Deck 20: Discriminant, Factor and Cluster Analysis

Question 1

The statistical explanation for discriminant analysis is that of maximizing the between-group variance relative to the within-group variance.

Answer 1

True

Question 2

A factor score is a measurement of how closely related each input variable is to a derived factor.

Answer 2

False

Question 3

One function of factor analysis is to identify underlying constructs in the data.

Answer 3

True

Question 4

The cutoff score is the criterion score) against which each individual's discriminant score is judged to determine into which group the individual should be classified

Question 5

Factor analysis is usefully employed when it is desirable to combine several questions, thereby creating a new variable.

Question 6

Each respondent has a factor score on each factor in addition to the respondent's rating on the original variables.

Question 7

One rule of thumb in deciding on the number of factors to retain is to include all factors that explain at least 50 percent of the variance.

Question 8

In discriminant analysis, with 'm' groups and 'p' predictor variables, min p,m-1) gives the number of discriminant functions.

Question 9

Discriminant analysis can only be used for description and not for prediction purposes.

Question 10

Larger values of Wilks lambda indicate that the group means appear to be different.

Question 11

Discriminant analysis techniques are used to classify into one of two or more alternate groups based on a set of measurements.

Question 12

The objective of a discriminant analysis is to predict the value of the dependent variable based on the values of the fixed independent variables.

Question 13

Factor analysis is usefully employed when there is a need to determine the direction of causality between two or three variables.

Question 14

Discriminant analysis involves the maximization of the between-group variance relative to the within-group variance

Question 15

The underlying assumption in a discriminant analysis is that the independent variables are assumed to be normally distributed.

Question 16

Regression and Discriminant analyses are computationally similar

Question 17

Factor loadings are a measurement of the correlations between the factors and the original variables.

Question 18

A factor is a variable or construct that is not directly observable but needs to be inferred from the input variables.

Question 19

In discriminant analysis, predictors with a large coefficient contribute more to the discriminating power of the function.

Question 20

The group mean, in a discriminant analysis, is known as the centroid.

Question 21

A nonhierarchical clustering program is one in which objects are allowed to leave one cluster to join another as clusters are being formed if the clustering criterion will be improved by doing so.

Question 22

Common factor analysis focuses on shared variance, hence communalities are used in the diagonal of the matrix

Question 23

The first factor accounts for more of the variation in the data than the second factor.

Question 24

An attractive feature of principal components analysis is the easy interpretability of the factors.

Question 25

An attractive feature of varimax rotation is that it may retain the variance explained, while reducing the number of factors in the solution as compared to principal components analysis).

Question 26

In the hierarchical approach, the commonly used methods are single linkage, complete linkage, average linkage, Ward's method, and the centroid method.

Question 27

In both principal components analysis and varimax rotation, the factors are constrained to be uncorrelated or geometrically perpendicular.

Question 28

Rotation of factors changes the interpretation of the factors while retaining the principal component patterns of loadings.

Question 29

After performing a principal components analysis, a researcher finds that the cumulative variance explained by the solution is 0.56.He can increase the explained variance by performing a varimax rotation.

Question 30

Communality is the percent of a variable's variance which contributes to the correlation with other variables or is common to other variables.

Question 31

Simple Euclidean distance is a common measurement of similarity on a perceptual map.

Question 32

The percent of variance explained is a summary measurement indicating how much of the total original variance of all the respondents is represented by the factor.

Question 33

The basic task in cluster analysis is to uncover competing explanations for a causal phenomenon.

Question 34

If a clustering procedure starts with one cluster and subdivides until all objects are in their own single-object cluster, the procedure is termed top-down hierarchical clustering.

Question 35

The ABC Company is involved in trying to segment its market so that it can better design specific marketing programs directed at each segment.One method of segmenting that it might use is cluster analysis.

Question 36

A major advantage of cluster analysis is the availability of standard statistical tests to ensure that the output does not represent pure randomness.

Question 37

While analyzing and interpreting consumer perception data using factor analysis, a researcher found the factor loading on Factor 1 to be high.However, he could not interpret the factor meaningfully.A probable cause for this situation is computation error or shortsightedness in his interpretation, since a high loading ensures meaningfulness.

Question 38

All factor analysis methods constrain the factors to be uncorrelated.

Question 39

The variation in variable 3 is shown to be completely explained by the two-factor solution.

Question 40

Factor loadings and correlations are identical if each variable has its mean subtracted and is divided by its standard deviation.

Question 41

A plot of eigenvalues against the number of factors is called a) factor loading b) scree c) factor score d) communality

Question 42

In discriminant analysis, with M groups and p predictor variables, the number of discriminant functions is given by

A)m-1, p-1)
B)m-1, p)
C)m, p-1)
D)m, p)

Question 43

The coefficients that link the factors to the variables are called

A)factor loadings
B)screes
C)factor scores
D)eigenvalues

Question 44

The analysis technique used to identify variables that contribute to differences in the a prior defined groups is

A)regression.
B)discriminant analysis.
C)conjoint analysis.
D)factor analysis.

Question 45

Given multivariate data, cluster analysis techniques seek to identify natural groupings of objects.

Question 46

Initial starting points in nonhierarchical clustering is represented by a) cluster membership b) cluster seeds c) cluster centurions d) none of the above

Question 47

Factor is observable that is why it is a variable.

Question 48

The amount of variance a variable shares with other variables is called a) communality b) factor loading c) factor score d) none of the above

Question 49

Which of the following statements is not true of Wilks' Lamba? a) it is the ratio of within-group variance to total variance b) it takes values between 0 and 1 c) larger values indicate that group means do not appear to be different d) none of the above

Question 50

Which one of the following is not an objective of discriminant analysis?

A)Determining linear combinations of the predictor variables to separate groups
B)Developing procedures for assigning new objects
C)Determining the variables that explain the intergroup differences
D)Predicting the level of the dependent variable when the independent variable is changed.

Question 51

In factor analysis each subsequent factor accounts for a) increasing amount of variance in data b) decreasing amount of variance in data c) same amount of variance in data d) none of the above

Question 52

All of the following are true about factor analysis except

A)it is a technique that serves to combine questions, thereby creating new variables.
B)it is an analysis of interdependence technique that analyzes the interdependence between questions, variables, or objects.
C)it can help the analyst determine which questions, variables, or objects are redundant and what they are measuring.
D)all of these are true

Question 53

The simple correlation between the independent variable and the discriminant function is represented by a) discriminant loading b) structure correlation c) total correlation matrix d) centroid

Question 54

Nonhierarchical clustering will produce tighter clusters due to the fact that an object will be admitted into a cluster only if it improves the clustering criterion.

Question 55

Which of the following is not true about cluster analysis?

A)it is a technique for grouping individuals or objects into unknown groups.
B)there are two approaches to clustering- hierarchical and nonhierarchical.
C)the centroid - the average value of the objects in a cluster on each of the variables making up each object's profile - is used to describe the clusters.
D)there is a single approach to determining the appropriate number of clusters

Question 56

The amount of variance in the original variables that is associated with a factor is represented by

A)factor loading
B)scree
C)factor score
D)eigenvalue

Question 57

For discrimination to be based on all predictors the most appropriate function estimation method is a) sequential b) direct c) pooled d) stepwise

Question 58

If the primary purpose is data reduction one would use a) cluster analysis b) factor analysis c) discriminant analysis d) conjoint analysis