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

Department of Sociology

27 Citations (Scopus)

2382 Downloads (Pure)

Abstract

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.

Original language	English
Journal	Sociological Methods & Research
Volume	43
Issue number	4
Pages (from-to)	571-605
Number of pages	35
ISSN	0049-1241
DOIs	https://doi.org/10.1177/0049124114544224
Publication status	Published - 12 Nov 2014

Keywords

Faculty of Social Sciences
logit
probit
nonlinear probability models
correlation
group comparisons

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Correlations and non-linear probability models (SMR 2014, 43)Accepted author manuscript, 320 KBLicence: Unspecified

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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

Y1 - 2014/11/12

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

U2 - 10.1177/0049124114544224

DO - 10.1177/0049124114544224

M3 - Journal article

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VL - 43

SP - 571

EP - 605

JO - Sociological Methods and Research

JF - Sociological Methods and Research

IS - 4

ER -

Correlations and Non-Linear Probability Models

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Keywords

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