Quiz on the Orthogonal Factor Model

What is the primary purpose of factor analysis?

• To analyze single variables

• To create a correlation matrix

• To reduce observed variables into unobserved factors

• To increase the number of observed variables

In the orthogonal factor model, what does it mean for factors to be uncorrelated?

• They are identical

• They are dependent on each other

• They have a correlation of one

• They are orthogonal

What does the symbol 'μ' represent in the model equation?

• The mean vector of observed variables

• The vector of unique factors

• The matrix of factor loadings

• The vector of common factors

What does 'Cov(F) = I_m' signify in the model's assumptions?

• Factors are correlated

• Factors have variance greater than one

• Factors are uncorrelated and have variance of one

• Factors are dependent on observed variables

What does the covariance matrix of observed variables represent?

• The correlation between errors

• The unique variances of each variable

• The average of each observed variable

• The total variability in the observed data

What is the first step in the numerical example provided?

• Reconstruct the covariance matrix

• Calculate unique variances

• Estimate initial communalities

• Compute factor loadings

What does a high communality value indicate?

• The factor is irrelevant

• Most of the variation is explained by the factor

• The variable is independent

• The variable has low variance

What is the purpose of calculating the reconstructed covariance matrix?

• To determine the total variability

• To find the average of observed variables

• To see how much variability is explained by the factor

• To estimate unique variances

What does the matrix Ψ represent in the context of the model?

• The explained part of the covariance matrix

• The mean vector

• The unique variances or errors

• The factor loadings

What does a non-zero off-diagonal value in Ψ suggest?

• The factors are correlated

• More factors may be needed

• The errors are independent

• The model is perfectly accurate