Model Fit in Structural Equation Models with Censored, Ordinal, and Dichotomous Variables
Testing Vanishing Tetrads
Bibliographic Data
| ID | 8019786 |
|---|---|
| Authors | J R Hipp (0000-0001-9006-2587, University of North Carolina at Chapel Hill), K A Bollen (0000-0002-6710-3800, University of North Carolina at Chapel Hill) |
| Year | 2003 |
| Volume | 33 |
| Issue | 1 |
| Pages | 267-305 |
| Publication date | 2003-08-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Sociological Methodology (JOURNAL) |
| Journal identifiers | ISSN: 0081-1750 • E-ISSN: 1467-9531 |
| Publisher | SAGE Publishing (PUBLISHER • US) |
| DOI | 10.1111/j.0081-1750.2003.00133.x |
| OpenAlex | W2099948111 |
| Language | EN |
| Citations received | 8 |
| References cited | 40 |
Although the methodology for handling ordinal and dichotomous observed variables in structural equation models (SEMs) is developing rapidly, several important issues are unresolved. One of these is the optimal test statistic to apply as a test of overall model fit. We propose a new “vanishing tetrad” test statistic for such models. We build on Bollen's (1990) simultaneous test statistic for testing multiple vanishing tetrads and on Bollen and Ting's (1993) confirmatory tetrad analysis (CTA) for hypothesis testing of model structures. These and other works on vanishing tetrads assume continuous observed variables and do not consider observed categorical variables. In this paper we present a method to test models when some or all of the observed variables are collapsed or categorical versions of underlying continuous variables. The test statistic that we provide is an alternative “overall fit” statistic for SEMs with censored, ordinal, or dichotomous observed variables. Furthermore, the vanishing tetrad test sometimes permits us to compare the fit of some models that are not nested in the traditional likelihood ratio test. We illustrate the new test statistic with examples and a small simulation experiment comparing it with two other tests of model fit for SEMs with ordinal or dichotomous endogenous variables
Categorical variable · Econometrics · Ordinal data · Statistic · Statistical hypothesis testing · Statistics · Structural equation modeling · Test statistic · Tetrad · Crime Patterns and Interventions · Mathematics · Qualitative Comparative Analysis Research
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| Unique citing works | 8 |
|---|---|
| Citations per year | 0,38 |
| Citation span | 2005 - 2021 (17) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 8 |