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Expected versus observed information in SEM with incomplete normal and nonnormal data.

Victoria Savalei¹

¹Department of Psychology, University of British Columbia, 2136West Mall, Vancouver, British Columbia V6T 1Z4, Canada. vsavalei@psych.ubc.ca

Psychological Methods

|September 22, 2010

Summary

This summary is machine-generated.

For structural equation modeling with missing data, using observed information is crucial for accurate standard errors, especially with nonnormal data. Expected information can lead to inconsistent results in these scenarios.

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Area of Science:

Statistics
Psychometrics
Quantitative Psychology

Background:

Maximum likelihood estimation is standard in structural equation modeling (SEM).
Standard errors in SEM rely on information matrices, estimated via expected or observed information.
Consistency of estimates is known for complete data but differs with incomplete data.

Purpose of the Study:

To investigate the impact of using observed versus expected information for standard errors and test statistics in SEM.
To compare performance under conditions of normal and nonnormal data with missingness.
To provide recommendations for researchers and software developers regarding information matrix estimation.

Main Methods:

The study involved two simulation studies.
Data conditions included complete vs. incomplete (missing at random - MAR) and normal vs. nonnormal distributions.
Evaluated the consistency and accuracy of standard errors and test statistics derived from observed and expected information matrices.

Main Results:

With missing at random (MAR) data, standard errors based on expected information are not consistent.
Nonnormality further complicates robust computations when using the estimated information matrix.
Observed information consistently outperformed expected information across all simulated conditions.

Conclusions:

Observed information is the preferred method for estimating standard errors and test statistics in SEM, particularly with MAR and nonnormal data.
The use of expected information can lead to incorrect robust computations in these complex data scenarios.
Recommendations emphasize the adoption of observed information for improved accuracy and reliability in SEM analyses.