Question 1

The first step in conducting factor analysis is .

Accepted Answer

A)   determine the method of factor analysis
B)   construct the correlation matrix
C)   formulate the problem
D)   determine the number of factorsE) B) and C)
F) C) and D)

Question 2

The equation Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ... + Aim Fm + ViUi , represents the common factors expressed as linear combinations of the observed variables.

Accepted Answer

A) True 
 B)False

Question 3

is an approach to factor analysis that considers the total variance in the data.

Accepted Answer

A)   Common factor analysis
B)   Unweighted least squares
C)   Omega method
D)   Principal components analysisE) A) and B)
F) A) and C)

Question 4

Describe principal components analysis and common factor analysis and the differences between the two methods of factor analysis.

Accepted Answer

In principal components analysis, the total variance in the data is considered. The diagonal of the correlation matrix consists of unities, and full variance is brought into the factor matrix. Principal components analysis is recommended when the primary concern is to determine the minimum number of factors that will account for maximum variance in the data for use in subsequent multivariate analysis. The factors are called principal components.
In common factor analysis, the factors are estimated based only on the common variance. Communalities are inserted in the diagonal of the correlation matrix. This method is appropriate when the primary concern is to identify the underlying dimensions and the common variance is of interest. This method is also known as principal axis factoring.
A major difference between the two methods of factor analysis is that principal components analysis considers the total variance in the data whereas common factor analysis considers only the common variance. In common factor analysis, the factors are estimated based only on the common variance.

Question 5

Only in the case of principal components analysis is it possible to compute exact factor scores.

Accepted Answer

A) True 
 B)False

Question 6

Discuss the process of selecting surrogate variables. Also discuss how the researcher should decide on which variable to choose in complex situations.

Accepted Answer

Selection of substitute, or surrogate va...

Question 7

The represents the total variance explained by each factor.

Accepted Answer

A)   residual
B)   eigenvalue
C)   communality
D)   percentage of varianceE) C) and D)
F) A) and B) B

Question 8

The amount of variance a variable shares with all other variables included in the factor analysis is referred to as .

Accepted Answer

A)   percentage of variance
B)   total variance
C)   shared variance
D)   communalityE) A) and B)
F) B) and D)

Question 9

The differences between the observed correlations (as given in the input correlation matrix) and the reproduced correlations (as estimated from the factor matrix) can be examined to determine model fit.

Accepted Answer

A) True 
 B)False

Question 10

Factors can be estimated so that their factor scores are not correlated and the first factor accounts for the highest variance in the data, the second factor the second highest and so on.

Accepted Answer

A) True 
 B)False

Question 11

Factor scores should be computed if the goal of factor analysis is to use the results in subsequent multivariate analysis.

Accepted Answer

A) True 
 B)False

Question 12

Rotation does not affect the communalities and the percentage of total variance explained.

Accepted Answer

A) True 
 B)False

Question 13

is an approach to factor analysis that estimates the factors based only on the common variance.

Accepted Answer

A)   Principal components analysis
B)   Unweighted least squares
C)   Omega method
D)   Common factor analysisE) B) and D)
F) All of the above

Question 14

Which of the following statements is not true about factor rotation?

Accepted Answer

A)   Different methods of rotation may result in the identification of different factors.
B)   Through rotation, the factor matrix is transformed into a simpler one that is easier to interpret.
C)   Rotation affects the communalities and the percentage of total variance explained.
D)   Preferably, each factor should have a nonzero, or significant, loadings or coefficients for only some of the variables.E) A) and B)
F) A) and D) C

Question 15

is an index that compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficient.

Accepted Answer

A)   Wilks' lambda
B)   KMO measure of sampling adequacy
C)   Bartlett's test of sphericity
D)   Mahalanobis ratioE) A) and B)
F) All of the above

Question 16

Residuals are the differences between the observed correlations, as given in the input correlation matrix, and the reproduced correlations, as estimated from the factor matrix.

Accepted Answer

A) True 
 B)False

Question 17

Factor analysis can be used in which of the following circumstances?

Accepted Answer

A)   to identify a new, smaller set of uncorrelated variables to replace the original set of correlated variables in subsequent multivariate analysis
B)   to identify underlying dimensions, or factors, that explain the correlations among a set of variables
C)   to identify a smaller set of salient variables from a larger set for use in subsequent multivariate analysis
D)   All are correct circumstances.E) A) and B)
F) C) and D)

Question 18

Factor analysis examines the whole set of interdependent relationships among variables.

Accepted Answer

A) True 
 B)False

Question 19

When using eigenvalues to determine the number of factors, only factors with eigenvalues greater than .05 are retained.

Accepted Answer

A) True 
 B)False

Question 20

m represents in the factor model, Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ... + Aim Fm + ViUi.

Accepted Answer

A)   the number of common factors
B)   the mth standardized variable i = Ai1 F1 + Ai2 F2 + Ai3 F3 + ... + Aim Fm + ViUi. 
A)   the number of common factors 
B)   the mth standardized variable   
C)   the common factors 
D)   the number of variables" class="answers-bank-image d-inline" rel="preload" >
C)   the common factors
D)   the number of variablesE) A) and B)
F) A) and C)

Exam 19: Factor Analysis

The first step in conducting factor analysis is .

Correct Answer
verified

The equation X_i= A_i1F₁+ A_i2F₂₊A_i3F₃+ ... + A_imF_m₊V_iU_i, represents the common factors expressed as linear combinations of the observed variables.

Correct Answer
verified

is an approach to factor analysis that considers the total variance in the data.

Correct Answer
verified

Describe principal components analysis and common factor analysis and the differences between the two methods of factor analysis.

Only in the case of principal components analysis is it possible to compute exact factor scores.

Correct Answer
verified

Discuss the process of selecting surrogate variables. Also discuss how the researcher should decide on which variable to choose in complex situations.

Correct Answer
verified
Selection of substitute, or surrogate va...
View Answer

The represents the total variance explained by each factor.

Correct Answer
verified
B

The amount of variance a variable shares with all other variables included in the factor analysis is referred to as .

Correct Answer
verified

The differences between the observed correlations (as given in the input correlation matrix) and the reproduced correlations (as estimated from the factor matrix) can be examined to determine model fit.

Correct Answer
verified

Factors can be estimated so that their factor scores are not correlated and the first factor accounts for the highest variance in the data, the second factor the second highest and so on.

Correct Answer
verified

Factor scores should be computed if the goal of factor analysis is to use the results in subsequent multivariate analysis.

Correct Answer
verified

Rotation does not affect the communalities and the percentage of total variance explained.

Correct Answer
verified

is an approach to factor analysis that estimates the factors based only on the common variance.

Correct Answer
verified

Which of the following statements is not true about factor rotation?

Correct Answer
verified
C

is an index that compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficient.

Correct Answer
verified

Residuals are the differences between the observed correlations, as given in the input correlation matrix, and the reproduced correlations, as estimated from the factor matrix.

Correct Answer
verified

Factor analysis can be used in which of the following circumstances?

Correct Answer
verified

Factor analysis examines the whole set of interdependent relationships among variables.

Correct Answer
verified

When using eigenvalues to determine the number of factors, only factors with eigenvalues greater than .05 are retained.

Correct Answer
verified

m represents in the factor model, X_i= A_i1F₁+ A_i2F₂+ A_i3F₃+ ... + A_imF_m+ V_iU_i.

Correct Answer
verified

Exam 19: Factor Analysis

The first step in conducting factor analysis is .

Correct AnswerverifiedShow Answer

The equation Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ... + Aim Fm + ViUi , represents the common factors expressed as linear combinations of the observed variables.

Correct AnswerverifiedShow Answer

is an approach to factor analysis that considers the total variance in the data.

Correct AnswerverifiedShow Answer

Describe principal components analysis and common factor analysis and the differences between the two methods of factor analysis.

Only in the case of principal components analysis is it possible to compute exact factor scores.

Correct AnswerverifiedShow Answer

Discuss the process of selecting surrogate variables. Also discuss how the researcher should decide on which variable to choose in complex situations.

Correct AnswerverifiedSelection of substitute, or surrogate va...View AnswerShow Answer

The represents the total variance explained by each factor.

Correct AnswerverifiedB

The amount of variance a variable shares with all other variables included in the factor analysis is referred to as .

Correct AnswerverifiedShow Answer

The differences between the observed correlations (as given in the input correlation matrix) and the reproduced correlations (as estimated from the factor matrix) can be examined to determine model fit.

Correct AnswerverifiedShow Answer

Factors can be estimated so that their factor scores are not correlated and the first factor accounts for the highest variance in the data, the second factor the second highest and so on.

Correct AnswerverifiedShow Answer

Factor scores should be computed if the goal of factor analysis is to use the results in subsequent multivariate analysis.

Correct AnswerverifiedShow Answer

Rotation does not affect the communalities and the percentage of total variance explained.

Correct AnswerverifiedShow Answer

is an approach to factor analysis that estimates the factors based only on the common variance.

Correct AnswerverifiedShow Answer

Which of the following statements is not true about factor rotation?

Correct AnswerverifiedC

is an index that compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficient.

Correct AnswerverifiedShow Answer

Residuals are the differences between the observed correlations, as given in the input correlation matrix, and the reproduced correlations, as estimated from the factor matrix.

Correct AnswerverifiedShow Answer

Factor analysis can be used in which of the following circumstances?

Correct AnswerverifiedShow Answer

Factor analysis examines the whole set of interdependent relationships among variables.

Correct AnswerverifiedShow Answer

When using eigenvalues to determine the number of factors, only factors with eigenvalues greater than .05 are retained.

Correct AnswerverifiedShow Answer

m represents in the factor model, Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ... + Aim Fm + ViUi.

Correct AnswerverifiedShow Answer

Correct Answer
verified

The equation X_i= A_i1F₁+ A_i2F₂₊A_i3F₃+ ... + A_imF_m₊V_iU_i, represents the common factors expressed as linear combinations of the observed variables.

Correct Answer
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Correct Answer
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Correct Answer
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Selection of substitute, or surrogate va...
View Answer

Correct Answer
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B

Correct Answer
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Correct Answer
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C

Correct Answer
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Correct Answer
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m represents in the factor model, X_i= A_i1F₁+ A_i2F₂+ A_i3F₃+ ... + A_imF_m+ V_iU_i.

Correct Answer
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