tetrachoric correlation coefficient

　

WordNet

1. a correlation coefficient computed for two normally distributed variables that are both expressed as a dichotomy (同)tetrachoric correlation
2. a reciprocal relation between two or more things (同)correlativity
3. a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other (同)correlational statistics
4. a constant number that serves as a measure of some property or characteristic

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1. 〈C〉(…間の)相互関係《+『between』+『名』》;(…との)関連《+『with』+『名』》 / 〈U〉《文》関連させること;相関関係にある状態 / 〈C〉相関グラフ
2. (数学で)係数,(物理で)係数,率

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/06/12 01:47:31」(JST)

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In statistics, polychoric correlation is a technique for estimating the correlation between two theorised normally distributed continuous latent variables, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are dichotomous. These names derive from the polychoric and tetrachoric series, mathematical expansions once, but no longer, used for estimation of these correlations.

Applications and examples

This technique is frequently applied when analysing items on self-report instruments such as personality tests and surveys that often use rating scales with a small number of response options (e.g., strongly disagree to strongly agree). The smaller the number of response categories, the more a correlation between latent continuous variables will tend to be attenuated. Lee, Poon & Bentler (1995) have recommended a two-step approach to factor analysis for assessing the factor structure of tests involving ordinally measured items. This aims to reduce the effect of statistical artifacts, such as the number of response scales or skewness of variables leading to items grouping together in factors.

Software

• polycor package in R by John Fox[1]
• psych package in R by William Revelle[2]
• PRELIS
• POLYCORR program
• An extensive list of software for computing the polychoric correlation, by John Uebersax [3]

References

• Lee, S.-Y., Poon, W. Y., & Bentler, P. M. (1995). "A two-stage estimation of structural equation models with continuous and polytomous variables". British Journal of Mathematical and Statistical Psychology, 48, 339–358.

• Bonett, D. G., & Price R. M. (2005). "Inferential Methods for the Tetrachoric Correlation Coefficient". Journal of Educational and Behavioral Statistics, 30, 213.

External links

• The Tetrachoric and Polychoric Correlation Coefficients

UpToDate Contents

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English Journal

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• Sawicki GS1, Garvey KC2, Toomey SL3, Williams KA4, Chen Y5, Hargraves JL6, Leblanc J6, Schuster MA3, Finkelstein JA3.
• The Journal of adolescent health : official publication of the Society for Adolescent Medicine.J Adolesc Health.2015 Sep;57(3):282-7. doi: 10.1016/j.jadohealth.2015.06.004.
• PURPOSE: Significant gaps exist in health care transition (HCT) preparation that can impact care and outcomes in young adults with chronic illness. No quality measure exists to directly assess adolescent experiences of HCT preparation. Our objective was to develop an adolescent-reported measure of t
• PMID 26299555

• Combined evaluation of adenosine deaminase level and histopathological findings from pleural biopsy with Cope's needle for the diagnosis of tuberculous pleurisy.

• Behrsin RF1, Junior CT2, Cardoso GP2, Barillo JL3, de Souza JB3, de Araújo EG3.
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• INTRODUCTION: Closed needle pleural biopsy (CNPB) has historically been the gold standard procedure for the diagnosis of pleural tuberculosis. Adenosine deaminase (ADA) is an efficient biomarker for tuberculosis that is measurable in pleural fluids.OBJECTIVE: We compared the diagnostic accuracy of t
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• CFA with binary variables in small samples: a comparison of two methods.

• Savalei V1, Bonett DG2, Bentler PM3.
• Frontiers in psychology.Front Psychol.2015 Jan 7;5:1515. doi: 10.3389/fpsyg.2014.01515. eCollection 2014.
• Asymptotically optimal correlation structure methods with binary data can break down in small samples. A new correlation structure methodology based on a recently developed odds-ratio (OR) approximation to the tetrachoric correlation coefficient is proposed as an alternative to the LPB approach prop
• PMID 25709585

Japanese Journal

• 四分相関係数の分布に関する漸近展開(一般セッション 数学・統計(1))

• 小笠原 春彦
• 日本行動計量学会大会発表論文抄録集 39, 209-210, 2011-09-11
• … Accurate distributions of the estimator of the tetrachoric correlation coefficient and, more generally, functions of sample proportions for the 2 by 2 contingency table are derived. … Numerical examples were used to illustrate advantages of the studentized estimator of Fisher's z transformation of the tetrachoric correlation coefficient. …
• NAID 110009573190

• プロスペクト理論における「リスク追求」傾向のIRTによる尺度化の試み

• 豊田 秀樹,川端 一光,中村 健太郎
• 教育心理学研究 55(2), 161-169, 2007-06-30
• 行動ファイナンスの領域で代表的なバイアス質問を利用した,リスク追求傾向に関する尺度構成が試みられた。401名の被験者の項目への回答比率の分析から,大半の項目がプロスペクト理論によって説明が可能であることが明らかになり,項目間の四分相関係数の検討により,項目が測定している尺度が「リスク追求」の次元であることが明らかになった。同データの探索的カテゴリカル因子分析の結果から,項目が測定する次元数は1であ …
• NAID 110006343689

• 項目応答理論による全部床義歯装着者を対象とした咀嚼能力検査表の開発

• 竹内 一夫
• 日本補綴歯科學會雜誌 = The journal of the Japan Prosthodontic Society 42(6), 961-971, 1998-12-10
• … Forty-one items showed unidimensionality based on principal factor analysis of the tetrachoric correlation matrix, except 17 items whose proportions of correct answers were above 0.90.<BR>2. … The KR-20 coefficient of the scale was 0.83.<BR>5. …
• NAID 10008171443

Related Links

• The Tetrachoric and Polychoric Correlation Coefficients

Pros and Cons: Tetrachoric and Polychoric Correlation Coefficients Pros: These statistics express rater association in a familiar form--a correlation coefficient. They provide a way to separately quantify association and similarity of ...

• Application of tetrachoric and polychoric correlation ...

Original scientific paper UDC 551.501.45 Application of tetrachoric and polychoric correlation coefficients to forecast verification Josip Juras and Zoran Pasari} Department of Geophysics, Faculty of Science, University of Zagreb ...

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