Deck 18: Discriminant and Logit Analysis

Question 1

In discriminant analysis, the value of the coefficient for a particular predictor depends on the other predictors included in the discriminant function.

Answer 1

True

Question 2

The stepwise discriminant analysis method is appropriate when, based on previous research or a theoretical model, the researcher wants the discrimination to be based on all the predictors.

Answer 2

False

Question 3

When conducting discriminant analysis, the analysis sample is that part of the total sample used to check the results of the estimation sample.

Answer 3

False

Question 4

The hit ratio is the percentage of cases correctly classified by the discriminant analysis.

Question 5

Discriminant functions are linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups).

Question 6

The hit ratio is the number of variables found to be significant by the discriminant analysis.

Question 7

In discriminant analysis, rejecting the null hypothesis means there is significant discrimination between groups.

Question 8

With the leave-one-out cross-validation option in SPSS, the discriminant model is re-estimated as many times as there are respondents in the sample.

Question 9

The first step in discriminant analysis is to formulate the problem by identifying the objectives, the criterion variable, and the independent variables.

Question 10

A characteristic profile is an aid to interpreting discriminant analysis results by describing each group in terms of the group means for the predictor variables..

Question 11

Also referred to as discriminant loadings, the structure correlations represent the simple correlations between the predictors and the discriminant function in discriminant analysis.

Question 12

The null hypothesis in discriminant analysis, that in the population, the means of all discriminant functions in all groups are not equal, can be statistically tested.

Question 13

The direct method is an approach to discriminant analysis that involves estimating the discriminant function so that all the predictors are included simultaneously.

Question 14

When the dependent variable is binary, the logit model can also be used instead of two-group discriminant analysis.

Question 15

In discriminant analysis, there is no multicollinearity in the predictor variables. Therefore, there is no ambiguous measure of the relative importance of the predictors in discriminating between groups.

Question 16

If attitude towards the brand is measured on a seven-point scale from unfavorable to favorable, it could be categorized as unfavorable (1, 2, 3), neutral (4), or favorable (5, 6, 7).

Question 17

In two-group discriminant analysis it is possible to derive only one discriminant function.

Question 18

When the criterion variable has two categories, the technique is referred to as multiple discriminant analysis.

Question 19

The last step in conducting discriminant analysis is to interpret the results (Figure 18.2 in the text).

Question 20

In the discriminant analysis model, the coefficients, or weights (b), are estimated so that the groups differ as much as possible on the values of the discriminant function. This occurs when the ratio of between-group sum of squares to within-group sum of squares for the discriminant scores is at a maximum.

Question 21

An examination of differences across groups lies at the heart of the basic concept of ________.

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

Question 22

The Mahalanobis procedure is based on minimalizing a generalized measure of the distance between the two closest groups.

Question 23

Discriminant analysis can be used to answer questions such as ________.

A)How much of the variation in sales can be explained by advertising expenditures, prices, and level of distribution?
B)In terms of demographic characteristics, how do customers who exhibit store loyalty differ from those who do not?
C)What are the distinguishing characteristics of consumers who respond to direct mail solicitations?
D)Both B and C are correct.

Question 24

As one of the statistics associated with discriminant analysis, the ________ (unstandardized)are the multipliers of variables when the variables are in the original units of measurement.

A)Wilks' λ
B)discriminant scores
C)discriminant function coefficients
D)eigenvalue

Question 25

When the dependent variable is binary and there is one independent variable that is nonmetric, in addition to two-group discriminant analysis one can also use OLS regression, logit, and probit models for estimation.

Question 26

The logit model falls somewhere between regression and discriminant analysis in application.

Question 27

When the probability of success, P, is modeled using OLS regression, P is constrained to lie between 0 and 1.

Question 28

Discriminant analysis is available in EXCEL.

Question 29

The linear combinations of independent variables developed by discriminant analysis that will best discriminate between the categories of the dependent variable are ________.

A)discriminant functions
B)discriminant scores
C)characteristic profiles
D)classification matrix

Question 30

The nature of dependent and independent variables in the binary logit model is similar to that in ________.

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

Question 31

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

A)examination of whether significant differences exist among the groups, in terms of the criterion variables
B)determination of which predictor variables contribute to most of the intergroup differences
C)classification of cases to one of the groups based on the values of the predictor variables
D)evaluation of the accuracy of classification

Question 32

Discriminant/logit analysis is similar to regression and ANOVA in which of the areas stated below (Table 18.1 in the text)?

A)number of dependent variables
B)number of independent variables
C)both A and B
D)none of the above

Question 33

D is the ________ in the model D = b₀ + b₁ X₁ + b₂ X₂ + b₃X₃ + ...+ b_kX_k.

A)discriminant score
B)disordinal interaction
C)difference variable
D)discriminant coefficients or weights

Question 34

The procedure that is used to estimate the parameters of the binary logit model is called the maximum likelihood method.

Question 35

In discriminant analysis, the criterion or dependent variable is ________ and the predictor or independent variables are ________ in nature.

A)interval; categorical
B)ordinal; interval
C)categorical; interval
D)ordinal; categorical

Question 36

Discriminant/logit analysis is similar to regression and ANOVA in which of the areas stated below (Table 18.1 in the text)?

A)nature of the dependent variables
B)nature of the independent variables
C)both A and B
D)none of the above

Question 37

As one of the statistics associated with discriminant analysis, ________ are obtained when the unstandardized coefficients are multiplied by the values of the variables and the products are summed and added to the constant term.

A)Wilks' λ
B)discriminant scores
C)discriminant function coefficients
D)eigenvalue

Question 38

Sometimes also called confusion or prediction matrix, the ________ contains the number of correctly classified and misclassified cases.

A)classification matrix
B)total correlation matrix
C)pooled within-group correlation matrix
D)identity matrix

Question 39

The results obtained from a classification matrix based on the analysis sample are invariably better than leave-one-out classification or the classification obtained on the holdout sample.

Question 40

The binary logit model commonly deals with the issue of how likely an observation is to belong to each group. It estimates the probability of an observation belonging to a particular group

Question 41

When the dependent variable is binary and there are several independent variables that are metric, in addition to two-group discriminant analysis all of the following models can be used except ________.

A)OLS regression
B)the logit model
C)multiple discriminant analysis
D)the probit model

Question 42

If you are using the direct method or stepwise discriminant analysis, you are at the ________ step of conducting discriminant analysis.

A)formulate the problem
B)estimate the discriminant function coefficients
C)assess the validity of the discriminant analysis
D)determine the size of the discriminant function

Question 43

A ________ is a tool for assessing discriminant analysis results that plots the group membership of each case on a graph.

A)characteristic profile
B)scattergram
C)territorial map
D)pie chart

Question 44

The binary logit model is also called ________.

A)stepwise regression
B)logistic regression
C)OLS regression
D)none of the above

Question 45

What does it mean if the discriminant function is estimated and the square of the canonical correlation is .64?

A)64% of the variance in the dependent variable is explained by the model.
B)The null hypothesis is not rejected.Therefore, there is no significant discrimination between groups.
C)64% of the explained variance is accounted for.
D)B and C are correct.

Question 46

The ________ is used for estimating the ________; the ________ is used for developing the ________.

A)analysis sample; discriminant function; validation sample; classification matrix
B)validation sample; discriminant function; analysis sample; classification matrix
C)classification matrix; discriminant function; validation sample; analysis sample
D)none of the above

Question 47

The ________ is a test of significance of the logistic regression coefficient based on the asymptotic normality property of maximum likelihood estimates.

A)Nagelkerke R2
B)Wald statistic
C)Wilks' λ
D)Cox and Snell R square

Question 48

When the probability of success, P is modeled using a binary logit model, it is constrained to lie between ________.

A)0 to -1
B)-1 to 1
C)1 to 100
D)0 and 1

Question 49

Which of the following statements is true about stepwise discriminant analysis?

A)The predictors are entered sequentially based on their ability to discriminate between groups.
B)The predictor with the highest F ratio is the first to be selected for inclusion in the discriminant function, if it meets certain significance and tolerance criteria.
C)Each predictor selected is tested for retention based on its association with the other predictors selected.
D)All of the above statements are true.

Question 50

Which of the following is not one of the steps involved in the "formulating the problem" step in discriminant analysis?

A)convert the dependent variable into categories
B)divide the sample into analysis and validation samples
C)estimate the discriminant function coefficients
D)repeatedly conduct the validation of the discriminant function

Question 51

Discriminant analysis can be conducted via all of the following except ________.

A)SPSS
B)EXCEL
C)MINITAB
D)SAS

Question 52

In discriminant analysis, we can obtain some idea of the relative importance of the variables by ________.

A)examining the absolute magnitude of the standardized discriminant function coefficients
B)examining the structure correlations, or canonical loadings or discriminant loadings
C)examining the unstandardized discriminant function coefficients
D)A and B are correct

Question 53

The assumptions in discriminant analysis are that each of the groups is a sample from a ________ population and all of the populations have the same ________.

A)multivariate normal; standard deviation
B)multivariate normal; covariance matrix
C)multivariate normal; standard error
D)multivariate normal; variance

Question 54

If there are 10 groups and 8 predictors, how many discriminant functions can be estimated?

A)ten
B)nine
C)eight
D)seven

Question 55

In multiple discriminant analysis, the interpretation of results is aided by an examination of all of the following except ________.

A)the standardized discriminant function coefficients
B)the correlation coefficients
C)the structure correlations
D)certain plots

Question 56

As one of the statistics associated with discriminant analysis, the ________ for each predictor is the ratio of the within-group sum of squares to the total sum of squares. Its value varies between 0 and 1.

A)Wilks' λ
B)discriminant scores
C)discriminant function coefficients
D)eigenvalue

Question 57

Discuss the similarities and differences among ANOVA, regression, and discriminant analysis (Table 18.1 in the text).

Question 58

If you are using the leave-out option of SPSS, you are at the ________ step of discriminant analysis.

A)estimate the discriminant coefficients
B)determine the significance of the discriminant function
C)interpret the results
D)assess validity of discriminant analysis

Question 59

Cox and Snell R square and Nagelkerke R2 are measures of model fit used in ________.

A)logistic regression
B)OLS regression
C)the binary logit model
D)Both A and C are correct.