STAT4443 R Path Analysis
Ronald Wesonga (PhD)
2024-12-18
Abstract
We study concepts related to Path Analysis.Introduction
labData <- read.csv(file = "C:\\Users\\wesonga\\Documents\\Learning\\S4443\\Lecture\\04\\eatingDisorderSimData.csv", header = TRUE)Sample Covariance Matrices using the cov() function
Quick review:
str(labData) #structure## 'data.frame': 1339 obs. of 7 variables:
## $ BMI : num 0.377 0.302 -1.098 -1.13 -2.797 ...
## $ SelfEsteem : num 0.0685 -0.3059 1.4755 -0.1329 1.3538 ...
## $ Accu : num 1.782 0.491 -0.682 2.224 0.892 ...
## $ DietSE : num -0.0544 -2.3957 0.168 1.1851 0.5131 ...
## $ Restrictive: num -0.525 2.067 0.364 -1.656 0.743 ...
## $ Bulimia : num 0.432 0.196 -1.434 -0.675 -0.858 ...
## $ Risk : num 0.508 0.91 -0.777 -0.554 -0.314 ...head(labData) #first few lines## BMI SelfEsteem Accu DietSE Restrictive Bulimia
## 1 0.3769721 0.0685226 1.7822103 -0.05436952 -0.5251424 0.4322272
## 2 0.3015484 -0.3058876 0.4909857 -2.39569010 2.0671867 0.1959765
## 3 -1.0980232 1.4754543 -0.6819827 0.16801384 0.3638750 -1.4337656
## 4 -1.1304059 -0.1329290 2.2235223 1.18505959 -1.6557519 -0.6748446
## 5 -2.7965343 1.3537804 0.8922687 0.51311551 0.7431860 -0.8575733
## 6 0.7205735 -1.9361462 -1.0307704 0.79749119 -1.8609143 0.3290163
## Risk
## 1 0.50794715
## 2 0.90996098
## 3 -0.77678045
## 4 -0.55411733
## 5 -0.31385631
## 6 0.08012833colnames(labData) #column names## [1] "BMI" "SelfEsteem" "Accu" "DietSE" "Restrictive"
## [6] "Bulimia" "Risk"- How many observations are in this dataset?
- Number of observations = number of rows, with 1 person per row
nrow(labData) #1339## [1] 1339let’s save this number as n
n <- nrow(labData)Let’s look at the sample covariance matrix of these variables using the cov() function:
cov(labData)## BMI SelfEsteem Accu DietSE Restrictive
## BMI 1.07399214 -0.1380786 -0.02076620 -0.10688665 -0.13056197
## SelfEsteem -0.13807862 1.0021547 0.03501750 0.10557111 -0.11991676
## Accu -0.02076620 0.0350175 0.97176431 -0.02069863 -0.09050653
## DietSE -0.10688665 0.1055711 -0.02069863 0.96607293 -0.15678475
## Restrictive -0.13056197 -0.1199168 -0.09050653 -0.15678475 1.01695732
## Bulimia 0.16177119 -0.3171776 -0.09549788 -0.21922044 0.58684522
## Risk 0.07938074 -0.2286471 -0.10327073 0.07119772 0.78960193
## Bulimia Risk
## BMI 0.16177119 0.07938074
## SelfEsteem -0.31717764 -0.22864713
## Accu -0.09549788 -0.10327073
## DietSE -0.21922044 0.07119772
## Restrictive 0.58684522 0.78960193
## Bulimia 1.03637890 0.87337921
## Risk 0.87337921 1.05356717let’s save this sample cov as capital S:
S = cov(labData)If we wanted, we could look at a subset of the dataset, e.g.,:
cov(labData[,c("BMI", "SelfEsteem", "Accu")])## BMI SelfEsteem Accu
## BMI 1.0739921 -0.1380786 -0.0207662
## SelfEsteem -0.1380786 1.0021547 0.0350175
## Accu -0.0207662 0.0350175 0.9717643This is often useful if our analysis will only contain certain variables.
If only two variables:
cov(labData$BMI, labData$SelfEsteem)## [1] -0.1380786If only one variable (variance):
cov(labData$BMI, labData$BMI)## [1] 1.073992Check out the help page of a particular function, say sem():
help(sem)## starting httpd help server ... done?semUsing Lavaan For Path Models
Every analysis in lavaan has three main parts.
- Part I: Writing the Model Syntax
- Part II: Analyzing the Model Using Your Dataset
- Part III: Examining the results.
PART I: Follow the set of equations:
Self-Efficacy = BMI + Self-Esteem + Disturbance
Bulimic Symptoms = BMI + Self-Esteem + Self-Efficacy + Disturbance
Restrictive Symptoms = BMI + Self-Esteem + Self-Efficacy + Disturbance
Overall Risk = BMI + Self-Esteem + Self-Efficacy + Acculturation + Disturbance
Let’s write some model syntax:
ex1PathSyntax <- " #opening a quote
# Tilda ~ : Regression
# M ~ X regression (X predicts M)
# Each line corresponds to an equation
# Disturbance is automatically included for each regression
# (i.e. no extra term needed)
DietSE ~ BMI + SelfEsteem #DietSE is predicted by BMI and SelfEsteem
Bulimia ~ DietSE + BMI + SelfEsteem
Restrictive ~ DietSE + BMI + SelfEsteem
Risk ~ DietSE + BMI + SelfEsteem + Accu
" Things to note here:
- We are calling our saved model syntax object ex1PathSyntax
- We assign it using <- as usual
- Then we open a quotation ”
- Then we write each part of the model on separate lines.
- Then we close the quotation ”
- The variables names need to match those in the dataset (case matters!)
- Add comments inside the model syntax using hashtag
PART II Let’s run our model!
To run this model, we will start by using the sem() function.
Sensible defaults for estimating CFA models like assumptions of linear regression, so we don’t actually have to write some constraints into the model above
Alternatively, one can use lavaan() function [with the fewest default settings] or cfa() function [with similar defaults as sem() function]
To use lavaan(), you have to specify all 22 parameters in the model.
ex1fit
You can run the sem() function using two different sources of data:
- The raw dataset, using:
lavaan::sem(model = ex1PathSyntax, data = labData)example:
ex1fit <- lavaan::sem(model = ex1PathSyntax, data = labData)If you encounter errors like:
Error in if ((!is.matrix(model)) | ncol(model) != 3) stop(“model argument must be a 3-column matrix”) : argument is of length zero
IT IS PROBABLY BECAUSE YOU HAVEN’T LOADED THE lavaan PACKAGE.
To make sure you are using the sem() function from the lavaan package, add PackageName:: before a function:
ex1fit <- lavaan::sem(model = ex1PathSyntax, data = labData)Then we can obtain complete results using the summary() function:
summary(ex1fit)## lavaan 0.6.17 ended normally after 36 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
##
## Number of observations 1339
##
## Model Test User Model:
##
## Test statistic 16.429
## Degrees of freedom 3
## P-value (Chi-square) 0.001
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## DietSE ~
## BMI -0.088 0.026 -3.381 0.001
## SelfEsteem 0.093 0.027 3.480 0.001
## Bulimia ~
## DietSE -0.185 0.026 -6.994 0.000
## BMI 0.096 0.025 3.796 0.000
## SelfEsteem -0.284 0.026 -10.871 0.000
## Restrictive ~
## DietSE -0.166 0.027 -6.039 0.000
## BMI -0.154 0.026 -5.892 0.000
## SelfEsteem -0.123 0.027 -4.561 0.000
## Risk ~
## DietSE 0.105 0.028 3.766 0.000
## BMI 0.055 0.027 2.057 0.040
## SelfEsteem -0.232 0.028 -8.425 0.000
## Accu 0.007 0.009 0.783 0.434
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .Bulimia ~~
## .Restrictive 0.536 0.029 18.389 0.000
## .Risk 0.814 0.034 23.983 0.000
## .Restrictive ~~
## .Risk 0.785 0.034 22.996 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .DietSE 0.946 0.037 25.875 0.000
## .Bulimia 0.890 0.034 25.875 0.000
## .Restrictive 0.955 0.037 25.875 0.000
## .Risk 0.989 0.038 25.875 0.000ex1PathSyntax_noCov
To change those defaults, one needs to explicitly fix those disturbance covariances at 0 (this is a strong assumption):
http://lavaan.ugent.be/tutorial/syntax2.html
ex1PathSyntax_noCov <- " #opening a quote
# ~~ indicates a two-headed arrow (variance or covariance)
# 0* in front of the 2nd variable fixes the covariance at 0
DietSE ~ BMI + SelfEsteem #DietSE is predicted by BMI and SelfEsteem
Bulimia ~ DietSE + BMI + SelfEsteem
Restrictive ~ DietSE + BMI + SelfEsteem
Risk ~ DietSE + BMI + SelfEsteem + Accu
#Disturbance covariances (fixed at 0):
DietSE ~~ 0*Bulimia
DietSE ~~ 0*Restrictive
DietSE ~~ 0*Risk
Bulimia ~~ 0*Restrictive
Bulimia ~~ 0*Risk
Restrictive ~~ 0*Risk
# These lines above say that there is no covariance among the disturbances of all endogenous variables
"
ex1fit_noCov <- lavaan::sem(model = ex1PathSyntax_noCov, data = labData)
summary(ex1fit_noCov)## lavaan 0.6.17 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 16
##
## Number of observations 1339
##
## Model Test User Model:
##
## Test statistic 3536.813
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## DietSE ~
## BMI -0.088 0.026 -3.381 0.001
## SelfEsteem 0.093 0.027 3.480 0.001
## Bulimia ~
## DietSE -0.185 0.026 -6.994 0.000
## BMI 0.096 0.025 3.796 0.000
## SelfEsteem -0.284 0.026 -10.871 0.000
## Restrictive ~
## DietSE -0.166 0.027 -6.039 0.000
## BMI -0.154 0.026 -5.892 0.000
## SelfEsteem -0.123 0.027 -4.561 0.000
## Risk ~
## DietSE 0.102 0.028 3.686 0.000
## BMI 0.053 0.026 2.000 0.045
## SelfEsteem -0.228 0.027 -8.332 0.000
## Accu -0.095 0.027 -3.449 0.001
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .DietSE ~~
## .Bulimia 0.000
## .Restrictive 0.000
## .Risk 0.000
## .Bulimia ~~
## .Restrictive 0.000
## .Risk 0.000
## .Restrictive ~~
## .Risk 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .DietSE 0.946 0.037 25.875 0.000
## .Bulimia 0.890 0.034 25.875 0.000
## .Restrictive 0.955 0.037 25.875 0.000
## .Risk 0.979 0.038 25.875 0.000ex1fit_noCov_freeX
fixed.x=FALSE asks for the variances/covariances/means of the exogenous variables to be freely estimated instead of being fixed at the values found from the sample
This usually makes no difference from ex1fit_noCov, except that it prints more lines
ex1fit_noCov_freeX <- lavaan::sem(model = ex1PathSyntax_noCov, data = labData, fixed.x = FALSE)
summary(ex1fit_noCov_freeX)## lavaan 0.6.17 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 22
##
## Number of observations 1339
##
## Model Test User Model:
##
## Test statistic 3536.813
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## DietSE ~
## BMI -0.088 0.026 -3.381 0.001
## SelfEsteem 0.093 0.027 3.480 0.001
## Bulimia ~
## DietSE -0.185 0.026 -6.994 0.000
## BMI 0.096 0.025 3.796 0.000
## SelfEsteem -0.284 0.026 -10.871 0.000
## Restrictive ~
## DietSE -0.166 0.027 -6.039 0.000
## BMI -0.154 0.026 -5.892 0.000
## SelfEsteem -0.123 0.027 -4.561 0.000
## Risk ~
## DietSE 0.102 0.028 3.686 0.000
## BMI 0.053 0.026 2.000 0.045
## SelfEsteem -0.228 0.027 -8.332 0.000
## Accu -0.095 0.027 -3.449 0.001
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .DietSE ~~
## .Bulimia 0.000
## .Restrictive 0.000
## .Risk 0.000
## .Bulimia ~~
## .Restrictive 0.000
## .Risk 0.000
## .Restrictive ~~
## .Risk 0.000
## BMI ~~
## SelfEsteem -0.138 0.029 -4.828 0.000
## Accu -0.021 0.028 -0.744 0.457
## SelfEsteem ~~
## Accu 0.035 0.027 1.298 0.194
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .DietSE 0.946 0.037 25.875 0.000
## .Bulimia 0.890 0.034 25.875 0.000
## .Restrictive 0.955 0.037 25.875 0.000
## .Risk 0.979 0.038 25.875 0.000
## BMI 1.073 0.041 25.875 0.000
## SelfEsteem 1.001 0.039 25.875 0.000
## Accu 0.971 0.038 25.875 0.000ex1fit_noCov_lavaan
As a bonus, here is how you would write the model syntax if you use lavaan() instead of sem()…
ex1PathSyntax_lavaan <- " #opening a quote
# ~~ indicates a two-headed arrow (variance or covariance)
#regression coefficients (12)
DietSE ~ BMI + SelfEsteem
Bulimia ~ DietSE + BMI + SelfEsteem
Restrictive ~ DietSE + BMI + SelfEsteem
Risk ~ DietSE + BMI + SelfEsteem + Accu
#variances of exogenous variables (3)
BMI ~~ BMI
SelfEsteem ~~ SelfEsteem
Accu ~~ Accu
#disturbance variances (4)
DietSE ~~ DietSE
Bulimia ~~ Bulimia
Restrictive ~~ Restrictive
Risk ~~ Risk
#covariances among exogenous variables (3)
BMI ~~ SelfEsteem
BMI ~~ Accu
SelfEsteem ~~ Accu
#total: 22 parameters
"
ex1fit_noCov_lavaan <- lavaan(model = ex1PathSyntax_lavaan, data = labData)
summary(ex1fit_noCov_lavaan)## lavaan 0.6.17 ended normally after 11 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 22
##
## Number of observations 1339
##
## Model Test User Model:
##
## Test statistic 3536.813
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## DietSE ~
## BMI -0.088 0.026 -3.381 0.001
## SelfEsteem 0.093 0.027 3.480 0.001
## Bulimia ~
## DietSE -0.185 0.026 -6.994 0.000
## BMI 0.096 0.025 3.796 0.000
## SelfEsteem -0.284 0.026 -10.871 0.000
## Restrictive ~
## DietSE -0.166 0.027 -6.039 0.000
## BMI -0.154 0.026 -5.892 0.000
## SelfEsteem -0.123 0.027 -4.561 0.000
## Risk ~
## DietSE 0.102 0.028 3.686 0.000
## BMI 0.053 0.026 2.000 0.045
## SelfEsteem -0.228 0.027 -8.332 0.000
## Accu -0.095 0.027 -3.449 0.001
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## BMI ~~
## SelfEsteem -0.138 0.029 -4.828 0.000
## Accu -0.021 0.028 -0.744 0.457
## SelfEsteem ~~
## Accu 0.035 0.027 1.298 0.194
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## BMI 1.073 0.041 25.875 0.000
## SelfEsteem 1.001 0.039 25.875 0.000
## Accu 0.971 0.038 25.875 0.000
## .DietSE 0.946 0.037 25.875 0.000
## .Bulimia 0.890 0.034 25.875 0.000
## .Restrictive 0.955 0.037 25.875 0.000
## .Risk 0.979 0.038 25.875 0.000which yields the same output as ex1fit_noCov_freeX.
Sigma Matrices
Let’s have a look at the model-implied covarinace matrix from our final model ex1fit_noCov_freeX and save it as Sigma:
fitted(ex1fit_noCov_freeX)## $cov
## DietSE Bulimi Rstrct Risk BMI SlfEst Accu
## DietSE 0.965
## Bulimia -0.219 1.036
## Restrictive -0.157 0.051 1.016
## Risk 0.069 0.060 0.005 1.052
## BMI -0.107 0.162 -0.130 0.079 1.073
## SelfEsteem 0.105 -0.317 -0.120 -0.228 -0.138 1.001
## Accu 0.005 -0.013 -0.002 -0.101 -0.021 0.035 0.971Sigma <- fitted(ex1fit_noCov_freeX)$covHow close is Sigma to S?
- Rearrange the rows and columns of Sigma (important!) and take the difference
diff = Sigma[colnames(S), colnames(S)] - S
round(diff, 3)## BMI SelfEsteem Accu DietSE Restrictive Bulimia Risk
## BMI -0.001 0.000 0.000 0.000 0.000 0.000 0.000
## SelfEsteem 0.000 -0.001 0.000 0.000 0.000 0.000 0.000
## Accu 0.000 0.000 -0.001 0.026 0.089 0.083 0.003
## DietSE 0.000 0.000 0.026 -0.001 0.000 0.000 -0.002
## Restrictive 0.000 0.000 0.089 0.000 -0.001 -0.536 -0.785
## Bulimia 0.000 0.000 0.083 0.000 -0.536 -0.001 -0.814
## Risk 0.000 0.000 0.003 -0.002 -0.785 -0.814 -0.001How about the default model that include disturbance covariances?
Sigma0 <- fitted(ex1fit)$cov
diff0 = Sigma0[colnames(S), colnames(S)] - S
round(diff0, 3)## BMI SelfEsteem Accu DietSE Restrictive Bulimia Risk
## BMI -0.001 0.000 0.000 0.000 0.000 0.000 0.000
## SelfEsteem 0.000 -0.001 0.000 0.000 0.000 0.000 0.000
## Accu 0.000 0.000 -0.001 0.026 0.089 0.083 0.101
## DietSE 0.000 0.000 0.026 -0.001 0.000 0.000 0.000
## Restrictive 0.000 0.000 0.089 0.000 -0.001 0.000 0.000
## Bulimia 0.000 0.000 0.083 0.000 0.000 -0.001 0.000
## Risk 0.000 0.000 0.101 0.000 0.000 0.000 0.001Practical Tips:
- To begin with, constraint the disturbance covariances to be 0 ;
- Keep the model if the model fits the data well;
- Relax the constraints the disturbance covariances if the initial model did not fit well.
PART III: Summarizing Our Analysis:
There are some useful options we can ask for with summary():
summary(ex1fit_noCov_freeX, fit.measures = T) #include model fit measures
summary(ex1fit_noCov_freeX, standardized = T) #This includes standardized estimates. std.all contains usual regression standardization.
summary(ex1fit_noCov_freeX, ci = T) #Include confidence intervals
# Add them all!If we JUST want the parameter estimates:
parameterEstimates(ex1fit_noCov_freeX)## lhs op rhs est se z pvalue ci.lower ci.upper
## 1 DietSE ~ BMI -0.088 0.026 -3.381 0.001 -0.138 -0.037
## 2 DietSE ~ SelfEsteem 0.093 0.027 3.480 0.001 0.041 0.146
## 3 Bulimia ~ DietSE -0.185 0.026 -6.994 0.000 -0.237 -0.133
## 4 Bulimia ~ BMI 0.096 0.025 3.796 0.000 0.046 0.145
## 5 Bulimia ~ SelfEsteem -0.284 0.026 -10.871 0.000 -0.335 -0.233
## 6 Restrictive ~ DietSE -0.166 0.027 -6.039 0.000 -0.220 -0.112
## 7 Restrictive ~ BMI -0.154 0.026 -5.892 0.000 -0.205 -0.103
## 8 Restrictive ~ SelfEsteem -0.123 0.027 -4.561 0.000 -0.176 -0.070
## 9 Risk ~ DietSE 0.102 0.028 3.686 0.000 0.048 0.157
## 10 Risk ~ BMI 0.053 0.026 2.000 0.045 0.001 0.105
## 11 Risk ~ SelfEsteem -0.228 0.027 -8.332 0.000 -0.282 -0.175
## 12 Risk ~ Accu -0.095 0.027 -3.449 0.001 -0.149 -0.041
## 13 DietSE ~~ Bulimia 0.000 0.000 NA NA 0.000 0.000
## 14 DietSE ~~ Restrictive 0.000 0.000 NA NA 0.000 0.000
## 15 DietSE ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 16 Bulimia ~~ Restrictive 0.000 0.000 NA NA 0.000 0.000
## 17 Bulimia ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 18 Restrictive ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 19 DietSE ~~ DietSE 0.946 0.037 25.875 0.000 0.874 1.018
## 20 Bulimia ~~ Bulimia 0.890 0.034 25.875 0.000 0.822 0.957
## 21 Restrictive ~~ Restrictive 0.955 0.037 25.875 0.000 0.883 1.028
## 22 Risk ~~ Risk 0.979 0.038 25.875 0.000 0.905 1.054
## 23 BMI ~~ BMI 1.073 0.041 25.875 0.000 0.992 1.154
## 24 BMI ~~ SelfEsteem -0.138 0.029 -4.828 0.000 -0.194 -0.082
## 25 BMI ~~ Accu -0.021 0.028 -0.744 0.457 -0.075 0.034
## 26 SelfEsteem ~~ SelfEsteem 1.001 0.039 25.875 0.000 0.926 1.077
## 27 SelfEsteem ~~ Accu 0.035 0.027 1.298 0.194 -0.018 0.088
## 28 Accu ~~ Accu 0.971 0.038 25.875 0.000 0.897 1.045parameterEstimates(ex1fit_noCov_freeX, standardized = T) #include standardized solution....## lhs op rhs est se z pvalue ci.lower ci.upper
## 1 DietSE ~ BMI -0.088 0.026 -3.381 0.001 -0.138 -0.037
## 2 DietSE ~ SelfEsteem 0.093 0.027 3.480 0.001 0.041 0.146
## 3 Bulimia ~ DietSE -0.185 0.026 -6.994 0.000 -0.237 -0.133
## 4 Bulimia ~ BMI 0.096 0.025 3.796 0.000 0.046 0.145
## 5 Bulimia ~ SelfEsteem -0.284 0.026 -10.871 0.000 -0.335 -0.233
## 6 Restrictive ~ DietSE -0.166 0.027 -6.039 0.000 -0.220 -0.112
## 7 Restrictive ~ BMI -0.154 0.026 -5.892 0.000 -0.205 -0.103
## 8 Restrictive ~ SelfEsteem -0.123 0.027 -4.561 0.000 -0.176 -0.070
## 9 Risk ~ DietSE 0.102 0.028 3.686 0.000 0.048 0.157
## 10 Risk ~ BMI 0.053 0.026 2.000 0.045 0.001 0.105
## 11 Risk ~ SelfEsteem -0.228 0.027 -8.332 0.000 -0.282 -0.175
## 12 Risk ~ Accu -0.095 0.027 -3.449 0.001 -0.149 -0.041
## 13 DietSE ~~ Bulimia 0.000 0.000 NA NA 0.000 0.000
## 14 DietSE ~~ Restrictive 0.000 0.000 NA NA 0.000 0.000
## 15 DietSE ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 16 Bulimia ~~ Restrictive 0.000 0.000 NA NA 0.000 0.000
## 17 Bulimia ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 18 Restrictive ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 19 DietSE ~~ DietSE 0.946 0.037 25.875 0.000 0.874 1.018
## 20 Bulimia ~~ Bulimia 0.890 0.034 25.875 0.000 0.822 0.957
## 21 Restrictive ~~ Restrictive 0.955 0.037 25.875 0.000 0.883 1.028
## 22 Risk ~~ Risk 0.979 0.038 25.875 0.000 0.905 1.054
## 23 BMI ~~ BMI 1.073 0.041 25.875 0.000 0.992 1.154
## 24 BMI ~~ SelfEsteem -0.138 0.029 -4.828 0.000 -0.194 -0.082
## 25 BMI ~~ Accu -0.021 0.028 -0.744 0.457 -0.075 0.034
## 26 SelfEsteem ~~ SelfEsteem 1.001 0.039 25.875 0.000 0.926 1.077
## 27 SelfEsteem ~~ Accu 0.035 0.027 1.298 0.194 -0.018 0.088
## 28 Accu ~~ Accu 0.971 0.038 25.875 0.000 0.897 1.045
## std.lv std.all std.nox
## 1 -0.088 -0.092 -0.089
## 2 0.093 0.095 0.095
## 3 -0.185 -0.179 -0.179
## 4 0.096 0.097 0.094
## 5 -0.284 -0.279 -0.279
## 6 -0.166 -0.162 -0.162
## 7 -0.154 -0.158 -0.153
## 8 -0.123 -0.122 -0.122
## 9 0.102 0.098 0.098
## 10 0.053 0.053 0.052
## 11 -0.228 -0.223 -0.223
## 12 -0.095 -0.091 -0.092
## 13 0.000 0.000 0.000
## 14 0.000 0.000 0.000
## 15 0.000 0.000 0.000
## 16 0.000 0.000 0.000
## 17 0.000 0.000 0.000
## 18 0.000 0.000 0.000
## 19 0.946 0.980 0.980
## 20 0.890 0.859 0.859
## 21 0.955 0.940 0.940
## 22 0.979 0.931 0.931
## 23 1.073 1.000 1.073
## 24 -0.138 -0.133 -0.138
## 25 -0.021 -0.020 -0.021
## 26 1.001 1.000 1.001
## 27 0.035 0.035 0.035
## 28 0.971 1.000 0.971For standardized solutions, there is also this function:
standardizedSolution(ex1fit_noCov_freeX, type = "std.all") ## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 DietSE ~ BMI -0.092 0.027 -3.395 0.001 -0.146 -0.039
## 2 DietSE ~ SelfEsteem 0.095 0.027 3.496 0.000 0.042 0.148
## 3 Bulimia ~ DietSE -0.179 0.025 -7.093 0.000 -0.228 -0.129
## 4 Bulimia ~ BMI 0.097 0.026 3.811 0.000 0.047 0.148
## 5 Bulimia ~ SelfEsteem -0.279 0.025 -11.284 0.000 -0.328 -0.231
## 6 Restrictive ~ DietSE -0.162 0.026 -6.115 0.000 -0.213 -0.110
## 7 Restrictive ~ BMI -0.158 0.027 -5.962 0.000 -0.210 -0.106
## 8 Restrictive ~ SelfEsteem -0.122 0.027 -4.593 0.000 -0.175 -0.070
## 9 Risk ~ DietSE 0.098 0.027 3.702 0.000 0.046 0.150
## 10 Risk ~ BMI 0.053 0.027 2.003 0.045 0.001 0.106
## 11 Risk ~ SelfEsteem -0.223 0.026 -8.536 0.000 -0.274 -0.172
## 12 Risk ~ Accu -0.091 0.026 -3.462 0.001 -0.143 -0.039
## 13 DietSE ~~ Bulimia 0.000 0.000 NA NA 0.000 0.000
## 14 DietSE ~~ Restrictive 0.000 0.000 NA NA 0.000 0.000
## 15 DietSE ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 16 Bulimia ~~ Restrictive 0.000 0.000 NA NA 0.000 0.000
## 17 Bulimia ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 18 Restrictive ~~ Risk 0.000 0.000 NA NA 0.000 0.000
## 19 DietSE ~~ DietSE 0.980 0.008 129.769 0.000 0.965 0.995
## 20 Bulimia ~~ Bulimia 0.859 0.018 48.727 0.000 0.824 0.894
## 21 Restrictive ~~ Restrictive 0.940 0.013 74.768 0.000 0.915 0.965
## 22 Risk ~~ Risk 0.931 0.013 69.534 0.000 0.904 0.957
## 23 BMI ~~ BMI 1.000 0.000 NA NA 1.000 1.000
## 24 BMI ~~ SelfEsteem -0.133 0.027 -4.958 0.000 -0.186 -0.080
## 25 BMI ~~ Accu -0.020 0.027 -0.744 0.457 -0.074 0.033
## 26 SelfEsteem ~~ SelfEsteem 1.000 0.000 NA NA 1.000 1.000
## 27 SelfEsteem ~~ Accu 0.035 0.027 1.300 0.194 -0.018 0.089
## 28 Accu ~~ Accu 1.000 0.000 NA NA 1.000 1.000Plotting SEM model
# install.packages("semPlot")
#library(semPlot)
# Plot!
semPaths(ex1fit_noCov_freeX)
# estimates instead of paths only
semPaths(ex1fit_noCov_freeX, what='est',
edge.label.cex=1.25, curvePivot = TRUE,
fade=FALSE)
# standardized solutions
semPaths(ex1fit_noCov_freeX, what='std',
edge.label.cex=1.25, curvePivot = TRUE,
fade=FALSE)
semPaths(ex1fit_noCov_freeX, what='est',
rotation = 2, # default rotation = 1 with four options
edge.label.cex=1.25, curvePivot = TRUE,
fade=FALSE)
customize it your way
semPaths(ex1fit_noCov_freeX, whatLabels="est", # plot model not parm ests
rotation = 2, # default rotation = 1 with four options
asize = 5, # arrows' size
esize = 2, # width of paths' lines / curves
edge.label.cex = 0.8, # font size of regr'n coeffs
sizeMan = 10, # font size of manifest variable names
nCharNodes = 0,
nCharEdges = 0, # don't limit variable name lengths
fade = FALSE, # don't weight path width to reflect strength
curvePivot = TRUE, # make straight edges instead of round ones
curve = 2, # pull covariances' curves out a little
style = "lisrel", # no variances vs. # "ram"'s 2-headed for variances
color = "green", # color of variables
edge.color = "black", # color of edges/paths
layout = "tree2", # tree, spring, circle, circle2
residuals = TRUE) # residuals variances included in the path diagram
semPaths(ex1fit_noCov_freeX, what='est',
rotation = 2, # default rotation = 1 with four options
curve = 2, # pull covariances' curves out a little
nCharNodes = 0,
nCharEdges = 0, # don't limit variable name lengths
sizeMan = 8, # font size of manifest variable names
style = "lisrel", # single-headed arrows vs. # "ram"'s 2-headed for variances
edge.label.cex=1.2, curvePivot = TRUE,
fade=FALSE)