Material accompanying the manuscript "Estimating, Testing and Comparing Specific Effects in SEM: The Phantom Model Approach"

The following page contains the material accompanying the manuscript: Estimating, Testing and Comparing Specific Effects in SEM: The Phantom Model Approach. The material comprises the following types of files:

r     An excel data file

r     Amos graphic files of the models used in the examples

r     R files for estimating models and specific effects using the R package OpenMx.

1.    Data (data.zip)

The excel file data.xls contains data for Examples 1-3 in the text as well as for the example of Bollen (1987, 1989). The three sheets in the file contain the following data:

Sheet

Description

Ex_1_2

Data of Example 1 & 2 (Tsai, Chen, & Liu, 2007, Table 2 on p.1576)

Ex_3

Data for Example 3 (Kurdek, 1989, Table 4, on p.504)

Bollen

Data sampled from the multivariate normal distribution using the covariance matrix provided by Bollen (1989)

2.    AMOS Graphic Files (AMOS.zip):

AMOS (Version 18, 17 and 5) graphic files for estimating and bootstrapping effects:

File

Description

Tsai 2007 (Ex.1).amw

Example 1: Covariance matrix of estimated parameters

Tsai 2007 (Ex.2).amw

Example 2: Covariance matrix of estimated parameters

Kurdek 1998 (Ex.3).amw

Example 3: Covariance matrix of estimated parameters

Bollen (1987) Method of Bollen.amw

Emulation of the method of Bollen (1987)

Bollen (1987) Alternative Method to Bollen.amw

Alternative model for estimating the specific effect of Bollen (1987)

3.    R-Files for estimating models and specific effects using OpenMx (R-OpenMx.zip):

R-Files for modeling using OpenMx as well as a documentation of matrices involved in the computations:

File

Description

Tsai 2007 (Ex.1, Bootstrap).R

Example 1 (Bootstrapping confidence intervals)

Tsai 2007 (Ex.1, Monte Carlo).R

Example 1 (Monte Carlo method)

Tsai 2007 (Ex.2, Bootstrap).R

Example 2 (Bootstrapping confidence intervals)

Tsai 2007 (Ex.2, Monte Carlo).R

Example 2 (Monte Carlo method)

Kurdek 1998 (Ex.3, Bootstrap).R

Example 3 (Bootstrapping confidence intervals)

Kurdek 1998 (Ex.3, Monte Carlo).R

Example 3 (Monte Carlo method)

OpenMx (Docu).pdf

Documentation of the matrices used for implement­ing models in OpenMx as well as of the bootstrap and Monte Carlo results.

Comment:

The Monte Carlo method takes B = 10000 samples of parameters from the normal distribution with the estimated parameter vector (from the observed sample) as mean and the estimated covariance matrix of the estimated parameters as covariance matrix. For each sample the specific effect is computed. The 95 percent confidence intervals for the specific effects are computed using the percentile method. The method was proposed by MacKinnon, Lockwood, & Williams (2004). The observed information matrix was used for computing the covariance matrix of the estimated parameters.

4.    References:

Bollen, K. A. (1987). Total, direct, and indirect effects in structural equation models. Sociological Methodology, 17, 37-69.

Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.

Tsai, W.-C., Chen, C.-C., & Liu, H.-L. (2007). Test of a model linking employee positive moods and task performance. Journal of Applied Psychology, 92, 1570-1583.

Kurdek, L. A. (1998). The nature and predictors of the trajectory of change in marital quality over the first 4 years of marriage for first-married husbands and wives. Journal of Family Psychology, 12, 494-510.

MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distributions of the product of resampling methods. Multivariate Behavioral Research, 39, 99-128.

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