[SOLVED] R 2019 2

2019 2
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Instructions: Please use the R programming language for all the following questions. And include your R codes and outputs along with your answers.
I. Using the EFA.csv data set on the class website perform a principal axis factor analysis with varimax rotation. Report the factor loadings table with cut off at 0.3, and plot structure diagram.
II. Consider the following confirmatory factor analysis model with two latent variables and six observed variables. The model indicates that the first three observed variables measure the latent variable Factor1 and the last three observed variables measure the latent variable Factor2.
Correlation matrix is given below together with standard deviation and sample size information.
Variable name X1
X2
X3
X4
X5
X6 Standard deviation Sample size
X1
1.00 0.487 0.236 0.242 0.163 0.064
2.500 500
X2
1.00 0.206 0.179 0.090 0.040
3.200 500
X3 X4 X5 X6
1.00
0.253 1.00
0.125 0.481 1.00
0.025 0.106 0.136 1.00
2.600 3.349 2.613
500 500 500 500
3.373

1. Read the data given in Table into R.
2. Using the Lavaan package in R, perform a confirmatory factor analysis on the data.
3. Report the standardized loadings, their significance, the chi-square for the model, and
several fit indices (i.e. CFI, TLI, RMSEA, SRMR, etc.). Does this model fit the data well?
4. Draw a path diagram of the fitted CFA model with the estimated parameters superimposed,
using the function semPaths() in the R package semPlot.
5. Can you extend the two factor model to significantly improve the model-fit?
III. Please run the SEM model described in the figure below using the enclosed dataset (SEM.xlsx). All the observed variables were measured on a four-point Likert scale ranging from 1 (strongly disagree) to 4 (strongly agree).
1. Construct and estimate the model in R.
2. What are the fit indices? Are they good?
3. What are the path coefficients between latent variables? Are they significant?
4. What is the explained variance in the endogenous constructs? (those constructs which have
at least one predictor)?
5. Draw a diagram of the model with standardized parameter estimates (path coefficients, error
variances, or covariances)
6. What is the highest modification index? What does it tell us?