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COMPARING LATENT INTERACTION EFFECTS IN MULTI-SAMPLE STRUCTURAL EQUATION MODELING: QUASI-MAXIMUM LIKELIHOOD VERSUS THIRD MOMENT METHODS

Pohlig, Ryan T. (2013) COMPARING LATENT INTERACTION EFFECTS IN MULTI-SAMPLE STRUCTURAL EQUATION MODELING: QUASI-MAXIMUM LIKELIHOOD VERSUS THIRD MOMENT METHODS. Doctoral Dissertation, University of Pittsburgh.

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    Abstract

    A simulation study was performed comparing the quasi-maximum likelihood (QML; Klein & Muthén, 2007) and third moment (Mooijaart & Bentler, 2010) methods for estimating latent interaction effects in multi-sample structural equation modeling. Both of these methods estimate latent interaction effects without the use of product indicators or the need to specify nonlinear constraints. The purpose of this study was to evaluate the power and type-I error rates for testing group differences of a latent interaction effect. This study also evaluated the parameter recovery of the two methods. A bootstrapping procedure was also proposed for the third moment method that tested the differences of empirical sampling distributions of interaction effects using a two-sample Kolmogorov-Smirnov test. There were four independent variables: i) sample size, ii) non-normality of errors, iii) effect size, and iv) estimation methods. The QML method performed better than the third moment method. QML had lower type-I error and more power. QML had less absolute bias for estimating smaller interaction effects. For smaller sample sizes, QML had less error in estimating interaction effects, main effects and covariances than the third-moment method. The nonnormality conditions had no impact on the results. Based on the pattern of results found, it is recommended that QML method be used for testing if a latent interaction differs between groups. If the M-B method is to be used the sample size to parameter ratio should be greater than 20:1. Care should be taken in interpreting parameter estimates in the presence of a large interaction effect as both methods overestimated an interaction coefficient as it increased in magnitude. Both methods also had more error in estimating main effects and covariances as the interaction effect increased.


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    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmailORCID
    Committee ChairKim, Kevin H.khkim@pitt.edu
    Committee MemberYe, Feifeifeifeiye@pitt.edu
    Committee MemberStone, Clement A.cas@pitt.edu
    Committee MemberShook, Jeffrey J.jes98@pitt.edu
    Title: COMPARING LATENT INTERACTION EFFECTS IN MULTI-SAMPLE STRUCTURAL EQUATION MODELING: QUASI-MAXIMUM LIKELIHOOD VERSUS THIRD MOMENT METHODS
    Status: Published
    Abstract: A simulation study was performed comparing the quasi-maximum likelihood (QML; Klein & Muthén, 2007) and third moment (Mooijaart & Bentler, 2010) methods for estimating latent interaction effects in multi-sample structural equation modeling. Both of these methods estimate latent interaction effects without the use of product indicators or the need to specify nonlinear constraints. The purpose of this study was to evaluate the power and type-I error rates for testing group differences of a latent interaction effect. This study also evaluated the parameter recovery of the two methods. A bootstrapping procedure was also proposed for the third moment method that tested the differences of empirical sampling distributions of interaction effects using a two-sample Kolmogorov-Smirnov test. There were four independent variables: i) sample size, ii) non-normality of errors, iii) effect size, and iv) estimation methods. The QML method performed better than the third moment method. QML had lower type-I error and more power. QML had less absolute bias for estimating smaller interaction effects. For smaller sample sizes, QML had less error in estimating interaction effects, main effects and covariances than the third-moment method. The nonnormality conditions had no impact on the results. Based on the pattern of results found, it is recommended that QML method be used for testing if a latent interaction differs between groups. If the M-B method is to be used the sample size to parameter ratio should be greater than 20:1. Care should be taken in interpreting parameter estimates in the presence of a large interaction effect as both methods overestimated an interaction coefficient as it increased in magnitude. Both methods also had more error in estimating main effects and covariances as the interaction effect increased.
    Date: 10 January 2013
    Date Type: Publication
    Defense Date: 15 November 2012
    Approval Date: 10 January 2013
    Submission Date: 12 December 2012
    Release Date: 10 January 2013
    Access Restriction: No restriction; The work is available for access worldwide immediately.
    Patent pending: No
    Number of Pages: 152
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    Uncontrolled Keywords: Multi-Sample Structural Equation Modeling, Moderation, Latent Interaction, Quasi-Maximum Likelihood, Third Moment
    Schools and Programs: School of Education > Psychology in Education
    Date Deposited: 10 Jan 2013 10:04
    Last Modified: 16 Jul 2014 17:09

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