### Abstract

External misspecification, the omission of key variables from a structural model, can fundamentally alter the inferences one makes without such variables present. This article presents 2 strategies for dealing with omitted variables, the first a fixed parameter approach incorporating the omitted variable into the model as a phantom variable where all associated parameter values are fixed, and the other a random parameter approach specifying prior distributions for all of the phantom variable's associated parameter values under a Bayesian framework. The logic and implementation of these methods are discussed and demonstrated on an applied example from the educational psychology literature. The argument is made that such external misspecification sensitivity analyses should become a routine part of measured and latent variable modeling where the inclusion of all salient variables might be in question.

Original language | English (US) |
---|---|

Pages (from-to) | 616-631 |

Number of pages | 16 |

Journal | Psychological Methods |

Volume | 22 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2017 |

Externally published | Yes |

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### Keywords

- Bayesian analysis
- external misspecification
- phantom variables
- structural equation modeling

### ASJC Scopus subject areas

- Psychology (miscellaneous)

### Cite this

*Psychological Methods*,

*22*(4), 616-631. https://doi.org/10.1037/met0000103

**Using Phantom Variables in Structural Equation Modeling to Assess Model Sensitivity to External Misspecification.** / Harring, Jeffrey R.; McNeish, Daniel; Hancock, Gregory R.

Research output: Contribution to journal › Article

*Psychological Methods*, vol. 22, no. 4, pp. 616-631. https://doi.org/10.1037/met0000103

}

TY - JOUR

T1 - Using Phantom Variables in Structural Equation Modeling to Assess Model Sensitivity to External Misspecification

AU - Harring, Jeffrey R.

AU - McNeish, Daniel

AU - Hancock, Gregory R.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - External misspecification, the omission of key variables from a structural model, can fundamentally alter the inferences one makes without such variables present. This article presents 2 strategies for dealing with omitted variables, the first a fixed parameter approach incorporating the omitted variable into the model as a phantom variable where all associated parameter values are fixed, and the other a random parameter approach specifying prior distributions for all of the phantom variable's associated parameter values under a Bayesian framework. The logic and implementation of these methods are discussed and demonstrated on an applied example from the educational psychology literature. The argument is made that such external misspecification sensitivity analyses should become a routine part of measured and latent variable modeling where the inclusion of all salient variables might be in question.

AB - External misspecification, the omission of key variables from a structural model, can fundamentally alter the inferences one makes without such variables present. This article presents 2 strategies for dealing with omitted variables, the first a fixed parameter approach incorporating the omitted variable into the model as a phantom variable where all associated parameter values are fixed, and the other a random parameter approach specifying prior distributions for all of the phantom variable's associated parameter values under a Bayesian framework. The logic and implementation of these methods are discussed and demonstrated on an applied example from the educational psychology literature. The argument is made that such external misspecification sensitivity analyses should become a routine part of measured and latent variable modeling where the inclusion of all salient variables might be in question.

KW - Bayesian analysis

KW - external misspecification

KW - phantom variables

KW - structural equation modeling

UR - http://www.scopus.com/inward/record.url?scp=85038628027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038628027&partnerID=8YFLogxK

U2 - 10.1037/met0000103

DO - 10.1037/met0000103

M3 - Article

C2 - 29265846

AN - SCOPUS:85038628027

VL - 22

SP - 616

EP - 631

JO - Psychological Methods

JF - Psychological Methods

SN - 1082-989X

IS - 4

ER -