Chapter 12 Multiple choice questions

. 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.

Expert ratings of the freedom of the press in 1960 and in 1965.

Freedom of political opposition in 1960 and effectiveness of the elected legislature in 1960.

The inanimate energy consumption per captia in 1960 and the fairness of elections in 1965.

. Now calculate correlation coefficients between all the variables. What is the largest correlation between two different variables?

0.67

0.74

0.85

0.89

. 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

0.938

0.002

0.101

. 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

0.15

2.18

1.82

. 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

Industrialisation and Political democracy 1965

Political democracy 1960 and Political democracy 1965

All latent variables have the same parameter estimates

. 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

The original model, because it has a bigger AIC score

The new model, because it has a smaller AIC score

The original model, because it has a smaller AIC score

. 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

4.26 and 0.04

3.54 and 0.11

0.58 and 0.33

. 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

y3

y5

y7

. 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)

The model is dramatically improved (p = 0.0001)

There is no significant change in the model's fit (p = 0.6)

The score test cannot be calculated for this modification

. What is the change in root mean squared error between the original model, and the model with the extra link added?

0.001

0.004

0.01

0.04

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