entity with the same instrument, the observed or inferred distribution is expected to satisfy the Gaussian law of measurement error. A characteristic of this distribution, which ensures it is unimodal with a smooth transition between adjacent probabilities, is that it is strictly log-concave. Many assessments in the social sciences begin by analogy to measurements in that an idealised linear continuum is partitioned by successive thresholds into contiguous, ordered categories. However, the distances between successive thresholds, generally finite, are not equal and assessments remain ordinal. The paper establishes that if the thresholds in the probabilistic Rasch measurement model used to transform ordinal assessments into measurements are in their natural order, then the distribution is also strictly log-concave. Therefore it is proposed that the Rasch model with ordered thresholds be referred to as the law of ordinal error. Accordingly, by analogy to the expectation that the distribution of replicated measurements satisfy the law of measurement error, it is proposed that the observed or inferred distribution of replicated ordinal assessments be expected to satisfy the proposed law of ordinal error.

AB - When no systematic factor disturbs replicated measurements of the same entity with the same instrument, the observed or inferred distribution is expected to satisfy the Gaussian law of measurement error. A characteristic of this distribution, which ensures it is unimodal with a smooth transition between adjacent probabilities, is that it is strictly log-concave. Many assessments in the social sciences begin by analogy to measurements in that an idealised linear continuum is partitioned by successive thresholds into contiguous, ordered categories. However, the distances between successive thresholds, generally finite, are not equal and assessments remain ordinal. The paper establishes that if the thresholds in the probabilistic Rasch measurement model used to transform ordinal assessments into measurements are in their natural order, then the distribution is also strictly log-concave. Therefore it is proposed that the Rasch model with ordered thresholds be referred to as the law of ordinal error. Accordingly, by analogy to the expectation that the distribution of replicated measurements satisfy the law of measurement error, it is proposed that the observed or inferred distribution of replicated ordinal assessments be expected to satisfy the proposed law of ordinal error.

UR - http://www.scopus.com/inward/record.url?scp=85049535280&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1044/1/012055

DO - 10.1088/1742-6596/1044/1/012055

M3 - Conference article

VL - 1044

JO - Journal of Physics: Conference Series (Print)

JF - Journal of Physics: Conference Series (Print)

SN - 1742-6588

IS - 1

M1 - 012055

ER -