Correlations and Non-Linear Probability Models

Richard Breen; Anders Holm; Kristian Bernt Karlson

doi:10.1177/0049124114544224

Correlations and Non-Linear Probability Models

Richard Breen, Anders Holm, Kristian Bernt Karlson

Sociologisk Institut

27 Citationer (Scopus)

2382 Downloads (Pure)

Abstract

Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models.

Originalsprog	Engelsk
Tidsskrift	Sociological Methods & Research
Vol/bind	43
Udgave nummer	4
Sider (fra-til)	571-605
Antal sider	35
ISSN	0049-1241
DOI	https://doi.org/10.1177/0049124114544224
Status	Udgivet - 12 nov. 2014

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T1 - Correlations and Non-Linear Probability Models

AU - Breen, Richard

AU - Holm, Anders

AU - Karlson, Kristian Bernt

PY - 2014/11/12

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N2 - Although the parameters of logit and probit and other nonlinear probability models (NLPMs) are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of NLPMs, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of NLPMs.

AB - Although the parameters of logit and probit and other nonlinear probability models (NLPMs) are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of NLPMs, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of NLPMs.

KW - Faculty of Social Sciences

KW - logit

KW - probit

KW - nonlinear probability models

KW - correlation

KW - group comparisons

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DO - 10.1177/0049124114544224

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VL - 43

SP - 571

EP - 605

JO - Sociological Methods & Research

JF - Sociological Methods & Research

IS - 4

ER -

Correlations and Non-Linear Probability Models

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