Newsom
Structural Equation Modeling
Winter 2015
1
Path Analysis Example
Mplus (output excerpts)
Note: I use the bootstrap approach here for testing the indirect effect. The bootstrap approach will generally
produce preferable standard errors for the indirect effect test, but we will come back to this technique later.
Mplus VERSION 7.3
MUTHEN & MUTHEN
01/14/2015
9:32 PM
INPUT INSTRUCTIONS
title: Data from social exchanges pretest;
data: file=path1.dat;
listwise=on;
format=free;
variable: names = sex hostile negaff;
missing = sex-negaff (-99);
! analysis:
type=basic;
analysis: type=general; estimator=ml; matrix=covariance;
bootstrap = 1000;
! at least 500 bootstrap samples are recommended;
model:
hostile on sex;
negaff on hostile sex;
Model indirect:
negaff ind sex;
output: stdyx ;
!* cinterval can be added to the output line
to obtain confidence intervals for indirect effects
but I omitted here to save space. cinterval(bcbootstrap)
obtains bias-corrected bootstrap intervals for
nonsymmetric sampling distribution*!
INPUT READING TERMINATED NORMALLY
Data from social exchanges pretest;
SUMMARY OF ANALYSIS
Number of groups
Number of observations
1
271
Number of dependent variables
Number of independent variables
Number of continuous latent variables
2
1
0
Estimator
ML
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters
7
Loglikelihood
H0 Value
H1 Value
-550.577
-550.577
Information Criteria
Akaike (AIC)
Bayesian (BIC)
Sample-Size Adjusted BIC
(n* = (n + 2) / 24)
1115.154
1140.369
1118.174
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
0.000
0
0.0000
Newsom
Structural Equation Modeling
Winter 2015
MODEL RESULTS
2
Two-Tailed
P-Value
Estimate
S.E.
Est./S.E.
0.006
0.077
0.078
0.938
NEGAFF
ON
HOSTILE
SEX
0.344
-0.125
0.090
0.087
3.846
-1.435
0.000
0.151
Intercepts
HOSTILE
NEGAFF
0.578
1.603
0.054
0.089
10.761
18.054
0.000
0.000
Residual Variances
HOSTILE
0.405
NEGAFF
0.493
STANDARDIZED MODEL RESULTS
0.054
0.053
7.424
9.339
0.000
0.000
HOSTILE
SEX
ON
StdYX
Estimate
HOSTILE
SEX
ON
0.005
NEGAFF
ON
HOSTILE
SEX
0.297
-0.084
Intercepts
HOSTILE
NEGAFF
0.909
2.172
R-SQUARE
Observed
Variable
Estimate
HOSTILE
0.000
NEGAFF
0.095
TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS
Two-Tailed
Estimate
S.E. Est./S.E.
P-Value
Effects from SEX to NEGAFF
Total
-0.123
Total indirect
0.002
0.090
0.028
-1.360
0.075
0.174
0.940
0.002
0.028
0.075
0.940
-0.125
0.087
-1.435
0.151
Specific indirect
NEGAFF
HOSTILE
SEX
Direct
NEGAFF
SEX
Sample write-up:
To investigate whether hostility mediates the relation between gender and negative affect, a path
model was tested using Mplus Version 7.3 (Muthen & Muthen, 1998-2012). Results indicated that,
although hostility significantly predicted negative affect (β = .344, SE = .090, β* = .297, p < .001),
gender was not significantly related to hostility (β = .006, SE = .077, β* = .005, ns). As would be
expected from these results, the indirect effect tested using bootstrapped standard errors was also
nonsignficant (β = .002, SE = .028, β* = .001, ns). (Note: The standardized indirect coefficient was
deleted from the output). These findings do not support the hypothesized mediational model.
Muthén, L.K. and Muthén, B.O. (1998-2012). Mplus User’s Guide. Seventh Edition. Los Angeles, CA: Muthén & Muthén
Newsom
Structural Equation Modeling
Winter 2015
3
lavaan (output excerpts)
Input
library(lavaan) # always call lavaan library first
# first time use on the computer, install the lavaan package with the following command
# install.packages("lavaan", dependencies=TRUE)
## Path Example for Newsom's SEM Class
path1 = read.table ("c:/jason/R/lavaan/semclass/path1.dat", header=FALSE)
# read the raw data
names(path1) = c("sex", "hostile", "negaff")
# name the variables (must be in the correct order)
path1[path1 == -99] <- NA
# tells R that -99 is missing (NA is the missing designation)
model = '
negaff ~ c*sex
hostile ~ a*sex
negaff ~ b*hostile
# note that all the model commands are enclosed single quotes
#indirect effect
ab := a*b
#total effect
total := c + (a*b)
'
fit = sem(model, data = path1, missing = 'listwise',se = 'bootstrap')
summary(fit,fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
Output
lavaan (0.5-17) converged normally after
14 iterations
Used
271
Number of observations
Estimator
Minimum Function Test Statistic
Degrees of freedom
Total
275
ML
0.000
0
Parameter estimates:
Information
Standard Errors
Number of requested bootstrap draws
Number of successful bootstrap draws
Regressions:
negaff ~
sex
hostile ~
sex
negaff ~
hostile
Estimate
Std.err
Z-value
P(>|z|)
Std.lv
Std.all
(c)
-0.125
0.086
-1.453
0.146
-0.125
-0.084
(a)
0.006
0.079
0.076
0.939
0.006
0.005
(b)
0.344
0.089
3.887
0.000
0.344
0.297
0.493
0.405
0.054
0.055
0.493
0.405
0.905
1.000
0.002
-0.123
0.028
0.091
0.002
-0.123
0.001
-0.082
Variances:
negaff
hostile
Defined parameters:
ab
total
R-Square:
negaff
hostile
Observed
Bootstrap
1000
1000
0.095
0.000
0.074
-1.351
0.941
0.177
Newsom
Structural Equation Modeling
Winter 2015
4
Amos (excerpts)
Note: this analysis, conducted with Version 22.
Estimates (Group number 1 - Default model)
Analysis Summary
Date and Time
Date: Wednesday, January 14, 2015
Time: 10:55:45 PM
Title
path1_15: Wednesday, January 14, 2015 10:55 PM
Scalar Estimates (Group number 1 - Default model)
Maximum Likelihood Estimates
Regression Weights: (Group number 1 - Default model)
Estimate S.E.
C.R.
P
hostile <--- sex
.006
.078 .077
.938
negaff <--- hostile .344
.067 5.127
***
negaff <--- sex
-.125
.086 -1.446 .148
Label
Standardized Regression Weights: (Group number 1 - Default model)
Estimate
hostile <--- sex
.005
negaff <--- hostile .297
negaff <--- sex
-.084
Means: (Group number 1 - Default model)
Estimate S.E.
C.R.
P
sex
.565
.030 18.711 ***
Intercepts: (Group number 1 - Default model)
Estimate S.E.
C.R.
P
hostile
.578
.059 9.860
***
negaff
1.602
.076 21.221 ***
Label
Label
Variances: (Group number 1 - Default model)
Estimate S.E.
C.R.
P
Label
sex
.246
.021 11.619 ***
e1
.405
.035 11.619 ***
e2
.493
.042 11.619 ***
Squared Multiple Correlations: (Group number 1 - Default model)
Estimate
hostile
.000
negaff
.095
Newsom
Structural Equation Modeling
Winter 2015
5
Matrices (Group number 1 - Default model)
Total Effects (Group number 1 - Default model)
sex
hostile
hostile .006
.000
negaff
-.123 .344
Standardized Total Effects (Group number 1 - Default model)
sex
hostile
hostile .005
.000
negaff
-.082 .297
Direct Effects (Group number 1 - Default model)
sex
hostile
hostile .006
.000
negaff
-.125 .344
Standardized Direct Effects (Group number 1 - Default model)
sex
hostile
hostile .005
.000
negaff
-.084 .297
Indirect Effects (Group number 1 - Default model)
sex
hostile
hostile .000 .000
negaff
.002 .000
Standardized Indirect Effects (Group number 1 - Default model)
sex
hostile
hostile .000 .000
negaff
.001 .000
Negative
Smallest
Iteration
Condition #
Diameter
eigenvalues
eigenvalue
0
e 0
26.858
9999.000
1
e 0
35.946
.448
2
e 0
31.246
.126
3
e 0
30.455
.050
4
e 0
30.188
.006
5
e 0
30.498
.000
F
NTries
Ratio
38.116
8.562
.598
.007
.000
.000
0
1
1
1
1
1
9999.000
.669
1.142
1.068
1.009
1.000