Multivariate analysis[1]

Multivariate analysis : 

Multivariate analysis -

What does multivariate mean? : 

9/19/2010 Latent Variable Modeling 2 What does multivariate mean? More than one variable are needed to describe a system For example Weather: 1.Humidity 2.Temperature 3.Pressure And so on

MANOVA ~ the definition : 

MANOVA ~ the definition Technique for assessing group differences across multiple metric dependent variables (DV’s) simultaneously, based on a set of categorical (non-metric) variables acting as independent variables (IV’s)

ANOVA vs. MANOVA : 

ANOVA vs. MANOVA ANOVA ~ only 1 dependent variable MANOVA ~ 2 or more dependent variables Both are used with experimental designs in which researchers manipulate or control one or more independent variables to determine the effect on one (ANOVA) or more (MANOVA) dependent variables

Equations : 

Equations ANOVA Y1 = X1 + X2 + X3 +...+ Xn (metric DV) (non-metric IV’s) MANOVA Y1 + Y2 + ... + Yn = X1 + X2 + X3 +...+ Xn (metric DV’s) (non-metric IV’s)

MANOVA and Regression : 

MANOVA and Regression In multiple regression, univariate and multivariate/multiple refer to the number of IV’s In ANOVA and MANOVA discussions, univariate and multivariate refer to the number of DV’s

Univariate Research Example : 

Univariate Research Example Subjects shown different advertising messages Emotional or Informational or ?? Viewers rate appeal of the message using scores from 1 to 10 Ad appeal?

Univariate Review ~ t Test : 

Univariate Review ~ t Test Two commercials shown (emotional~informational) Single treatment/factor with two levels Use a t Test: One IV’s, one DV, two treatment groups The t statistic = M1 - M2 ---------------------- SEM1 M2

Univariate Review ~ ANOVA : 

Univariate Review ~ ANOVA Two or more commercials (emotional~informational~funny~etc) Single treatment/factor with two or more levels Use ANOVA : Multiple IV’s, one DV, two or more treatment groups F statistic = MSB ------ MSW

Univariate Hypothesis Testing : 

Univariate Hypothesis Testing Null Hypothesis (H0) ~ That there is no difference between the DV means of the treatment groups Alternate Hypothesis (HA) ~ That there is a statistically significant difference between the DV means of the treatment groups

Multivariate Research Example : 

Multivariate Research Example Subjects shown different advertising messages Emotional or Informational or ?? Viewers rate appeal of the message using scores from 1 to 10 Ad appeal? Will I buy?

Multivariate Procedures : 

Multivariate Procedures One IV, multiple DV’s, two groups The k Group Case: MANOVA Multiple IV’s, multiple DV’s, more than two treatment groups Null Hypothesis ~ that there is no difference between vectors of means of multiple DV’s across the treatment groups

Null Hypothesis Testing : 

Null Hypothesis Testing ANOVA H0: M1 = M2 =...Mk H0: All the group means are equal, that is, they come from the same populations MANOVA M11 M21 Mp1 M12 M22 Mp2 M1k M2k Mpk = =...= H0: All the group mean vectors are equal, that is, they come from the same populations

When to use MANOVA : 

When to use MANOVA When you have multiple dependent variables Control of Experimentwide Error Rate Repeated univariate procedures can dramatically increase Type I errors DV’s that are not highly correlated with one another will cause the most trouble Differences among a Combination of Dependent Variables Multiple univariate procedures do not equal a multivariate procedure

Three Main Functions : 

9/19/2010 Latent Variable Modeling 15 Three Main Functions Control Elaboration Prediction

Benefits of Multivariate Analysis : 

9/19/2010 Latent Variable Modeling 16 Benefits of Multivariate Analysis Control- Multivariate Analysis allows the researcher to control association between variables by using cross tabulation, partial correlation and multiple regression.

: 

9/19/2010 Latent Variable Modeling 17 Elaboration- Multivariate analysis allows the researcher to elaborate on the relationship between two variables in order to determine the relationship between the variables or to determine the conditions necessary to create a specific relationship between variables. Introduces other variables to determine the links between the independent and dependent variables or to specify the conditions under which the association takes place Benefits of Multivariate Analysis

Benefits of Multivariate Analysis : 

9/19/2010 Latent Variable Modeling 18 Benefits of Multivariate Analysis Prediction (Path Analysis?)- uses bivariate and multiple linear regression to test the causal relations among the variables specified in the model. 3 steps: researcher draws a path diagram based on a theory, researcher calculates path coefficients, researcher determines indirect effects.

Difficulties/demerites of Multivariate Analysis : 

9/19/2010 Latent Variable Modeling 19 Difficulties/demerites of Multivariate Analysis

IT Takes a Long Time : 

9/19/2010 Latent Variable Modeling 20 IT Takes a Long Time

The Math is HARD : 

9/19/2010 Latent Variable Modeling 21 The Math is HARD

It’s Expensive : 

9/19/2010 Latent Variable Modeling 22 It’s Expensive

It’s Complicated : 

9/19/2010 Latent Variable Modeling 23 It’s Complicated

IT’S Difficult to Display : 

9/19/2010 Latent Variable Modeling 24 IT’S Difficult to Display

Types of MANOVA : 

Types of MANOVA

Classification of Multivariate Methods : 

9/19/2010 Latent Variable Modeling 26 Classification of Multivariate Methods 18-4

1 Multiple Regression : 

9/19/2010 Latent Variable Modeling 27 1 Multiple Regression An extension of bivariate regression Allows for the simultaneous investigation two or more independent variables a single interval-scaled dependent variable

Regression Analysis : 

Regression Analysis Attempts to explain the variability in a dependent variable (e.g., sales) using one or more independent variables (e.g., advertising, price, promotion etc.) A composite (usually linear) of the independent variables that is close in magnitude to the value of the dependent variable (*) Sales = a + b Advertising - c Price + Error Known: Values of Sales, Advertising and Price Unknown: a, b, c, Error Strategy: Assuming some properties for the Error, come up with values of a, b, and c that satisfy * above

Issues in Regression Modeling : 

Issues in Regression Modeling A model is an abstraction of reality In developing a Marketing model, three points to note are: Variables and their operationalizations Nature of relationships among variables Functional form governing the relationship Operationalization is critical: Are sales defined as shipments, warehouse withdrawals, or retail sales? Nature of relationships: Is the effect of price / advertising interaction positive or negative

Discriminant Analysis : 

9/19/2010 Latent Variable Modeling 30 Discriminant Analysis A research team uses discriminant analysis to classify groups or objects by a set of independent variables. Discriminant analysis enables a marketing researcher to determine linear combinations of the independent variables of interest to the client. 18-11

Discriminant Analysis: An Example to Consider : 

9/19/2010 Latent Variable Modeling 31 Discriminant Analysis: An Example to Consider 18-12 X2 X1 Lifestyle-Eating Nutritious Meals Income ($)

2 Discriminant Analysis : 

2 Discriminant Analysis MANOVA ~ sort of a mirror image of discriminant analysis DV’s in MANOVA become IV’s of DA DV of DA becomes IV of MANOVA

Multiple Discriminant Analysis : 

9/19/2010 Latent Variable Modeling 33 Multiple Discriminant Analysis A statistical technique for predicting the probability of objects belonging in two or more mutually exclusive categories (dependent variable) based on several independent variables

Factor Analysis : 

9/19/2010 Latent Variable Modeling 34 Factor Analysis A research team uses factor analysis to distill the information contained in a large number of variables into a smaller number of sub-groups called “factors”. 18-6

Factor Analysis: An Example to Consider : 

9/19/2010 Latent Variable Modeling 35 Factor Analysis: An Example to Consider 18-7

Factor Analysis: Another Example to Consider : 

9/19/2010 Latent Variable Modeling 36 Factor Analysis: Another Example to Consider 18-8

3 Factor Analysis : 

9/19/2010 Latent Variable Modeling 37 3 Factor Analysis Factor analysis is a class of techniques which reduce and summarize data For example, taking 14 variables, and finding similarities and reducing those 14 variables to 4 factors (These reduced variables are known as factors)

Factor Analysis : 

9/19/2010 Latent Variable Modeling 38 Factor Analysis Factor analysis is not about making predictions from variables—it is about finding relationships between whole sets of variables, and finding the strength of those relationships

Factor Analysis—Example : 

9/19/2010 Latent Variable Modeling 39 Factor Analysis—Example A grocery store administers a survey to customers, asking them to rate stores in a variety of traits Convenient / inconvenient location Low-quality / high-quality products Modern / old-fashioned Unfriendly / friendly staff Sophisticated / unsophisticated customers Cluttered / spacious Fast / slow check-out Unorganized / organized layout Enjoyable / unenjoyable shopping experience Bad / good reputation Good / bad service Unhelpful / helpful clerks Good / bad selection Dull / exciting

Factor Analysis—Example : 

9/19/2010 Latent Variable Modeling 40 Factor analysis shows that the 14 variables fit into 4 factors For each respondent, a factor score to be used in future analysis is generated for each respondent by taking the sum of the products of the variable and a weighting for that variable Factor1= (Variable1 x Weight1) + (V2 x W2) + … Factor Analysis—Example Factor 1 Quality products Modern stores Reputation Selection Factor 2 Customers Check-out Dull Factor 3 Friendliness of clerks Cluttered Layout Factor 4 Location Shopping experience Service Helpfulness of clerks

Factor Analysis : 

Height Weight Occupation Education Source of Income Size Social Status Factor Analysis Latent Variable ModelingCopyright © 2000 Harcourt, Inc. All rights reserved.

Cluster Analysis : 

9/19/2010 Latent Variable Modeling 42 Cluster Analysis Marketing researchers draw upon the power of cluster analysis to classify objects or respondents into groups that have something in common. Cluster analysis, to put it another way, pinpoints what’s similar within groups but different between them. 18-9

Cluster Analysis: An Example to Consider : 

9/19/2010 Latent Variable Modeling 43 Cluster Analysis: An Example to Consider 18-10 High High Low Low Extent ofEating Outat Restaurants Extent of Patronizinga Fast-Food Restaurant

4 Cluster Analysis Defined : 

9/19/2010 Latent Variable Modeling 44 4 Cluster Analysis Defined Grouping instances into groups that show as little difference between instances within the group, and maximum differences between the different groups Techniques designed to identify objects, people, or variables that are similar with respect to some criteria or characteristics

Cluster Analysis : 

9/19/2010 Latent Variable Modeling 45 Cluster Analysis There are many approaches to finding “clusters” or groups of data points with similar values, always through use of mathematical formulas Most statistical software packages have tools to do all of the calculations

Applications of Cluster Analysis : 

9/19/2010 Latent Variable Modeling 46 Applications of Cluster Analysis Segmentation Breaking consumers into different groups so that they have similar preferences and reactions to product configurations or promotions Product positioning Allows marketers to see how various products are positioned relative to competing brands

5 Conjoint Analysis : 

9/19/2010 Latent Variable Modeling 47 5 Conjoint Analysis Shows the economic trade-offs people make when different product traits (brand, configuration, packaging, etc.) are combined Helps identify both important attributes and ideal product configurations

Conjoint Example : 

9/19/2010 Latent Variable Modeling 48 Conjoint Example Product manager for dairy has the following ice cream options: 3 ice cream formulations (gelato, premium, cheap) 12 different base flavors (vanilla, chocolate, strawberry, mocha, etc.) 6 different flavor sworls (marshmallow, chocolate syrup, fudge, strawberry, caramel) 12 different mix-ins (pralines, peanuts, brownie bits, cookie dough, etc.) (3 x 12 x 6 x 12) = 2,592 different flavor combinations By giving test subjects the choice of different combinations of attributes, the relative importance of each category emerges, and the preferred level or trait in each falls out

Conjoint Analysis : 

9/19/2010 Latent Variable Modeling 49 Conjoint Analysis Marketing researchers draw upon the power of conjoint analysis to estimate the value (utility) respondents associate with different product and/or service features. Conjoint analysis, then, lets a marketing research team communicate the most preferred combination of features to a client. 18-13

Conjoint Analysis: An Example to Consider : 

9/19/2010 Latent Variable Modeling 50 Conjoint Analysis: An Example to Consider 18-14