# What Is Conjoint Analysis? DSC 410/510 Multivariate Statistical Methods. How Is Conjoint Analysis Done? Empirical Example

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1 What Is Conjoint Analysis? DSC 410/510 Multivariate Statistical Methods Conjoint Analysis 1 A technique for understanding how respondents develop preferences for products or services Also known as trade-off analysis Premise: consumers evaluate overall utility by combining values for each attribute of the product Subjective preference judgment unique to each individual Encompasses all product or service features Products/services with higher utility are more preferred and have a better chance of choice 2 How Is Conjoint Analysis Done? Hatco Example: Industrial Cleanser Describe product/service in terms of its attributes/characteristics/features (factors( factors) Select possible values for each factor (levels( levels) Construct a set of products/services (treatments( or stimuli) ) by combining levels of each factor Present stimuli to respondents who provide their overall evaluations Determine preference structure influence of each factor and each level on respondent s utility judgment individually and collectively 3 3 factors: ingredients, form, brand 2 levels for each factor: phosphate-free/ phosphate-based, liquid/powder, Hatco/generic 2 V 2 V 2 = 8 stimuli, e.g. Hatco phosphate-free powder Hatco customers asked to: either rank-order 8 stimuli or rate each stimuli on a preference scale 4 The Additive Model For Individuals Empirical Example Utility for any stimuli estimated from part-worths Utility for product with level i for factor 1, level j for factor 2,, level n for factor N = part-worth for level i for factor 1 + part-worth for level j for factor part-worth for level n for factor N For example, Hatco phosphate-free powder utility = part-worth of Hatco brand + part-worth of phosphate-free ingredients + part-worth of powder form Two respondents ranked 8 stimuli: Stimuli Form Ingredients Brand D1 D2 D3 Res 1 Res 2 S1 Liquid Phosphate-free Hatco S2 Liquid Phosphate-free Generic S3 Liquid Phosphate-based Hatco S4 Liquid Phosphate-based Generic S5 Powder Phosphate-free Hatco S6 Powder Phosphate-free Generic S7 Powder Phosphate-based Hatco S8 Powder Phosphate-based Generic worth of powder form 5 6 Conjoint Analysis 1

2 Estimating Part-Worths Calculate average ranks of each level of each factor: Respondent 1 Respondent 2 Part- Part- Factor Level Ranks Ave. Worth Ranks Ave. Worth Form Liquid 1,2,5, ,2,3, Powder 3,4,7, ,6,7, Ingredients Phosphate-free 1,2,3, ,2,5, Phosphate-based 5,6,7, ,4,6, Brand Hatco 1,3,5, ,3,7, Generic 2,4,6, ,4,5, Part-Worths = overall average rank (4.5) average rank of level 7 Using Regression Instead We can obtain part-worths using regression Dependent variable = Rank Independent variables = D1 = dummy variable for Form D2 = dummy variable for Ingredients D3 = dummy variable for Brand Dummy variables use effects-coding coding (see end of Chapter 2 and slide 28 from Examining your data class notes) See hatco1res.xls Excel Spreadsheet on web-site (under data ) 8 Conditional Relative Importance Predicting Rankings CRI, also known as Factor Importance Ignore over-complicated method in Table 7.3 Calculate range of part-worths for each factor CRI for each factor is this range divided by the sum of the ranges across all factors For example, respondent 1 ranges are 2 (form), 4 (ingredients) and 1 (brand), summing to 7 CRI values are therefore 2/7 = 28.6% (form), 4/7 = 57.1% (ingredients) and 1/7 = 14.3% (brand) 9 Sum the part-worths for each stimuli to find overall utilities Predict rankings based on these utilities For example, respondent 1 utilities are 3.5, 2.5, 0.5, 1.5, 1.5, 0.5, 2.5, 3.5 Predicted rankings are therefore 1, 2, 5, 6, 3, 4, 7, 8 perfect prediction! Excel spreadsheet also calculates the CRI s and predicted rankings Or use SAS software - see handout on website ( Empirical example from p394 ) and Excel spreadsheet (hatco1raw.xls( hatco1raw.xls) 10 Managerial Uses of Conjoint Discover object/concept with optimal qualities Establish relative contributions of each attribute and each level to utility Predict utilities for other stimuli not evaluated Identify segments of consumers who put differing importance on attributes Explore market potential for feature combinations currently unavailable Unique Features of Conjoint Decompositional rather than compositional Separate models for predicting preference for each respondent (disaggregate) Individual results can be aggregated to calculate group utility also Handles nonlinear relationships as well as linear ones Conjoint Analysis 2

3 13 14 Define Objectives Determine contributions of factors and their levels to consumer preference e.g. how much does price contribute to willingness to buy, and which price is best? Find a valid model of consumer judgments valid models enable prediction of preference for any combination of factors/levels What decision criteria do consumers use to make choices for this type of product/service? turn these criteria into attributes that give value to the product/service Choosing Factors and Levels Include all attributes that create or detract from overall utility of product/service Consider positive and negative levels for factors since: focusing only on positive levels distorts respondents judgments respondents can subconsciously employ omitted negative levels Only include determinant factors that differentiate between objects e.g. car seat safety is important, but not determinant Develop Research Design 17 Select a conjoint method traditional, adaptive or choice-based Define factors and levels Specify model additive or interaction linear, quadratic or separate part-worths Collect data full-profile, pairwise,, or trade-off comparison presentation ranking or rating preferences survey administration 18 Conjoint Analysis 3

4 Conjoint Methods Factors and Levels Max. # factors Analysis level Model form Traditional 9 Individual or Aggregate Additive Adaptive 30 Individual or Aggregate Additive Choice-based 6 Aggregate Additive or Interaction 19 Must be communicable,, usually verbally (or use multimedia, virtual reality, or even actual products!) Must be actionable,, i.e. distinct and implementable Can use preliminary study to determine important factors Increasing the number of factors/levels either requires larger number of stimuli or reduces reliability of results Min. # stimuli = total levels across factors # factors + 1 Beware multicollinearity (interattribute or environmental correlation among factors), e.g. HP and MPG for cars create superattributes superattributes, e.g. performance, or eliminate unbelievable stimuli, or constrain part-worth estimation to conform to a prespecified relationship 20 Factors and Levels (continued) Model: Additive or Interaction Consider use of price as a factor carefully: positively associated with many quality attributes unrealistic high-quality low-price combinations price can become down-weighted weighted if there are many other positive features price can interact with features such as brand Equalize number of levels across factors Increasing range of levels can reduce multicollinearity but also reduce believability Ensure levels are realistic and feasible 21 Additive composition rule: add up part-worths for each factor/level combination to get overall utility Interaction effects: the whole is greater (or less) than the sum of its parts particular factor/level combinations are especially liked or disliked there is an interaction between factors A and B if rankings for levels of A vary with levels of B identifying interaction can be difficult! 22 Example of Interaction Stimuli Form Ingredients Brand Res 3 S1 Liquid Phosphate-free Hatco 1 S2 Liquid Phosphate-based Hatco 3 S3 Powder Phosphate-free Hatco 2 S4 Powder Phosphate-based Hatco 4 S5 Liquid Phosphate-free Generic 7 S6 Liquid Phosphate-based Generic 5 S7 Powder Phosphate-free Generic 8 S8 Powder Phosphate-based Generic 6 Respondent 3 prefers phosphate-free over phosphate-based for Hatco brand, but vice-versa versa for generic brand Part-Worth Relationship Most restrictive Most efficient estimation Linear Quadratic or ideal point Least restrictive Least efficient estimation Separate part-worths Can be specified separately for each factor Choice Choice can be guided theoretically or empirically Conjoint Analysis 4

5 Data Collection: Presentation Method Data Collection: Creating Stimuli Full-profile: Pairwise: Trade-off: liquid phosphate-free Hatco liquid phosphate-free Hatco Generic liquid?? rate or rank each stimuli vs. powder?? powder phosphate-based rank each combination Full factorial uses all combinations (becomes unmanageable quickly) Fractional factorial allows estimation of all main effects with far fewer stimuli: orthogonal, balanced designs are optimal, but can contain obvious or unbelievable stimuli, which can be deleted if resulting near orthogonal design is efficient and interattribute correlations are small (<.2) Bridging designs can be used with large number of factors Whatever the design, use no more than 20 or so stimuli Creating Stimuli Using SAS The SAS ADX application can be used to generate experimental designs for conjoint analysis experiments Multiply the number of levels in each factor together to find the full factorial number of stimuli needed If this is less than 20 then you can probably use the full factorial design, and there is no need to use SAS ADX Otherwise, better to run a fractional factorial for which you ll need to use SAS ADX For an example, see Assignment 3 which is based on the Jobs example from class handout on the Data Collection: Preference Measure Non-metric, i.e. rank-ordering (full-profile, pairwise, trade-off) (+) easy for respondent ( )) can be difficult to administer Metric, i.e. Rating, e.g scale (full-profile, pairwise) (+) easily analyzed and administered ( )) respondents can be less discriminating Personal interviews, mailed questionnaires, computer- based surveys, and telephone interviews can all work well class website Evaluate Assumptions Few statistical assumptions e.g. normality, homoscedasticity, independence checks not needed Strong conceptual assumptions e.g. specify model form (additive vs. interaction) before data are collected Conjoint Analysis 5

6 31 Estimate Model Rated preferences are analyzed using specialized software, e.g. SAS Proc Transreg,, Conjoint Analyzer, or SPSS Conjoint Add-on or even regression with dummy variables (effects coding) Rank-ordered preferences: can be analyzed using special procedures designed for ordinal data or can be analyzed using procedures designed for metric data, e.g. regression (beware unequally spaced preferences however) Specify part-worth relationship (separate, quadratic, or linear) for each factor 32 Assess Fit Fit can be assessed at both individual and aggregate levels Compare actual and predicted ranks Compute Multiple R, i.e. correlation between responses and predictions (note: R = (1/(1+df 2 /df 1 F))) Pearson correlation for metric ratings Spearman s ρ (Pearson correlation for ranks) or Kendall s τ (measure of concordant/discordant pairs) for rank-order preferences If Multiple R value > 0.95, additivity additivity assumption OK Use validation or holdout stimuli to avoid over-fitting For aggregate assessment, use holdout sample of respondents Interpret Results Plot Results, e.g Form Interpretation possible at both individual and aggregate levels Consider part-worth estimates for each factor: practical relevance correspondence to theory plot part-worths (y-axis) vs. levels (x-axis) to identify patterns: connect points with lines for each respondent or for aggregate results if population exhibits homogeneous behavior, aggregate results can predict market share Consider conditional relative importance (CRI) of factors Conjoint Analysis 6

8 Choice-Based Conjoint (continued) Example: see cell-phone example in book, but note typo in Table 7.7: 6th row, 4th column (stimulus 6, factor TWC) should be 1 not 0 Models constraint-based decision making well Often used in conjunction with other conjoint methods Allows closely comparable alternatives to be assessed Choice sets can be created to fit unique preferences Estimation technique based on multinomial logit independence of irrelevant alternatives problem can be addressed with random-coefficients models or hierarchical Bayes analysis Illustration of Conjoint Analysis See p in the text-book See Excel spreadsheets on website: hatco2raw.xls contains raw data which can be imported into SAS and analyzed using the Market Research application hatco2res.xls contains results for 5 of the respondents Conjoint Analysis 8

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