Deck 19: Factor Analysis

Question 1

The factors identified in factor analysis are overtly observed in the population.

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

It is possible to compute as many principal components as there are variables; in doing so, parsimony is gained.

Question 6

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

Question 7

Percentage of variance accounted for, scree plot, and a priori determination are all procedures for determining the number of factors.

Question 8

The various methods of factor analysis are differentiated by the approach used to derive the weights or factor score coefficients.

Question 9

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

Question 10

Generally, the number of factors determined by a scree plot will be one or a few less than that determined by the eigenvalue criterion.

Question 11

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

Question 12

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.

Question 13

The equation X_i = A_i1 F₁ + A_i2 F_{2 +} A_i3 F₃ + ...+ A_im F_{m +} V_iU_i , represents the common factors expressed as linear combinations of the observed variables.

Question 14

Bartlett's test of sphericity is one test of the appropriateness of the factor model.

Question 15

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.

Question 16

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

Question 17

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.

Question 18

Factor analysis does not classify variables as dependent or independent.

Question 19

The variables to be included in the factor analysis should be specified based on past research, theory, and the judgment of the researcher.

Question 20

Factor analysis is somewhat similar to discriminant analysis in that each variable is expressed as a linear combination of underlying factors.

Question 21

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

Question 22

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).

Question 23

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

Question 24

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

A)Regression analysis
B)Factor analysis
C)Discriminant analysis
D)Conjoint analysis

Question 25

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

Question 26

Factor loadings represent the correlations between sets of variables.

Question 27

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

Question 28

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

Question 29

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

Question 30

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.

Question 31

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

Question 32

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.

Question 33

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

Question 34

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

Question 35

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.

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

The factor matrix is also called the factor pattern matrix.

Question 41

Communality is ________.

A)the amount of variance a variable shares with all the other variables being considered
B)the percentage of the total variance attributed to each factor
C)the proportion of variance explained by the common factors
D)both A and C are correct

Question 42

m 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 mth standardized variable
D)the common factors

Question 43

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

A)Mahalanobis ratio
B)KMO measure of sampling adequacy
C)Bartlett's test of sphericity
D)Wilks' lambda

Question 44

Which is not a method of factor analysis?

A)principal components analysis
B)common factor analysis
C)omega method
D)unweighted least squares

Question 45

________ should be used when factors in the population are likely to be strongly correlated.

A)Orthogonal rotation
B)The varimax procedure
C)Oblique rotation
D)None of the above

Question 46

As a rough guideline, there should be at least ________ times as many observations (sample size)as there are variables.

A)two or three
B)three or four
C)four or five
D)five or six

Question 47

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

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

Question 48

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 ________.

A)a priori determination
B)determination based on split-half reliability
C)determination based on significance tests
D)determination based on scree plot

Question 49

Factor analysis may not be appropriate in all of the following situations except ________.

A)a small value for Bartlett's test of sphericity is found
B)small values of the KMO statistic are found
C)the variables are not correlated
D)the variables are correlated

Question 50

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

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

Question 51

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

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

Question 52

Which of the following is a way to interpret factors?

A)based on the variables that load high on a factor
B)by plotting the variables using the factor loadings as coordinates
C)both A and B
D)none of the above

Question 53

The first step in conducting factor analysis is ________.

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

Question 54

Which statement is not true about principal components analysis (PCA)?

A)The factors are estimated based only on the common variance.
B)The total variance in the data is considered.
C)PCA 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.
D)The diagonal of the correlation matrix consist of unities.

Question 55

A ________ is a lower triangle matrix showing the simple correlations, r, between all possible pairs of variables included in the analysis.

A)factor matrix
B)classification matrix
C)correlation matrix
D)total correlation matrix

Question 56

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?

A)one
B)two
C)four
D)six

Question 57

A ________ is a plot of the original variables using the factor loadings as coordinates.

A)scree plot
B)territorial map
C)factor loading plot
D)scattergram

Question 58

The ________ represents the total variance explained by each factor.

A)eigenvalue
B)percentage of variance
C)residual
D)communality

Question 59

It is recommended that the factors extracted should account for at least ________ of the variance.

A)50 %
B)60%
C)65%
D)70%

Question 60

________ are simple correlations between the variables and the factors.

A)Factor scores
B)Factor loadings
C)Correlation loadings
D)Both A and B are correct

Question 61

What are the steps involved in conducting factor analysis (Figure 19.3 in the text)?

Question 62

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

Question 63

________ is the last step in factor analysis.

A)Interpret the factors
B)Determine the model fit
C)Rotate the factors
D)Determine the number of factors

Question 64

If the goal of factor analysis is to reduce the original set of variables to a smaller set of composite variables for use in subsequent multivariate analysis, it is useful to ________.

A)compute factor scores for each respondent
B)compute discriminant scores for each respondent
C)select surrogate variables
D)both A and B are correct

Question 65

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

Question 66

Under what general circumstances is factor analysis used?

Question 67

Which statement is not correct concerning factor scores?

A)In principal components analysis it is possible to compute exact factor scores that are uncorrelated.
B)In common factor analysis, estimates of factor scores are obtained, and there is no guarantee that factors will be uncorrelated with each other.
C)Factor scores can be used instead of the original variables in subsequent multivariate analysis.
D)All statements are correct.

Question 68

When selecting surrogate variables from variables with similarly high loadings, the choice should be based on ________.

A)measurement considerations
B)theoretical considerations
C)Both A and B are correct
D)the variable with the highest loading on a factor

Question 69

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

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

Question 70

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