Abstract
Since computer programs have been available for estimating and testing linear causal models (e.g. LISREL by Jöreskog & Sörbom) these models have been used increasingly in the behavioral sciences. This paper discusses the problem that very different causal structures may fit the same set of data equally well. Equivalence of models is defined as undecidability in principle and four rules are presented showing how equivalent models may be generated. Rules I and II refer to inversions in the causal order of variables and Rules III and IV to replacements of paths by the assumption of correlated residuals. Three examples are given to illustrate how the rules are applied.
Keywords
LISRELCausal modelEquivalence (formal languages)Causal inferenceSet (abstract data type)EconometricsComputer scienceMathematicsPath (computing)StatisticsStructural equation modelingDiscrete mathematics
Affiliated Institutions
Related Publications
Causal Inference, Path Analysis, and Recursive Structural Equations Models
Rubin's model for causal inference in experiments and observational studies is enlarged to analyze the problem of “causes causing causes” and is compared to path analysis and re...
Theory, Deduction, and Rules of Correspondence
Causal models are strictly untestable with a single indicator for each variable, unless one assumes very slight measurement error. With multiple indicators for each variable, in...
Principles of confounder selection
Abstract Selecting an appropriate set of confounders for which to control is critical for reliable causal inference. Recent theoretical and methodological developments have help...
A tetrad test for causal indicators.
The authors propose a confirmatory tetrad analysis test to distinguish causal from effect indicators in structural equation models. The test uses "nested" vanishing tetrads that...
In Search of Golden Rules: Comment on Hypothesis-Testing Approaches to Setting Cutoff Values for Fit Indexes and Dangers in Overgeneralizing Hu and Bentler's (1999) Findings
Abstract Goodness-of-fit (GOF) indexes provide "rules of thumb"—recommended cutoff values for assessing fit in structural equation modeling. Hu and Bentler (1999) proposed a mor...
Publication Info
- Year
- 1986
- Type
- article
- Volume
- 21
- Issue
- 3
- Pages
- 309-331
- Citations
- 192
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
192
OpenAlex
Cite This
Ingeborg Stelzl
(1986).
Changing a Causal Hypothesis without Changing the Fit: some Rules for Generating Equivalent Path Models.
Multivariate Behavioral Research
, 21
(3)
, 309-331.
https://doi.org/10.1207/s15327906mbr2103_3
Identifiers
- DOI
- 10.1207/s15327906mbr2103_3