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Exam 19: Factor Analysis

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Question 31

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For the factor analysis to be appropriate, the variables must be correlated.

A) True
B) False

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Question 32

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The factor scores for the ith factor may be estimated as follows: .

A) X_i = W_i1 F₁ + W_i2 F₂ + W_i3 F₃ + ... + W_im F_m
B) F_i = W_i1 X₁ + W_i2 X₂ + W_i3 Y₃ + ... + W_ik Y_k
C) F_i = W_i1 X₁ + W_i2 X₂ + W_i3 X₃ + ... + W_ik X_k
D) X_i = A_i1 F₁ + A_i2 F₂ + A_i3 F₃ + ... + A_im F_m

E) A) and B)
F) None of the above

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Question 33

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Which of the following is a way to interpret factors?

F represents in the factor model X_i = A_i1 F₁ + A_i2 F₂+ A_i3 F₃ + ... + A_im F_m + V_iU_i.

Principal components analysis is appropriate when the primary concern is to identify the underlying dimensions and the common variance is of interest.

Selecting surrogate variables works well if one factor loading for a variable is clearly higher than all other factor loadings.

are simple correlations between the variables and the factors.

The test statistic for sphericity is based on a chi- square transformation of the determinant of the correlation matrix. A large value of the test statistic will favor the acceptance of the null hypothesis.

In order to use factor analysis, it is important that the variables be appropriately measured on an ordinal or nominal scale.

Factor analysis does not classify variables as dependent or independent.

A principal components analysis was run and the following eigenvalue results were obtained: 2.731, 2.218, .442, .341, .183, and .085. How many factors would you retain using the eigenvalues to determine the number of factors?

Which statement is not correct concerning factor scores?

The percentage of the total variance attributed to each factor analysis model is called the percentage of variance.

Under what general circumstances is factor analysis used?

Factor analysis is a(n) in that the entire set of interdependent relationships is examined.

is the last step in factor analysis.

Sometimes, because of prior knowledge, the researcher knows how many factors to expect and thus can specify the number of factors to be extracted beforehand. This is referred to as .

List at least four of the procedures used for determining the number of factors.

The factor matrix is also called the factor pattern matrix.

A factor is an underlying dimension that explains the correlations among a set of variables.