2024 CMA Lecture 4_Students PDF

Week 2 Lecture 4 Customer Marketing Analytics Creating Perceptual Maps using Factor Analysis Jiska Eelen Associate Professor Marketing https://research.vu.nl/en/persons/jiska-eelen  Today’s lecture § Measurement and marketing § Different types of scales in marketing - Compar...

Week 2 Lecture 4 Customer Marketing Analytics Creating Perceptual Maps using Factor Analysis Jiska Eelen Associate Professor Marketing https://research.vu.nl/en/persons/jiska-eelen  Today’s lecture § Measurement and marketing § Different types of scales in marketing - Comparative scales - Non-comparative scales § Multiple item measurement theory § Scale evaluation - Reliability - Validity § Factor analysis and dimensionality of constructs (scale analysis) § Perceptual maps 2 2  Today’s lecture § Measurement and marketing § Different types of scales in marketing - Comparative scales - Non-comparative scales § Multiple item measurement theory § Scale evaluation - Reliability - Validity § Factor analysis and dimensionality of constructs (scale analysis) § Perceptual maps 3 3  Goals of Factor Analysis Key objective: Capture as much of the variance (information) in the original variables as possible with as few factors as possible § Data summarization: - Detecting structure in the relationship between variables (assessing dimensionality of constructs) § Data reduction (to a more manageable set): - Simplification for communication - Simplification for further analyses (e.g. summated scales or factor scores) 4  Intuition Behind Factor Analysis § Explain as much variance in observed variables X by means of only a few latent factors F (3 factors in the example) X3 u3 X8 u8 Not all variance F1 explained by the X9 u9 factors: u = unique X2 variance not explained u2 by the factor model X6 u6 (there is a unique term u for each item) F2: X7 u7 X4 u4 X1 u1 F3 X5 u5  Data summarization – Assignment 2 § Data summarization: - Detecting structure in the relationship between variables (assessing dimensionality of constructs) § What are the main dimensions of SERVQUAL? How can we summarize 22 items defining the domain of service quality? (Parasuraman et al. 1988)  Data reduction – Managerial skills § Data reduction (to a more manageable set): - Simplification for communication - Simplification for further analyses (e.g. summated scales or factor scores) § What are the dimensions underlying a set of 11 managerial skills? How do employees perceive their managerial skills (given the set tested!)?  Factor Analysis Step by Step § Survey of employees of a company (N=114) § 7-point Likert Scale (1=strongly disagree, 7=strongly agree) § 11 Questions: 1. I show confidence in my staff 2. I let my staff know they are doing well 3. I give feedback to staff on how well they are working 4. I would personally compliment staff if they did outstanding work 5. I believe in setting goals and achieving them 6. I achieve the things I want to get done in a day 7. I never try to put off until tomorrow what I can finish today 8. I plan the use of my time well 9. I remain clear headed when too many demands are made upon me 10.I rarely overlook important factors when plans are made 11.I handle complex problems efficiently 8  Factor Analysis Design § How many observations? Ø Rule of thumb: Minimum observations total = 50 Ø Rule of thumb: Minimum observations per variable 5:1 § What type of variables can be used? Ø You need a correlation measure to measure association between variables, hence metric data. § How many variables per factor? Ø Rule of thumb: if purpose of finding a structure, want ≥ 3-5 variables per factor 9  Factor Analysis Step by Step 1. Inspect correlation matrix: is FA appropriate? 2. Choose method of extraction. (Principle Component Analysis). 3. Determine number of factors underlying the data. (A-priori determination, Eigenvalue > 1, Scree Test). 4. Rotate the initial solution for proper interpretation. (Varimax). 5. Interpret the rotated solution and name the factors. 6. Calculate Cronbach a for each factor found. 7. Create summated scales or factor scores for further analysis. 10  Intuition Behind Factor Analysis § Assumes interval or ratio scaled data (Pearson correlation coefficient) § Finds specific patterns in the correlation matrix (finds groups of variables with strong correlations amongst each other) § Summarizes groups of variables with high inter-correlations in terms of common factors (creates a dimension for each group of highly correlated variables) Correlation Matrix (Sorted) x3 x8 x9 x2 x6 x7 x4 x1 x5 x3 1 x8 0,73 1 x9 0,77 0,71 1 x2 0,74 0,72 0,79 1 x6 0,42 0,31 0,43 0,45 1 x7 0,47 0,44 0,47 0,49 0,72 1 x4 0,43 0,43 0,48 0,5 0,71 0,72 1 x1 0,3 0,24 0,43 0,43 0,28 0,35 0,47 1 x5 0,31 0,24 0,41 0,41 0,33 0,38 0,47 0,77 1  Correlation Matrix: Is FA Appropriate? § Bartlett’s Test of Sphericity provides statistical significance that the correlation matrix has significant correlations among at least some of the variables. § H0: all possible correlations between variables = 0 § χ2 should be large, p 0.5 Ø Bartlett’s test of sphericity- H0 is rejected (p < 0.05)  Factor Analysis Step by Step 1. Inspect correlation matrix: is FA appropriate? 2. Choose method of extraction. (Principle Component Analysis). 3. Determine number of factors underlying the data. (A-priori determination, Eigenvalue > 1, Scree Test). 4. Rotate the initial solution for proper interpretation. (Varimax). 5. Interpret the rotated solution and name the factors. 6. Calculate Cronbach a for each factor found. 7. Create summated scales or factor scores for further analysis. 17  How many factors? (EV>1) 3 factors capture 69% of variance that is in the original 11 variables. 3 Eigenvalues > 1 à 3 factors 18  Number of Factors: Eigenvalue >1 § Each factor has its own eigenvalue § Eigenvalue = amount of variance explained by factor § Sum of all eigenvalues = number of variables % of variance explained by a factor = Eigenvalue Factor/Number of variables § Rule for selecting factors: Eigenvalue > 1 § We want each factor to explain the variance of at least a single variable (Note: Each variable has a variance of 1) How many factors? (Scree plot) “Elbow” rule: § Look for the “elbow” (break, sudden flattening in Elbow at k = 4 eigenvalues) (e.g., k) à 3 factors § Take the number of factors before the elbow (k-1) 20  Communalities Extracted Communalities Initial Extraction I show confidence in my 1.000.593 staff I let my staff know they are 1.000.803 All communalities doing well I give feedback to staff on are very high, so no 1.000.560 how well they are working variable should be I would personally compliment staff if they 1.000.704 eliminated. did outstanding work I believe in setting goals 1.000.660 and achieving them I achieve the things I want 1.000.727 to get done in a day I never try to put off until tomorrow what I can finish 1.000.710 today I plan the use of my time 1.000.772 well I remain clear headed when too many demands 1.000.720 are made upon me I rarely overlook important factors when plans are 1.000.650 made I handle complex 1.000.676 problems efficiently Extraction Method: Principal Component Analysis.  Communalities Extracted § The factor extraction analysis computes “communalities” of items with the common factor structure. § How much of the variance of each variable is captured by the extracted factors. § If communality is very low (say <.30), the item is “quite unique” since it correlates weakly with other variables. Such variable should be removed, as it is definitely measuring “something else.” § Since communality = row sum of squared factor loading -> communalities depend on the number of factors in your solution (more factors -> higher communalities)  Factor Analysis Step by Step 1. Inspect correlation matrix: is FA appropriate? 2. Choose method of extraction. (Principle Component Analysis). 3. Determine number of factors underlying the data. (A-priori determination, Eigenvalue > 1, Scree Test). 4. Rotate the initial solution for proper interpretation. (Varimax). 5. Interpret the rotated solution and name the factors. 6. Calculate Cronbach a for each factor found. 7. Create summated scales or factor scores for further analysis. 23  Interpretation of the Rotated Solution Rotated Component Matrixa Component 1 2 3 I show confidence in my -.023.721.270 staff Naming the Factors I let my staff know they are doing well.239.848.162 § Factor 1 (planning) I give feedback to staff on.156.705.195 how well they are working I would personally compliment staff if they.271.779.153 § Factor 2 (participation did outstanding work I believe in setting goals.746.312 -.079 with staff) and achieving them I achieve the things I want.793.061.307 to get done in a day I never try to put off until § Factor 3 (handling tomorrow what I can finish.787.251.167 today stress/efficiency) I plan the use of my time.817.040.322 well I remain clear headed when too many demands.072.283.797 are made upon me I rarely overlook important factors when plans are.226.375.677 made I handle complex.296.122.757 problems efficiently Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 6 iterations. 25  Interpretation of the Rotated Solution § Rotated Component Matrix presents factor loadings of each item = correlation between factor and each original item § Items with high loadings (i.e., close to 1 or -1) on a given factor are used for interpreting the factor § Factor loadings can be positive or negative (depends on item scaling) à consider absolute values of factor loadings for interpretation § Look for simple structure: each variable (hopefully) loads high on 1 factor and low on other factors § When interpreting highlight the highest factor loadings per row, and then look at highlighted items for each factor  Factor Analysis Step by Step 1. Inspect correlation matrix: is FA appropriate? 2. Choose method of extraction. (Principle Component Analysis). 3. Determine number of factors underlying the data. (A-priori determination, Eigenvalue > 1, Scree Test). 4. Rotate the initial solution for proper interpretation. (Varimax). 5. Interpret the rotated solution and name the factors. 6. Calculate Cronbach a for each factor found. 7. Create summated scales or factor scores for further analysis. 27  Calculate Cronbach’s a for each factor § After a factor analysis, select high loading variables on each factor and conduct reliability analysis Ø Recode items with negative factor loading Ø Calculate resulting Cronbach’s a Ø To increase reliability, look at item-total correlations and Cronbach’s a if item is deleted 28 Calculate Cronbach’s a for each factor Analyze > Scale > Reliability Analysis … Calculate Cronbach’s a for each factor § Factor 1 (planning) Cronbach’s a = 0.84 § Factor 2 (participation with staff) Cronbach’s a = 0.82 § Factor 3 (handling stress/efficiency) Cronbach’s a = 0.76 30  Factor Analysis Step by Step 1. Inspect correlation matrix: is FA appropriate? 2. Choose method of extraction. (Principle Component Analysis). 3. Determine number of factors underlying the data. (A-priori determination, Eigenvalue > 1, Scree Test). 4. Rotate the initial solution for proper interpretation. (Varimax). 5. Interpret the rotated solution and name the factors. 6. Calculate Cronbach a for each factor found. 7. Create summated scales or factor scores for further analysis. 31  Create summated scales or factor scores for further analysis § Next, we can compute summated scales or factor scores for subsequent analysis. § Three factor solution suggests three summated scales (or three factor scores) should be constructed. § These three new variables (replacing the original set of variables) are used for further analysis. § Summated scores or factor scores? § Theory testing? à Summated score; equal weights for all items in the new variables; more stable interpretation of scale § Data reduction, summarizing in practice? à Factor scores more data driven  Summated Scales: Compute Mean Scores on Dimensions Compute the mean of the high loading variables in each dimension In SPSS: Transform > Compute Variable 33 We had 11 columns. Now only 3.  Factor Scores Score of the individual respondent on the factor (incorporates all variables) In SPSS: § Analyze > Data Reduction > Factor... § Button: Scores  Conclusion § The 11 managerial skills can be grouped into 3 super-variables (dimensions): Planning, participation with staff, handling stress/efficiency § The scale is reliable: Cronbach’s a for each dimension >.70 § We can use the resulting 3 summated scales for subsequent analyses. § On average, how does Company X do on employee’s managerial skills? § How do employee’s managerial skills at Company X and Company Y compare? § To reduce high correlation among predictors in a regression. E.g., How do managerial skills predict organizational performance? To test whether impulsive buyers are more interested in using our brand, I would measure “product interest” and “impulsive buying tendency”. Next, I would test if the items of impulsive buying tendency load on one factor. Finally I would use xxxxx as the IBT score and correlate it with product interest. RIGHT HAND LEFT HAND The factor TWO HANDS The score (mean of I don’t know summated the items score (mean multiplied by of all items) their factor loading)  Today’s lecture § Measurement and marketing § Different types of scales in marketing - Comparative scales - Non-comparative scales § Multiple item measurement theory § Scale evaluation - Reliability - Validity § Factor analysis and dimensionality of constructs (scale analysis) § Perceptual maps 38 38  The Role of Consumer Perceptions Product Perceptions Preference Choice attributes Physical and What people What people perceived see/believe like 39  The Role of Consumer Perceptions An important input to marketing decision making is often an understanding of how consumers “perceive” the brand/product relative to competitors on relevant attributes (or “dimensions”). Brand positioning  Measuring Perceptions § We search for parsimony in our description of consumer decision making. § Evidence suggests that consumers do not process large numbers of attributes in practice. Therefore, we frequently try to capture the differences between products with fewer dimensions. We would like a (relatively) simple way of representing the key insights regarding positioning relative to the competition.  Perceptual Maps § A perceptual (or product) map is a representation of how the market sees a set of products or competing products in some memory-like or cognitive sense. “A 30,000 ft view of the market” § [A joint-space (or product-market) map displays both (brand) perceptions and consumer preferences on a single map.] § A very useful tool for understanding current position relative to competitors and for tracking efforts to re-position the firm’s product/ service offerings.  Edgy Hot Topic Wet Seal H&M Forever 21 American Eagle Abercrombie & Fitch Traditional Contemporary L.L. Bean Abercrombie & Fitch changed its positioning, to move from a traditional and conservative segment Abercrombie and to a more contemporary, Fitch edgy segment by adjusting Dickies several elements of its marketing mix, including products, store designs Carhart and locations, price points, and marketing Conservative communications.  Key Questions Answered § With whom do we compete? § How are we doing compared to our competitors? § On what dimensions? 44  Creating Perceptual Maps Attribute-based Methods: § Each object is rated on a series of pre-defined attributes. § The attributes are “reduced” to a smaller number of more general dimensions § Key methods: Factor Analysis (PCA), discriminant analysis, correspondence analysis 45  Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axes. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.]  Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axes. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.]  EXAMPLE: Motorcycles in Italy Objective: Understand perceptions of various brands of motorcycles amongst riders in Italy. A sample of 335 individuals rate eight brands on eight image attributes: Brands Attributes Aprilia Exclusive BMW Innovative Ducati Reliable Guzzi Performing Harley Trendy Honda Aggressive Suzuki Engaging Yamaha Winning 48 Collecting Perception Data: Survey Format LEFT HAND RIGHT HAND TWO HANDS Non- Comparative I don’t know comparative scale scale LEFT HAND Semantic TWO HANDS RIGHT HAND Continuous differential Likert scale rating scale scale  Data Matrix Data Matrix Respondent Brand Attribute 1 Attribute 2... Attribute A 1 1 x x... x 1 2 x x... x...... 1 B x x... x 2 1 x x... x 2 2 x x... x...... 2 B x x... x...... N 1 x x... x N 2 x x... x...... N B x x... x Data  Average Attribute Ratings by Brand SPSS: Analyze > Compare Means > Means. Drag brand to ‘Independent List’ and all eight attributes to ‘Dependent List.’ Click “Options” and leave only the mean in cell statistics. This provides a complete summary... but is not easy to digest / interpret quickly. Let’s now plot this table… Profile Plot Radar Chart  Reducing the Number of Dimensions § Our goal of a simple visual representation of the data means we need to capture the “essence” of the data on a smaller number of dimensions. § As a first step, consider the following correlation matrix computed on the raw data:  Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axes. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.]  Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axes. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.]  Recap Factor Analysis § A multivariate statistical technique designed to group together variables that are highly correlated: § A desire for simplification (data reduction) § Uncover underlying structure in the data (summarization) § Factor analysis examines interdependencies among variables. § Capture as much as the information in the original variables as possible with as few factors as possible. Determining the Number of Axes (Factors) Determining the Number of Axes Components/factors are the new axes that will underpin our PM. 1-> X-axis 2-> Y-axis Loadings are the coordinates of each attribute. Unrotated 0.735 0.455 64 § In the loading plot, we want variables to be close to only one of the axes (i.e. highly correlated with one factor, while uncorrelated with the other so that each variable loads only on one of the factors.) § If we rotate the axes, it may be easy to interpret the underlying factors and hence name the axes. Varimax rotation rotates until it finds a solution where each variable is correlated with only one factor, and uncorrelated with the other factor which is inferred in the plot by closeness to any axis. Let’s first do it manually!  Naming the Axes (re-do the analysis choosing Varimax rotation) Naming the Axes Page 94 Rotated 0.865 -0.012 Naming the Axes § The length of the attribute line represents the extent to which the variance of the ratings across brands on this attribute is captured by the two factors. § The angle of the attribute line with respect of each axis reflects the extent to which the attribute is correlated with the new variables/factors.  Naming the Axes Privileged Weak Accomplished Mainstream  Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axes. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.] Finding the Location of Each Brand on The Map § The location of each brand for each respondent on the two defined axes is given factor scores. § SPSS (re-do the analysis): Analyze > Dimension Reduction > Factor. Click on “Scores” button and select “save as variables” Finding the Location of Each Brand on The Map SPSS: Analyze > Compare Means > Means. Add factor scores to “dependent list” and brand to “independent list”. Click “options” and leave only “mean” in the cell statistic. Complete Perceptual Map Complete Perceptual Map Complete Perceptual Map  Interpreting the Perceptual Map § How do Suzuki and Yamaha compare overall?  Interpreting the Perceptual Map § Which brand is perceived as most mainstream?  Interpreting the Perceptual Map § How do Suzuki and Yamaha compare on the attribute performing? § Hint: To position a particular brand on an attribute, draw an imaginary perpendicular line from location of that brand onto the attribute. Use both direction and closeness to the attribute to interpret. Interpreting the Perceptual Map Interpreting the Perceptual Map 112 What happens if we take out Harley? 113 Who has the highest market share? 114  Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axes. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.]  Preference Model: Ideal-Point Model § Each customer or customer segment is represented by a point in the multidimensional space. § The location represents the “ideal level” on the underlying attributes. § Preference for a brand (and therefore share) is a function of its distance from the ideal point in the perceptual space.  Edgy Hot Topic Punk Teens Wet Seal H&M Forever 21 American Eagle Abercrombie & Fitch All American Traditional Teenagers Contemporary L.L. Bean Abercrombie & Fitch Baby Boomers changed its positioning, to Abercrombie and move from a traditional and Fitch conservative segment to a Dickies more contemporary, edgy segment by adjusting several Working elements of its marketing mix, including products, Man Carhart store designs and locations, price points, and marketing Conservative communications. 117  Creating a Perceptual Map: Specific Steps § Identify the relevant brands/products. § Identify the relevant attributes. § Collect data from an appropriate sample of individuals (rating each brand on each attribute). § Reduce the attributes to a set of “new variables” (factors) using factor analysis. Determine the number of axes and name the axis. § Determine the “rating” (location) of each brand on each factor. § Plot the brands on axes represented by the factors § [Overlay the preference information.] 118  Lecture 5 Monday, September 16th: Market Response Models (Multiple Regression Analysis) Lecture 6 Tuesday, September 17th: Advanced Topics: Mediation & Moderation