Introduction to Multivariate Data Analysis
第 17章 多元分析简介
本章概要
? To define multivariate analysis.
? To describe multiple regression analysis and
multiple discriminant analysis.
? To learn about factor analysis and cluster
analysis.
? To gain an appreciation of perceptual
mapping.
? To develop an understanding of conjoint
analysis.
Multivariate Analysis
多变量分析
The term multivariate analysis is used to analyze
multiple measurements on each individual or
object being studied.
Multivariate Techniques
多变量技术
- Multiple regression analysis（多重回归分析）
- Multiple discriminant analysis（多重判别分析）
- Cluster analysis（聚类分析）
- Factor analysis（因子分析）
- Perceptual mapping（感知图）
- Conjoint analysis（结合分析）
Multivariate Software
多变量分析软件
The computational requirements for the various
multivariate procedures discussed in this chapter
are substantial,As a practical matter,running the
various types of analyses presented requires a
computer and appropriate software.
Multiple Regression Analysis
多重回归分析
? Multiple Regression Analysis Defined
– Multiple regression analysis enables the researcher
to predict the level of magnitude of a dependent
variable based on the levels of more than one
independent variable.
Multiple Regression Analysis
? Basic Equation（方程）
Y = a + b1X1 + b2X2 + b3X3 + …+ B nXn
where
Y = dependent or criterion variable
X = estimated constant
b 1-n = coefficients associated with the predictor variables so that
a change of one unit in X will cause a change of b1 units in
Y; the values for the coefficients are estimated from the
regression analysis
X 1-n = predictor (independent) variables that influence the
dependent variable
Multiple Regression Analysis
? Measures（多量）
– Coefficient of Determination R-square
? This statistic can assume values from 0 to 1 and
provides a measure of the percentage of the
variation in the dependent variable that is explained
by variation in the independent variables,
? The b Values
? Or regression coefficients,indicate the effect of the
individual independent variables on the dependent
variable.
Multiple Regression Analysis
? Measures (continued)
– Dummy Variables（哑变量）
? In some situations,the analyst needs to include
nominally scaled independent variables such as
gender,marital status,occupation,or race in a
multiple regression analysis,Dummy variables can
be created for this purpose.
? Dichotomous nominally scaled independent
variables can be transformed into dummy variables
by coding one value (e.g,female) as 0 and the other
(e.g,male) as 1.
Multiple Regression Analysis
? Potential Problems in Using and Interpreting
Multiple Regression Analysis
– Collinearity（共线性）
? Occurs when the independent variables are correlated,
Collinearity leads to unstable regression coefficients.
– Scaling of Coefficients（系数尺度）
? The magnitude of the regression coefficients
associated with the various independent variables can
be compared directly only if they are scaled in the
same units of if the data have been standardized.
Multiple Regression Analysis
? Potential Problems in Using and Interpreting
Multiple Regression Analysis (continued)
– Sample Size（样本容量）
? The value R-square is influenced by the number of
predictor variables relative to sample size,
Discriminant Analysis
判别分析
? Discriminant Analysis Defined 定义
– Multiple discriminant analysis enables the
researcher to predict group membership on the
basis of two or more independent variables.
? Goals of Discriminant Analysis 目的
– Determine if there are statistically significant
differences between the average discriminant
score profiles of the two or more groups.
Discriminant Analysis
? Goals of Discriminant Analysis (continued)
– Establish a model for classifying individuals or
objects into groups on the basis of their values
on the independent variables.
– Determine how much of the difference in the
average score profiles of the two or more
groups is accounted for by each independent
variable.
Discriminant Analysis
? Basic Equation 基本方程 ---判别函数
Z = b1X1 + b2 X2 + b3Xn
where
Z = discriminant score
b1-n = discriminant weights
X 1-n = independent variables
Discriminant Analysis
? Types of Questions that Discriminant
Analysis can Address 用途
– How are consumers that purchase various
brands different from those that do not purchase
those brands?
– How do consumers that go to one fast food
restaurant most frequently differ in their
demographic and lifestyle characteristics from
consumers that go to another fast food
restaurant most frequently?
Cluster Analysis
聚类分析
? Cluster Analysis Defined
– Cluster analysis is a procedure for identifying
subgroups of individuals or items that are
homogeneous within subgroups and different
from other subgroups.
– Procedures for Clustering
– In general,cluster analysis procedures involve
measuring the similarity between people or
objects in regard to their values on the variables
used for clustering.
Factor Analysis
因子分析
? Factor Analysis Defined
– Factor analysis permits the analyst to reduce a
set of variables to a smaller set of factors or
composite variables by identifying dimensions
under the data.
– Objective of Factor Analysis
– The objective is to summarize the information
contained in a large number of metric measures
in a smaller number of summary measures,
called factors.
Factor Analysis
? Factor Scores
– Factor analysis produces one or more 揻
actors?or composite variables when applied to a
number of variables,
– A factor is a weighted summary score of a set
of related variables.
– With factor analysis,we calculate a factor score
on each factor for each subject in the data set.
Factor Analysis
? Factor Loadings
– The nature of the factors derived can be
determined by examining the factor loadings,
Using the scoring equations presented (in the
textbook),a pair of factor scores (F1 and F2) are
calculated for each respondent,
– Factor loadings are determined by calculating
the correlation (can vary from +1.0 to -1.0)
between each factor (F1 and F2) score and each
of the original ratings variables,
Factor Analysis
? Factor Loadings (continued)
– Each correlation coefficient represents the
loading of the associated variable on the
particular factor,
? Other Considerations
– Naming factors.
– How many factors?
Perceptual Mapping
感知图
? Perceptual Mapping Defined
– Perceptual mapping is appropriate when the
goal is to analyze consumer perception of
companies,products,brands,and so on.
? Producing Perceptual Maps
– A number of different approaches are used to
develop perceptual maps,including factor
analysis,multidimensional scaling,
discriminant analysis,and correspondence
analysis.
Perceptual Mapping
Sample Perceptual Map
Val
ue
ServicesSlow Fast
Good
Poor
Restaurant A
Restaurant B
Restaurant CRestaurant D
Conjoint Analysis
结合分析
? Conjoint Analysis Defined
– Conjoint analysis provides a basis to estimate
the utility that consumers associate with
different product features or attributes.
– Process of Conjoint Analysis
– A typical conjoint analysis application involves
a series of steps covering a variety of
procedures and is not a single procedure.
小结（ 1）
? Multivariate analysis refers to a group of
statistical procedures that are used to
simultaneously analyze multiple
measurements on each individual or object
being studied.
小结（ 2）
? Some of the more popular multivariate
techniques include multiple regression
analysis,multiple discriminant analysis,
factor analysis,cluster analysis,perceptual
mapping,and conjoint analysis.
? Multiple regression enables the researcher
to predict the magnitude of a dependent
variable based upon the levels of more than
one independent variable.
小结（ 3）
? Discriminant analysis can be used to
determine if statistically significant
differences exist between the average
discriminant score profiles of two or more
groups.
? Cluster analysis enables a researcher to
identify subgroups of individuals or objects
that are homogeneous within the subgroup
yet different from other subgroups.
小结（ 4）
? The purpose of factor analysis is to simplify
massive amounts of data.
? Perceptual maps provide a visual
representation of how brands,products,
companies,or other objects are perceived
relative to each other on key features such
as quality and value.
小结（ 5）
? Conjoint analysis is a technique that can be
used to measure the trade-offs potential
buyers make between different product or
service offerings available to them on the
basis of the features of each product or
service.
第 17章 多元分析简介
本章概要
? To define multivariate analysis.
? To describe multiple regression analysis and
multiple discriminant analysis.
? To learn about factor analysis and cluster
analysis.
? To gain an appreciation of perceptual
mapping.
? To develop an understanding of conjoint
analysis.
Multivariate Analysis
多变量分析
The term multivariate analysis is used to analyze
multiple measurements on each individual or
object being studied.
Multivariate Techniques
多变量技术
- Multiple regression analysis（多重回归分析）
- Multiple discriminant analysis（多重判别分析）
- Cluster analysis（聚类分析）
- Factor analysis（因子分析）
- Perceptual mapping（感知图）
- Conjoint analysis（结合分析）
Multivariate Software
多变量分析软件
The computational requirements for the various
multivariate procedures discussed in this chapter
are substantial,As a practical matter,running the
various types of analyses presented requires a
computer and appropriate software.
Multiple Regression Analysis
多重回归分析
? Multiple Regression Analysis Defined
– Multiple regression analysis enables the researcher
to predict the level of magnitude of a dependent
variable based on the levels of more than one
independent variable.
Multiple Regression Analysis
? Basic Equation（方程）
Y = a + b1X1 + b2X2 + b3X3 + …+ B nXn
where
Y = dependent or criterion variable
X = estimated constant
b 1-n = coefficients associated with the predictor variables so that
a change of one unit in X will cause a change of b1 units in
Y; the values for the coefficients are estimated from the
regression analysis
X 1-n = predictor (independent) variables that influence the
dependent variable
Multiple Regression Analysis
? Measures（多量）
– Coefficient of Determination R-square
? This statistic can assume values from 0 to 1 and
provides a measure of the percentage of the
variation in the dependent variable that is explained
by variation in the independent variables,
? The b Values
? Or regression coefficients,indicate the effect of the
individual independent variables on the dependent
variable.
Multiple Regression Analysis
? Measures (continued)
– Dummy Variables（哑变量）
? In some situations,the analyst needs to include
nominally scaled independent variables such as
gender,marital status,occupation,or race in a
multiple regression analysis,Dummy variables can
be created for this purpose.
? Dichotomous nominally scaled independent
variables can be transformed into dummy variables
by coding one value (e.g,female) as 0 and the other
(e.g,male) as 1.
Multiple Regression Analysis
? Potential Problems in Using and Interpreting
Multiple Regression Analysis
– Collinearity（共线性）
? Occurs when the independent variables are correlated,
Collinearity leads to unstable regression coefficients.
– Scaling of Coefficients（系数尺度）
? The magnitude of the regression coefficients
associated with the various independent variables can
be compared directly only if they are scaled in the
same units of if the data have been standardized.
Multiple Regression Analysis
? Potential Problems in Using and Interpreting
Multiple Regression Analysis (continued)
– Sample Size（样本容量）
? The value R-square is influenced by the number of
predictor variables relative to sample size,
Discriminant Analysis
判别分析
? Discriminant Analysis Defined 定义
– Multiple discriminant analysis enables the
researcher to predict group membership on the
basis of two or more independent variables.
? Goals of Discriminant Analysis 目的
– Determine if there are statistically significant
differences between the average discriminant
score profiles of the two or more groups.
Discriminant Analysis
? Goals of Discriminant Analysis (continued)
– Establish a model for classifying individuals or
objects into groups on the basis of their values
on the independent variables.
– Determine how much of the difference in the
average score profiles of the two or more
groups is accounted for by each independent
variable.
Discriminant Analysis
? Basic Equation 基本方程 ---判别函数
Z = b1X1 + b2 X2 + b3Xn
where
Z = discriminant score
b1-n = discriminant weights
X 1-n = independent variables
Discriminant Analysis
? Types of Questions that Discriminant
Analysis can Address 用途
– How are consumers that purchase various
brands different from those that do not purchase
those brands?
– How do consumers that go to one fast food
restaurant most frequently differ in their
demographic and lifestyle characteristics from
consumers that go to another fast food
restaurant most frequently?
Cluster Analysis
聚类分析
? Cluster Analysis Defined
– Cluster analysis is a procedure for identifying
subgroups of individuals or items that are
homogeneous within subgroups and different
from other subgroups.
– Procedures for Clustering
– In general,cluster analysis procedures involve
measuring the similarity between people or
objects in regard to their values on the variables
used for clustering.
Factor Analysis
因子分析
? Factor Analysis Defined
– Factor analysis permits the analyst to reduce a
set of variables to a smaller set of factors or
composite variables by identifying dimensions
under the data.
– Objective of Factor Analysis
– The objective is to summarize the information
contained in a large number of metric measures
in a smaller number of summary measures,
called factors.
Factor Analysis
? Factor Scores
– Factor analysis produces one or more 揻
actors?or composite variables when applied to a
number of variables,
– A factor is a weighted summary score of a set
of related variables.
– With factor analysis,we calculate a factor score
on each factor for each subject in the data set.
Factor Analysis
? Factor Loadings
– The nature of the factors derived can be
determined by examining the factor loadings,
Using the scoring equations presented (in the
textbook),a pair of factor scores (F1 and F2) are
calculated for each respondent,
– Factor loadings are determined by calculating
the correlation (can vary from +1.0 to -1.0)
between each factor (F1 and F2) score and each
of the original ratings variables,
Factor Analysis
? Factor Loadings (continued)
– Each correlation coefficient represents the
loading of the associated variable on the
particular factor,
? Other Considerations
– Naming factors.
– How many factors?
Perceptual Mapping
感知图
? Perceptual Mapping Defined
– Perceptual mapping is appropriate when the
goal is to analyze consumer perception of
companies,products,brands,and so on.
? Producing Perceptual Maps
– A number of different approaches are used to
develop perceptual maps,including factor
analysis,multidimensional scaling,
discriminant analysis,and correspondence
analysis.
Perceptual Mapping
Sample Perceptual Map
Val
ue
ServicesSlow Fast
Good
Poor
Restaurant A
Restaurant B
Restaurant CRestaurant D
Conjoint Analysis
结合分析
? Conjoint Analysis Defined
– Conjoint analysis provides a basis to estimate
the utility that consumers associate with
different product features or attributes.
– Process of Conjoint Analysis
– A typical conjoint analysis application involves
a series of steps covering a variety of
procedures and is not a single procedure.
小结（ 1）
? Multivariate analysis refers to a group of
statistical procedures that are used to
simultaneously analyze multiple
measurements on each individual or object
being studied.
小结（ 2）
? Some of the more popular multivariate
techniques include multiple regression
analysis,multiple discriminant analysis,
factor analysis,cluster analysis,perceptual
mapping,and conjoint analysis.
? Multiple regression enables the researcher
to predict the magnitude of a dependent
variable based upon the levels of more than
one independent variable.
小结（ 3）
? Discriminant analysis can be used to
determine if statistically significant
differences exist between the average
discriminant score profiles of two or more
groups.
? Cluster analysis enables a researcher to
identify subgroups of individuals or objects
that are homogeneous within the subgroup
yet different from other subgroups.
小结（ 4）
? The purpose of factor analysis is to simplify
massive amounts of data.
? Perceptual maps provide a visual
representation of how brands,products,
companies,or other objects are perceived
relative to each other on key features such
as quality and value.
小结（ 5）
? Conjoint analysis is a technique that can be
used to measure the trade-offs potential
buyers make between different product or
service offerings available to them on the
basis of the features of each product or
service.
