A note on the relationship between the number of indicators and their reliability in detecting regression coefficients in latent regression analysis

Conor V. Dolan; Jelte M. Wicherts; Peter C.M. Molenaar

doi:10.1207/s15328007sem1102_4

A note on the relationship between the number of indicators and their reliability in detecting regression coefficients in latent regression analysis

Conor V. Dolan, Jelte M. Wicherts, Peter C.M. Molenaar

Human Development and Family Studies

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators always results in an increase in the coefficient of determination and so in the power. We note that the coefficient of determination plays a similar role in determining the error variance of predicted factor scores.

Original language	English (US)
Pages (from-to)	210-216
Number of pages	7
Journal	Structural Equation Modeling
Volume	11
Issue number	2
DOIs	https://doi.org/10.1207/s15328007sem1102_4
State	Published - 2004

All Science Journal Classification (ASJC) codes

General Decision Sciences
General Economics, Econometrics and Finance
Sociology and Political Science
Modeling and Simulation

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title = "A note on the relationship between the number of indicators and their reliability in detecting regression coefficients in latent regression analysis",

abstract = "We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators always results in an increase in the coefficient of determination and so in the power. We note that the coefficient of determination plays a similar role in determining the error variance of predicted factor scores.",

author = "Dolan, {Conor V.} and Wicherts, {Jelte M.} and Molenaar, {Peter C.M.}",

note = "Funding Information: This work was supported by a grant from the Netherlands Organization for Scientific Research (NWO). We thank Raoul Grasman for his help with the matrix algebra. We thank Wim Krijnen for feedback and encouragement. We thank Tenko Raykov for pointing out that Equation 6 represents an approximation of λ (a point we had glossed over in a previous version).",

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doi = "10.1207/s15328007sem1102_4",

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T1 - A note on the relationship between the number of indicators and their reliability in detecting regression coefficients in latent regression analysis

AU - Dolan, Conor V.

AU - Wicherts, Jelte M.

AU - Molenaar, Peter C.M.

N1 - Funding Information: This work was supported by a grant from the Netherlands Organization for Scientific Research (NWO). We thank Raoul Grasman for his help with the matrix algebra. We thank Wim Krijnen for feedback and encouragement. We thank Tenko Raykov for pointing out that Equation 6 represents an approximation of λ (a point we had glossed over in a previous version).

PY - 2004

Y1 - 2004

N2 - We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators always results in an increase in the coefficient of determination and so in the power. We note that the coefficient of determination plays a similar role in determining the error variance of predicted factor scores.

AB - We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators always results in an increase in the coefficient of determination and so in the power. We note that the coefficient of determination plays a similar role in determining the error variance of predicted factor scores.

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JO - Structural Equation Modeling

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IS - 2

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A note on the relationship between the number of indicators and their reliability in detecting regression coefficients in latent regression analysis

Abstract

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