Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

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Abstract

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.

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Authors: Claes Fornell (University of Michigan); David F. Larcker iD (Northwestern University)
Published in: Journal of Marketing Research, vol. 18, no. 1, pp. 39
Publication date:01/02/1981
Publisher:SAGE Publishing
Document type:Article
Language:English
DOI: 10.1177/002224378101800104
ISSN:0022-2437, 1547-7193
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Cited by:108,728
Subjects:
Psychometric Methodologies and Testing (Social Sciences > Decision Sciences > Management Science and Operations Research)
Statistical Methods and Applications (Physical Sciences > Mathematics > Statistics and Probability)
Statistical Methods and Bayesian Inference (Physical Sciences > Mathematics > Statistics and Probability)
structural equation modeling, model fit assessment, chi-square test, measurement error, latent variables, type II error, shared variance, measurement model, explanatory power, sample size
Identifiers: OpenAlex W4235678817

Central index data: OpenAlex (CC0 license).

Summary:The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.
ISSN:0022-2437
1547-7193
DOI:10.1177/002224378101800104