Question 1

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 2

The represents the total variance explained by each factor.

Accepted Answer

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

Question 3

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. 
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. C

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

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

Question 6

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 7

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

Accepted Answer

A) True 
 B)False

Question 8

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 9

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 10

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 11

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

Question 12

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

Question 13

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. 
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.

Question 14

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 15

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

Accepted Answer

A) True 
 B)False

Question 16

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 17

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

Question 18

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

Question 19

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

Question 20

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

Exam 19: Factor Analysis

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

The represents the total variance explained by each factor.

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

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

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

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.

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

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

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.

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

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

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

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

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.

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

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

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

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

The first step in conducting factor analysis is .

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

Introduction to Marketing

Defining the Marketing Research

Research Design

Exploratory Research Design

Exploratory Research Design

Descriptive Research Design

Causal Research Design

Measurement and Scaling

Measurement and Scaling

Questionnaire and Form

Sampling: Design and

Sampling: Final and Initial

Fieldwork

Data Preparation

Frequency Distribution, Crosstabulation, and Hypothesis

Analysis of Variance and

Correlation and Regression

Discriminant and Logit

Cluster Analysis

Multidimensional Scaling and

Structural Equation Modeling

Report Preparation and

International Marketing

Filters

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

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.