Question 1

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

Accepted Answer

In principal components analysis (PCA), it is possible to compute exact factor scores because PCA assumes that the observed variables are linear combinations of the underlying factors, and the factor loadings are obtained as orthogonal transformations of the original variables. Thus, the factor scores can be computed as weighted sums of the original variables, with the weights given by the factor loadings. However, in other factor analysis methods, such as exploratory factor analysis (EFA), it is not possible to compute exact factor scores because EFA assumes that the observed variables are linear combinations of the underlying factors plus a unique error term, and the factor loadings are estimated as correlations between the observed variables and the underlying factors. Thus, the factor scores can only be estimated, not computed exactly.

Question 2

If interpreting factors using the rotated factor matrix, a negative coefficient for a negative variable (prevention of tooth decay is not important)would lead to a positive interpretation (prevention of tooth decay is important).

Accepted Answer

A negative coefficient in the rotated factor matrix indicates a negative relationship between the factor and the variable. However, when interpreting the factor, it is important to consider the meaning of the variable. In the case of a negative variable, a negative coefficient in the rotated factor matrix would suggest that the absence of the variable (e.g. the prevention of tooth decay) is associated with a positive factor score (e.g. the factor associated with good oral hygiene practices), which can be interpreted as the importance of preventing tooth decay.

Question 3

The unrotated factor matrix seldom results in factors that can be interpreted because the factors are correlated with many variables.

Accepted Answer

It is common for the unrotated factor matrix to have correlated factors that cannot be easily interpreted. Rotation techniques such as Varimax or Oblimin can be used to produce more interpretable factor solutions.

Question 4

________ is a class of procedures primarily used for data reduction and summarization.
A)Regression analysis
B)Factor analysis
C)Discriminant analysis
D)Conjoint analysis

Accepted Answer

Factor analysis is a statistical method used to reduce a large number of variables to a smaller number of underlying factors or dimensions. It is primarily used for data reduction and summarization, as it helps to identify the most important variables that contribute to a particular phenomenon or outcome. Regression analysis, discriminant analysis, and conjoint analysis are other statistical procedures that serve different purposes, such as modeling relationships between variables, predicting group membership, or measuring consumers' preferences and trade-offs.

Question 5

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

Accepted Answer

Selecting surrogate variables based on one factor loading being clearly higher than all other factor loadings ensures that the variable strongly represents the underlying factor it is associated with, making it a good representative or surrogate for that factor in analyses.

Question 6

Factor loadings represent the correlations between sets of variables.

Accepted Answer

The answer of Factor loadings represent the correlations between sets...

Question 7

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

Accepted Answer

Factor scores are computed from factor analysis in order to use the results in subsequent multivariate analysis. These scores represent the values of each individual on each factor and can be used as variables in further analysis.

Question 8

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

Accepted Answer

Rotation only changes the pattern of factor loadings, but it does not affect the communalities (because they are based on the original variables) or the percentage of total variance explained (because this is determined by the eigenvalues of the correlation matrix, which remain the same after rotation).

Question 9

If the variables are standardized, the factor model may be presented as ________. A)X_i= A_i1 F₁+ A_i2 F₂+A_i3 F₃+ ...+ A_im F_m+V_iU_i B)X_i = W_i1 F₁+ W_i2 F₂+W_i3 F₃+ ...+ W_im F_m+V_iU_i C)F_i = W_i1 X₁+ W_i2 X₂+W_i3 X₃+ ...+ W_im X_m+V_iU_i D)X_i = A_i1 F₁+ A_i2 F₂+A_i3 F_{3 + ...+} A_im F_m

Accepted Answer

The given equation is in the standard factor model form after standardization.

Question 10

Factor analysis can be used in which of the following circumstances?
A)To identify underlying dimensions, or factors, that explain the correlations among a set of variables.
B)To identify a new, smaller set of uncorrelated variables to replace the original set of correlated variables in subsequent multivariate analysis.
C)To identify a smaller set of salient variables from a larger set for use in subsequent multivariate analysis.
D)All are correct circumstances.

Accepted Answer

All of the options listed are appropriate uses of factor analysis. Factor analysis can be used to identify underlying dimensions among a set of variables, reduce the number of correlated variables in multivariate analysis, and identify salient variables from a larger set.

Question 11

Which method of analysis does not classify variables as dependent or independent?
A)regression analysis
B)discriminant analysis
C)analysis of variance
D)factor analysis

Accepted Answer

Factor analysis does not classify variables as dependent or independent. Instead, it explores the underlying structure of a set of variables and identifies factors that explain the patterns in the data.

Question 12

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

This statement is true. Differences between the observed and reproduced correlations can be used to assess the fit of a factor model.

Question 13

Interpretation is facilitated by identifying the variables that have small loadings on the same factor.

Accepted Answer

Interpretation is facilitated by identifying the variables that have large loadings on the same factor, as this indicates they share a common underlying construct or dimension.

Question 14

F represents ________ in the factor model X_i= A_i1 F₁+ A_i2 F₂+A_i3 F₃+ ...+ A_im F_m+V_iU_i? A)the number of variables B)the number of common factors C)the common factor D)a unique factor variable

Accepted Answer

The answer of F represents ________ in the factor model...

Question 15

Which of the following applications is appropriate for using factor analysis?
A)to understand the media consumption habits of the target market
B)to determine if variation in market share can be accounted for by the size of the sales force and advertising expenditures
C)to identify the characteristics of price-sensitive consumers
D)Both A and C are correct.

Accepted Answer

Factor analysis is appropriate for both A and C. A can benefit from factor analysis to identify patterns from media consumption habits of the target market. C can use factor analysis to identify the characteristics of price-sensitive consumers. B, on the other hand, requires regression analysis to determine cause-and-effect relationships between the sales force, advertising expenditures, and market share.

Question 16

Factor analysis is a(n)________ in that the entire set of interdependent relationships is examined.
A)KMO measure of sampling adequacy
B)orthogonal procedure
C)interdependence technique
D)varimax procedure

Accepted Answer

Factor analysis is an interdependence technique where the relationships among variables are examined in order to identify underlying factors. KMO measure of sampling adequacy, orthogonal procedure, and varimax procedure are all specific components or methods used in the factor analysis process.

Question 17

When selecting variables to serve as surrogate variables, you should look for the variable with the highest loading on a factor.

Accepted Answer

Surrogate variables are selected based on their high loading on a factor, which indicates that they are strongly associated with the underlying construct being measured.

Question 18

The amount of variance a variable shares with all other variables included in the factor analysis is referred to as ________.
A)communality
B)total variance
C)shared variance
D)percentage of variance

Accepted Answer

Communality is the amount of variance that a variable shares with all the other variables included in the factor analysis. It represents the portion of the variable's total variance that is accounted for by the common underlying factors. B, C, and D are not correct because they do not specifically refer to the variance shared with other variables in the analysis.

Question 19

A factor model that provides a good fit to the data has many large residuals.

Accepted Answer

A good fit to the data means that the model is able to explain the data well, resulting in smaller residuals. Large residuals indicate that the model is not capturing all the variability in the data and may not be a good fit.

Question 20

The factor matrix is also called the factor pattern matrix.

Accepted Answer

The factor matrix is also known as the factor pattern matrix, so the statement is true.

Quiz 19: Factor Analysis

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

If interpreting factors using the rotated factor matrix, a negative coefficient for a negative variable (prevention of tooth decay is not important)would lead to a positive interpretation (prevention of tooth decay is important).

The unrotated factor matrix seldom results in factors that can be interpreted because the factors are correlated with many variables.

________ is a class of procedures primarily used for data reduction and summarization.

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

Factor loadings represent the correlations between sets of variables.

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

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

If the variables are standardized, the factor model may be presented as ________.

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

Which method of analysis does not classify variables as dependent or independent?

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.

Interpretation is facilitated by identifying the variables that have small loadings on the same factor.

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

Which of the following applications is appropriate for using factor analysis?

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

When selecting variables to serve as surrogate variables, you should look for the variable with the highest loading on a factor.

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

A factor model that provides a good fit to the data has many large residuals.

The factor matrix is also called the factor pattern matrix.

Quiz 19: Factor Analysis

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

If interpreting factors using the rotated factor matrix, a negative coefficient for a negative variable (prevention of tooth decay is not important)would lead to a positive interpretation (prevention of tooth decay is important).

The unrotated factor matrix seldom results in factors that can be interpreted because the factors are correlated with many variables.

________ is a class of procedures primarily used for data reduction and summarization.

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

Factor loadings represent the correlations between sets of variables.

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

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

If the variables are standardized, the factor model may be presented as ________.

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

Which method of analysis does not classify variables as dependent or independent?

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.

Interpretation is facilitated by identifying the variables that have small loadings on the same factor.

F represents ________ in the factor model Xi = Ai1 F1 + Ai2 F2+ Ai3 F3 + ...+ Aim Fm + ViUi?

Which of the following applications is appropriate for using factor analysis?

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

When selecting variables to serve as surrogate variables, you should look for the variable with the highest loading on a factor.

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

A factor model that provides a good fit to the data has many large residuals.

The factor matrix is also called the factor pattern matrix.

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