Deck 19: Factor Analysis

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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 6

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

Question 7

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 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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 14

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

Question 15

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

Question 16

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

Question 17

Factor analysis does not classify variables as dependent or independent.

Question 18

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

Question 19

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

Question 20

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 21

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 22

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

Question 23

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

A) a unique factor variable
B) the number of common factors
C) the common factor
D) the number of variables

Question 24

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

Question 25

Factor loadings represent the correlations between sets of variables.

Question 26

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

Question 27

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

Question 28

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

A) Fi = Wi1 X1 + Wi2 X2 + Wi3 X3 + ...+ Wim Xm + ViUi
B) Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ...+ Aim Fm
C) Xi = Wi1 F1 + Wi2 F2 + Wi3 F3 + ...+ Wim Fm + ViUi
D) Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ...+ Aim Fm + ViUi

Question 29

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 30

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

A) total variance
B) communality
C) shared variance
D) percentage of variance

Question 31

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) varimax procedure
D) interdependence technique

Question 32

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

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

Question 33

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

Question 34

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 35

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

Question 36

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

Question 37

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

A) discriminant analysis
B) regression analysis
C) analysis of variance
D) factor analysis

Question 38

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

A) To identify a smaller set of salient variables from a larger set for use in subsequent multivariate analysis.
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 underlying dimensions,or factors,that explain the correlations among a set of variables.
D) All are correct circumstances.

Question 39

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

Question 40

The factor matrix is also called the factor pattern matrix.

Question 41

The ________ represents the total variance explained by each factor.

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

Question 42

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

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

Question 43

________ are simple correlations between the variables and the factors.

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

Question 44

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

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

Question 45

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 46

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

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

Question 47

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

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

Question 48

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

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

Question 49

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

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

Question 50

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

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) Preferably,each factor should have a nonzero,or significant,loadings or coefficients for only some of the variables.
D) Rotation affects the communalities and the percentage of total variance explained.

Question 51

The first step in conducting factor analysis is ________.

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

Question 52

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

A) the mth standardized variable
B) the common factors
C) the number of common factors
D) the number of variables

Question 53

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 54

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

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

Question 55

Which is not a method of factor analysis?

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

Question 56

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 57

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

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

Question 58

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

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

Question 59

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 60

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

Question 61

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

Question 62

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

Question 63

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 64

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

A) Fi = Wi1 X1 + Wi2 X2 + Wi3 Y3 + ...+ Wik Yk
B) Xi = Wi1 F1 + Wi2 F2 + Wi3 F3 + ...+ Wim Fm
C) Xi = Ai1 F1 + Ai2 F2 + Ai3 F3 + ...+ Aim Fm
D) Fi = Wi1 X1 + Wi2 X2 + Wi3 X3 + ...+ Wik Xk

Question 65

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

Question 66

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

Question 67

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

Question 68

________ is the last step in factor analysis.

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

Question 69

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

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