HW3 Template
Your Name
September 20, 2016
Load required libraries
library(lavaan)
library(semPlot)Ex A
- Assign the summarized data to a character vector
# Exercise and weight loss
exercise_lower <- '
1.0
.16 1.0,
.24, -.43, 1.0,
.31, .05, .07, 1.0 '
# Sample size
N1 <- 767- Convert to a full symmetric covariance/correlation matrix with names
exercise_cor <- getCov(exercise_lower,
names = c("exercise",
"food",
"wt_loss",
"attitude"))- Specify model
exercise_model <- '
# regressions
exercise ~ attitude
food ~ exercise
wt_loss ~ exercise + food '- fit the model
exercise_model_fit <- sem(exercise_model,
sample.cov = exercise_cor,
sample.nobs = N1)- Print a summary of the model estimates and print the standardized solution
summary(exercise_model_fit,
standardized = TRUE)lavaan (0.5-21) converged normally after 14 iterations
Number of observations 767
Estimator ML
Minimum Function Test Statistic 0.021
Degrees of freedom 2
P-value (Chi-square) 0.990
Parameter Estimates:
Information Expected
Standard Errors Standard
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
exercise ~
attitude 0.310 0.034 9.030 0.000 0.310 0.310
food ~
exercise 0.160 0.036 4.489 0.000 0.160 0.160
wt_loss ~
exercise 0.317 0.031 10.230 0.000 0.317 0.317
food -0.481 0.031 -15.517 0.000 -0.481 -0.481
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.exercise 0.903 0.046 19.583 0.000 0.903 0.904
.food 0.973 0.050 19.583 0.000 0.973 0.974
.wt_loss 0.716 0.037 19.583 0.000 0.716 0.7176.Plot the path diagram
semPaths(exercise_model_fit,
"par",
style = "ram",
layout = "spring")
Ex B
- Assign the summarized data to a character vector
# Arbuckle's analysis of Felson & Bornstedt's data
Arbuckle_lower <- '
1
.43 1
.50 .48 1
.49 .22 .32 1
.10 -.04 -.03 .18 1
.04 .02 -.16 -.10 .34 1
.09 .14 .43 .15 -.16 -.27 1 '
# Sample size
N2 <- 209- Convert to a full symmetric covariance/correlation matrix with names
Arbuckle_cor <- getCov(Arbuckle_lower,
names = c("academic",
"athletic",
"attract",
"GPA",
"height",
"weight",
"rating"))- Specify model
## replace the "**" with the model specification
Arbuckle_model <- '
# regressions
** ~ **
** ~ **
# correlations
** ~~ ** '- fit the model and print a summary of the model estimates.
# replace the "**" with the correct parameters
Arbuckle_model_fit <- sem( **,
sample.cov = **,
sample.nobs = **)- Print a summary of the model estimates and print the standardized solution
summary(Arbuckle_model_fit,
standardized = TRUE)lavaan (0.5-21) converged normally after 19 iterations
Number of observations 209
Estimator ML
Minimum Function Test Statistic 2.774
Degrees of freedom 2
P-value (Chi-square) 0.250
Parameter Estimates:
Information Expected
Standard Errors Standard
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
academic ~
attract -0.006 0.157 -0.039 0.969 -0.006 -0.006
GPA 0.492 0.079 6.256 0.000 0.492 0.492
attract ~
academic 0.525 0.114 4.610 0.000 0.525 0.525
height 0.003 0.059 0.050 0.960 0.003 0.003
weight -0.078 0.059 -1.324 0.185 -0.078 -0.078
rating 0.363 0.056 6.460 0.000 0.363 0.363
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.academic ~~
.attract -0.051 0.133 -0.383 0.702 -0.051 -0.076
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.academic 0.760 0.132 5.761 0.000 0.760 0.764
.attract 0.595 0.059 9.998 0.000 0.595 0.598We can also output a list of model matrices
lavInspect(Arbuckle_model_fit, "est")$lambda
acadmc attrct GPA height weight rating
academic 1 0 0 0 0 0
attract 0 1 0 0 0 0
GPA 0 0 1 0 0 0
height 0 0 0 1 0 0
weight 0 0 0 0 1 0
rating 0 0 0 0 0 1
$theta
acadmc attrct GPA height weight rating
academic 0
attract 0 0
GPA 0 0 0
height 0 0 0 0
weight 0 0 0 0 0
rating 0 0 0 0 0 0
$psi
acadmc attrct GPA height weight rating
academic 0.760
attract -0.051 0.595
GPA 0.000 0.000 0.995
height 0.000 0.000 0.179 0.995
weight 0.000 0.000 -0.100 0.338 0.995
rating 0.000 0.000 0.149 -0.159 -0.269 0.995
$beta
acadmc attrct GPA height weight rating
academic 0.000 -0.006 0.492 0.000 0.000 0.000
attract 0.525 0.000 0.000 0.003 -0.078 0.363
GPA 0.000 0.000 0.000 0.000 0.000 0.000
height 0.000 0.000 0.000 0.000 0.000 0.000
weight 0.000 0.000 0.000 0.000 0.000 0.000
rating 0.000 0.000 0.000 0.000 0.000 0.000Note that the psi matrix corresponds to the following compound matrix in the notes
\[ \begin{bmatrix} \boldsymbol \Psi & \mathbf 0\\ \mathbf 0 & \boldsymbol \Phi \end{bmatrix} \]
and the beta matrix to
\[ \begin{bmatrix} \mathbf B & \boldsymbol \Gamma\\ \mathbf 0 & \mathbf 0 \end{bmatrix} \]
- Plot the path diagram
semPaths(**,
"par",
style = "ram",
layout = "spring")EX 1
- Assign the summarized data to a character vector
# SES, IQ and Need Achievement data
SES_lower <- '
1
.30 1
.41 .16 1
.33 .57 .50 1'
# Sample size
N3 <- 306- Convert to a full symmetric covariance/correlation matrix with names
SES_cor <- getCov(SES_lower,
names = c("SES",
"IQ",
"nAch",
"GPA"))- Specify model
SES_model <- '
# regressions
** ~ **
** ~ **
# correlations
** ~~ ** '- Fit the model and print a summary of the model estimates.
SES_model_fit <- sem(**,
sample.cov = **,
sample.nobs = **)
summary(**,
standardized = TRUE)We can also output a list of model matrices
lavInspect(**, **)- Plot the path diagram
semPaths(**,
"par",
style = "ram",
layout = "spring")EX 2
- Assign the summarized data to a character vector
# Social status, actual and perceived income data
income_lower <- '
1.0000
0.3670 1.0000
0.5103 0.4310 1.0000
0.3633 0.1840 0.2772 1.0000
0.1574 0.2819 0.2311 0.2921 1.0000'
# Sample size
N4 <- 432- Convert to a full symmetric covariance/correlation matrix with names
income_cor <- getCov(income_lower,
names = c("subj_income",
"subj_prestige",
"subj_status",
"actual_income",
"actual_prestige"))- Specify model
income_model <- '
# regressions
** ~ **
# correlations
** ~~ ** '- Fit the model and print a summary of the model estimates.
income_model_fit <- sem(**,
sample.cov = **,
sample.nobs = **)
summary(**,
standardized = TRUE)We can also output a list of model matrices
lavInspect(**, **)- Plot the path diagram
semPaths(**,
"par",
style = "ram",
layout = "spring")