祝建华老师讲义

c’ = 0 (i.e., complete mediation), or b. c’ < c (partial mediation)
a.
X
Y
a
M
X M
c’
a
b
X
Y
4
SEM f CR
Decomposition of casual effects
SEM f CR
Significance test of indirect effects
Endogenous variables:

M
1 EM
The path from an error to an endogenous variable is fixed to a constant (usually “1”) to make the error to be solvable (e.g., identifiable).
10
SEM f CR
Procedure of path analysis in SEM
SEM f CR
Iterative nature of path analysis
Specification
1. Model specification (all relevant variables included?) 2. Model identification (all parameters sovable?) 3. Model estimation (what statistical tool to use?) 4. Model evaluation (how good of the results?) 5. Model respecification (if necessary) 6. Model interpretation (what the results mean?) 7. Model validation (results replicable? optional but highly recommended)
SEM f CR
Outline
Structural Equation Modeling for Communication Research
Jonathan J. H. Zhu, May 2010
Causal modeling, path analysis and mediation models
X2
9
Path coefficients: direct effects of exogenous variables on endogenous variables Covariances/correlations: unanalyzed relationships between exogenous variables
Input the data

Raw data (*.txt, *.xls, *.sav, etc.) Covariance matrix + means Correlation matrix + standard deviations + means Observed exogenous and endogenous variables Unobserved errors of endogenous variables Causal parameters linking exogenous variable to endogenous variables Unstandardized output Standardized output
1. 2.
SEM ቤተ መጻሕፍቲ ባይዱ CR
Test mediation models in OLS regression (Baron & Kenny steps)
c

3.
4.
test the significance, direction, and strength of the relationships jointly (the variables correlated?) explore the mechanism of the relationships (why correlated or uncorrelated? see Babbie’s Ch 15 on the elaboration paradigm) partition the components of the relationships into direct and indirect effects (what constitute the correlations? i.e., mediation model) compare alternative models (i.e., configurations of different directionalities and/or causal routes)
(c) Partially recursive (bow-free)
1 X1 Y1 E1
(d) Partially recursive (bowpattern), usually nonrecursive
1 X1 Y1 E1

When the above conditions are met:


Causal modeling and path analysis Mediation models Barron and Kenny steps Decomposition of effects and significance test Advanced issues in mediation models Get started with AMOS Graphics Test mediation models with observed variables Procedure of general path analysis in SEM
The Sobel test: calculate the std error of indirect effect (path ab): seab = a2sb2 + b2sa2 where sb and sa are std error of b and a, respectively. Online tool is available to calculate the Soble test at /~preacher/sobel/sobel.htm. Bootstrapping method: calculate the standard errors based on randomly generated data (directly available in AMOS or through a 3rd party macro in SPSS).
5 6
1
SEM f CR
Significance test of total effects
SEM f CR
Get started with AMOS Graphics
There is no known formulae to calculate the standard error of total effects In general, if both direct and indirect effects are significant, the total effects are significant as well. The significance test of total effects can be made using bootstrapped standard errors generated by bootstrapping (e.g., AMOS)
SEM f CR
Model identification for path analysis Necessary conditions:
1.
(a) Recursive model
1 X1 Y1 E1

X2
Y2
1 E 2
X2
Y2
1 E 2
2.
Unique elements in covariance matrix (k(k+1)/2, where k is the number of observed variables) ≥ estimated parameters (equivalently, df ≥ 0) All unobserved variables (i.e., errors) have a scale (i.e., a fixed value such as 1) for their paths Recursive models are always identifiable Nonrecursive models may, but are not guaranteed to, be identifiable
Total effects = Direct effects + Indirect effects If Y = by.xm+byx.mX+bym.xM and M = bm.x+bmxX, Direct effects = byx.m or yx.m Indirect effects = bmxbym.x or mxym.x Total effects = byx.m+bmxbym.x or yx.m+ mx ym.x The significance and strength of the indirect effects in relation to the direct effects provide evidence for mediation hypothesis