====== Path Analysis ======
===== Planned Behavior Modeling =====
######################################################
## data file: PlannedBehavior.csv
######################################################
df <- read.csv("http://commres.net/wiki/_media/r/plannedbehavior.csv")
head(df)
str(df)
######################################################
# attitude
# norms
# control
# intention
# behavior
######################################################
# install.packages("lavaan")
library(lavaan)
# Specify model
specmod <- "
intention ~ attitude + norms + control
"
# Estimate model
fitmod <- sem(specmod, data=df)
# Summarize model
summary(fitmod, fit.measures=TRUE, rsquare=TRUE)
====== Output ======
######################################################
> ## data file: PlannedBehavior.csv
> ######################################################
> df <- read.csv("http://commres.net/wiki/_media/r/plannedbehavior.csv")
> head(df)
attitude norms control intention behavior
1 2.31 2.31 2.03 2.50 2.62
2 4.66 4.01 3.63 3.99 3.64
3 3.85 3.56 4.20 4.35 3.83
4 4.24 2.25 2.84 1.51 2.25
5 2.91 3.31 2.40 1.45 2.00
6 2.99 2.51 2.95 2.59 2.20
> str(df)
'data.frame': 199 obs. of 5 variables:
$ attitude : num 2.31 4.66 3.85 4.24 2.91 2.99 3.96 3.01 4.77 3.67 ...
$ norms : num 2.31 4.01 3.56 2.25 3.31 2.51 4.65 2.98 3.09 3.63 ...
$ control : num 2.03 3.63 4.2 2.84 2.4 2.95 3.77 1.9 3.83 5 ...
$ intention: num 2.5 3.99 4.35 1.51 1.45 2.59 4.08 2.58 4.87 3.09 ...
$ behavior : num 2.62 3.64 3.83 2.25 2 2.2 4.41 4.15 4.35 3.95 ...
> ######################################################
> # attitude
> # norms
> # control
> # intention
> # behavior
> ######################################################
> # install.packages("lavaan")
> library(lavaan)
This is lavaan 0.6-9
lavaan is FREE software! Please report any bugs.
Warning message:
패키지 ‘lavaan’는 R 버전 4.1.2에서 작성되었습니다
>
> # Specify model
> specmod <- "
+ intention ~ attitude + norms + control
+ "
> # Estimate model
> fitmod <- sem(specmod, data=df)
>
> # Summarize model
> summary(fitmod, fit.measures=TRUE, rsquare=TRUE)
lavaan 0.6-9 ended normally after 11 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 4
Number of observations 199
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 91.633
Degrees of freedom 3
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -219.244
Loglikelihood unrestricted model (H1) -219.244
Akaike (AIC) 446.489
Bayesian (BIC) 459.662
Sample-size adjusted Bayesian (BIC) 446.990
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
intention ~
attitude 0.352 0.058 6.068 0.000
norms 0.153 0.059 2.577 0.010
control 0.275 0.058 4.740 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.intention 0.530 0.053 9.975 0.000
R-Square:
Estimate
intention 0.369
====== Model 2 ======
# Specify model
specmod2 <- "
intention ~ attitude + norms + control
attitude ~~ norms + control
norms ~~ control
"
# Estimate model
fitmod2 <- sem(specmod2, data=df)
# Summarize model
summary(fitmod2, fit.measures=TRUE, rsquare=TRUE)
fitmod <- lm(intention ~ attitude + norms + control, data=df)
summary(fitmod)
> # Specify model
> specmod2 <- "
+ intention ~ attitude + norms + control
+ attitude ~~ norms + control
+ norms ~~ control
+ "
> # Estimate model
> fitmod2 <- sem(specmod2, data=df)
>
> # Summarize model
> summary(fitmod2, fit.measures=TRUE, rsquare=TRUE)
lavaan 0.6-9 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 10
Number of observations 199
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 136.306
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1011.828
Loglikelihood unrestricted model (H1) -1011.828
Akaike (AIC) 2043.656
Bayesian (BIC) 2076.589
Sample-size adjusted Bayesian (BIC) 2044.908
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
intention ~
attitude 0.352 0.058 6.068 0.000
norms 0.153 0.059 2.577 0.010
control 0.275 0.058 4.740 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
attitude ~~
norms 0.200 0.064 3.128 0.002
control 0.334 0.070 4.748 0.000
norms ~~
control 0.220 0.065 3.411 0.001
Variances:
Estimate Std.Err z-value P(>|z|)
.intention 0.530 0.053 9.975 0.000
attitude 0.928 0.093 9.975 0.000
norms 0.830 0.083 9.975 0.000
control 0.939 0.094 9.975 0.000
R-Square:
Estimate
intention 0.369
>
> fitmod <- lm(intention ~ attitude + norms + control, data=df)
> summary(fitmod)
Call:
lm(formula = intention ~ attitude + norms + control, data = df)
Residuals:
Min 1Q Median 3Q Max
-1.80282 -0.52734 -0.06018 0.51228 1.85202
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.58579 0.23963 2.445 0.0154 *
attitude 0.35232 0.05866 6.006 9.13e-09 ***
norms 0.15250 0.05979 2.550 0.0115 *
control 0.27502 0.05862 4.692 5.09e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7356 on 195 degrees of freedom
Multiple R-squared: 0.369, Adjusted R-squared: 0.3593
F-statistic: 38.01 on 3 and 195 DF, p-value: < 2.2e-16
>
====== Model 3 ======
# Specify model
specmod3 <- "
# directional relationships
intention ~ attitude + norms + control
behavior ~ intention
# covariances
attitude ~~ norms + control
norms ~~ control
"
# Estimate model
fitmod3 <- sem(specmod3, data=df)
# Summarize model
summary(fitmod3, fit.measures=TRUE, rsquare=TRUE)
> df <- read.csv("http://commres.net/wiki/_media/r/plannedbehavior.csv")
> # Specify model
> specmod3 <- "
+ # directional relationships
+ intention ~ attitude + norms + control
+ behavior ~ intention
+
+ # covariances
+ attitude ~~ norms + control
+ norms ~~ control
+ "
> # Estimate model
> fitmod3 <- sem(specmod3, data=df)
>
> # Summarize model
> summary(fitmod3, fit.measures=TRUE, rsquare=TRUE)
lavaan 0.6-12 ended normally after 18 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Number of observations 199
Model Test User Model:
Test statistic 2.023
Degrees of freedom 3
P-value (Chi-square) 0.568
Model Test Baseline Model:
Test statistic 182.295
Degrees of freedom 10
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.019
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1258.517
Loglikelihood unrestricted model (H1) -1257.506
Akaike (AIC) 2541.035
Bayesian (BIC) 2580.555
Sample-size adjusted Bayesian (BIC) 2542.538
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.103
P-value RMSEA <= 0.05 0.735
Standardized Root Mean Square Residual:
SRMR 0.019
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
intention ~
attitude 0.352 0.058 6.068 0.000
norms 0.153 0.059 2.577 0.010
control 0.275 0.058 4.740 0.000
behavior ~
intention 0.453 0.065 7.014 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
attitude ~~
norms 0.200 0.064 3.128 0.002
control 0.334 0.070 4.748 0.000
norms ~~
control 0.220 0.065 3.411 0.001
Variances:
Estimate Std.Err z-value P(>|z|)
.intention 0.530 0.053 9.975 0.000
.behavior 0.699 0.070 9.975 0.000
attitude 0.928 0.093 9.975 0.000
norms 0.830 0.083 9.975 0.000
control 0.939 0.094 9.975 0.000
R-Square:
Estimate
intention 0.369
behavior 0.198
a <- (5*(5+1))/2
b <- 12
a-b