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Return to Research Methods Using R 1e Student Resources
Chapter 12 Multiple choice questions
Quiz Content
*
not completed
.
You can load in a dataset on political democracy by typing:
library(lavaan
)
dataset <- PoliticalDemocracy
To find out what the variables mean, use
help(PoliticalDemocracy)
.
Calculate the covariance matrix of the dataset using the
cov
function. Which pair of variables has the highest covariance?
The fairness of elections in 1960 and The freedom of political opposition in 1965.
correct
incorrect
Expert ratings of the freedom of the press in 1960 and in 1965.
correct
incorrect
Freedom of political opposition in 1960 and effectiveness of the elected legislature in 1960.
correct
incorrect
The inanimate energy consumption per captia in 1960 and the fairness of elections in 1965.
correct
incorrect
*
not completed
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Now calculate correlation coefficients between all the variables. What is the largest correlation between two different variables?
0.67
correct
incorrect
0.74
correct
incorrect
0.85
correct
incorrect
0.89
correct
incorrect
*
not completed
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As you will have seen from the help file, the data set describes industrialisation and political democracy in developing countries. We will test a model that has three latent variables intended to represent: industrialisation in 1960, democracy in 1960 and democracy in 1965. You can create the model as follows:
inddemomodel <- 'industrialisation =~ x1 + x2 + x3 + poldem1960 + poldem1965
poldem1960 =~ y1 + y2 + y3 + y4 + poldem1965
poldem1965 =~ y5 + y6 + y7 + y8'
Then fit the model to the dataset as follows:
fit <- cfa(inddemomodel, data = dataset
)
summary(fit, fit.measures = TRUE
)
What is the value of the comparitive fit index (CFI)?
0.953
correct
incorrect
0.938
correct
incorrect
0.002
correct
incorrect
0.101
correct
incorrect
*
not completed
.
What is the unstandardised parameter estimate for the link between the industrialisation latent variable and the x3 parameter? (Hint: you can find this out either from the main output, or by plotting the model with
whatLabels='par'
using the
semPaths
function from the
semPlot
package).
0.87
correct
incorrect
0.15
correct
incorrect
2.18
correct
incorrect
1.82
correct
incorrect
*
not completed
.
Plot the model with standardized parameters (whatLabels='std'). Which two latent variables have the highest standardized parameter estimate joining them?
Industrialisation and Political democracy 1960
correct
incorrect
Industrialisation and Political democracy 1965
correct
incorrect
Political democracy 1960 and Political democracy 1965
correct
incorrect
All latent variables have the same parameter estimates
correct
incorrect
*
not completed
.
Create a new model where there is no link between the industrialization and political democracy 1965 latent variables. This model has one less free parameter than the earlier one. According to Akaike's information criteria (AIC) which model provides the best description of the data set?
The new model, because it has a bigger AIC score
correct
incorrect
The original model, because it has a bigger AIC score
correct
incorrect
The new model, because it has a smaller AIC score
correct
incorrect
The original model, because it has a smaller AIC score
correct
incorrect
*
not completed
.
An alternative approach to removing a parameter is to use the Wald test. Using the method described on page 185, respecify the model so that it has a weight parameter (b1) applied to the poldem1965 variable in the line where the industrialisation variable is specified. Then rerun the model, and conduct a Wald test with the constraint that 'b1 == 0'. What is the value of the Wald statistic, and its accompanying p value?
1.25 and 0.06
correct
incorrect
4.26 and 0.04
correct
incorrect
3.54 and 0.11
correct
incorrect
0.58 and 0.33
correct
incorrect
*
not completed
.
Inspect the modification indices of your original fit using the
modindices
function. Which variable has the largest modification index for a link with the industrialisation latent variable?
y1
correct
incorrect
y3
correct
incorrect
y5
correct
incorrect
y7
correct
incorrect
*
not completed
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Conduct a Lagrange multiplier (score) test to see if adding the link identified in the previous question significantly improves the model. What is the result?
The model is significantly improved (
p
= 0.045)
correct
incorrect
The model is dramatically improved (
p
= 0.0001)
correct
incorrect
There is no significant change in the model's fit (
p
= 0.6)
correct
incorrect
The score test cannot be calculated for this modification
correct
incorrect
*
not completed
.
What is the change in root mean squared error between the original model, and the model with the extra link added?
0.001
correct
incorrect
0.004
correct
incorrect
0.01
correct
incorrect
0.04
correct
incorrect
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