Quantity

Conjoint Analysis

Attribute levels (often) are assumed to only have additive contributions (main effects only, no interactions, cf. analysis of variance) L4-6

Fit and (internal) predictive validity of partworth estimates

Individuallevel partworth estimates: goodness of fit

  • Pearson correlations r(stated preferences, predicted preferences) (= multiple correlation coefficient, R) will always be high
  • – adjusted R’s (how well will partworth estimates predict preferences for full, non calibration profiles) won’t be high
  • – partworth estimates have large confidence intervals (i.e. low reliability)

Solution
– Also elicit preferences for a number of full holdout profiles (not used for estimation)
– Compare predicted with stated preferences for holdouts
– Various holdout tasks with different measures of goodnessoffit
• may differ from calibration task
• rating  Pearson correlation
• ranking  rankorder correlation (e.g., Kendall’s tau)
• choices  firstchoice hit rate

Note

  • The importance of one attribute depends on the range of the attribute used to structure the stimuli, eg. price levels of 28,38,48 and levels of 28,32,36 (paper 4A)
  • a relationship between the number of levels and the inferred importance of the attribute to the respondent: more levels, more importance

Determine Criteria

Select Attributes

  • actionable
  • important to individuals; actually affect consumer choice

Attribute Levels

  • relatively large number of stimuli versus number of parameters
  • a relationship between the number of levels and the inferred importance of the attribute to the respondent: more levels, more importance

Attribute Combination

  • maximum 32 profiles
  • In terms of predictive validity: is it really necessary/useful to estimate (two and higherorder) interaction effects, or is estimation of only main effects (additive model) good enough?
  • interaction effects tend to have low predictive validity
  • Fractional factorial designs also exist for unconfounded estimation of all main effects and some interaction effects

Aggregation: Choiceshare predictions for simulation profiles

Transform predicted preferences into predicted choice probabilities

  • deterministic choice rule: winner gets all
    • max utility (also firstchoice) rule

  • probabilistic choice rules: winner gets most, but not all


    • BTL rule; logit rule


  • when to use deterministic and when to use probabilistic? Involvment dependent

Transform predicted choice probabilities into predicted choice shares: sum across respondents

Aggregation of part worths: comparability across respondents

  • One way to ensure comparability of results across respondents: L4-22

How many profiles?

  • Lower bound 1: (total number of attribute levels) - (total number of attributes) + 1
    – rationale: we need more data than to-be-estimated parameters
    – lower bound for fractional factorial (42x23) (maineffects) design?
  • Lower bound 2: (number of levels of attribute with most levels) x (number of levels of attribute with one butmost levels)

Scale development: Reliability and validity

Procedures

Step 1: Definition of the construct
• Domain: what is and what is not included?

Step 2: Generate item pool
• Theory and good thinking
• Literature research
• Expert interviews
• Qualitative research in target group (e.g., focus-group discussions)
• Rules
– Redundancy
– Item editing

  • S3 Select reduced set of items based on qualitative
    judgements
  • S4 Pilot test: collect data from reasonable sample (e.g.,
    n=200)
  • S5 Factor analysis: to investigate dimensionality
  • S6 Reliability analysis

Three ways to estimate reliability

  1. Test-retest method
    correlation between scores on same scale at two
    different points in time
    Problems: changes; remember; cannot measure first reaction;
  1. Alternative forms
    correlation between scores on equivalent scales at two
    different points in time
    Problems:
    -How to construct equivalent scales?
    -problems of test-retest

3a. Internal consistency: Split-half method
correlation between scores on two subsets, each with
k/2 items (random split)

  • Correlation between two halves gives reliability of scale of half the actual length
    • Reliability (rk) of the whole scale can be obtained by Spearman-Brown formula (L8-20)
  • Problems
  1. Subsets need not be equivalent (will this give a too high, or a too low
    estimate?)
  2. Different splits may give different results
  3. Perhaps too easy to stay consistent

3b. Internal consistency: Cronbach’s a:
• Gives average of all possible split-half reliabilities
Problems

  1. Subsets need not be equivalent
  2. Perhaps too easy to stay consistent
  3. Considered to only give a lower bound for the actual reliability
    – You can also get the standardized alpha (useful when items are measured on different, incommensurable scales)

Step 7. Purify scale
• If scale is not reliable enough
– compute a after deletion of item  candidates for deletion
– carefully inspect content (!!!)

Step 8. New data collection
• Face/content validity
does the set of items look OK?
• Criterion validity
does the scale predict what it is supposed to predict?
– concurrent (predict something else now) versus predictive (predict something in the future) criterion validity
• Construct validity
does the scale really measure the construct?

Step 9
• Develop norms
Who belongs to the high-involvement group?
Who passes and who fails the exam?

Compositional Perceptual Mapping
CMP

CPM within process of product positioning

  • identify (primary and secondary) competitors
  • determine how competitors and your own product are perceived and evaluated
  • determine competitors' and own position
  • analyze consumer preferences (and underlying needs, motivations, habits)(segments)
  • select attractive position, considering a particular segment
  • try to achieve the position with all elements of the marketing mix
  • monitor position over time

Steps in exploratory factor analysis

2) Number of factors to be retained?

  • A priori ideas/theory
  • Eigenvalue-larger-than-1
  • Elbow in scree plot (eigenvalue)
  • Cumulative % of variance accounted for (VAF) more than 60
  • Not more than 50% of (absolute) residual correlations larger than 0.05
  • Interpretability

3) Rotation

  • orthogonal rotation (VARIMAX, QUARTIMAX) or
    nonorthogonal rotation (OBLIMIN)

4) Interpretation

  • label/interpret components/factors ... by looking at (pattern) loadings (can be interpreted as contributions of factors to attributes)
    • statistically significant loadings
    • practically significant loadings (0.30, 0.40, 0.50)
  • Compute mean factor score for each product, on each
    dimension
  • Make a perceptual map with the products in it, on the basis
    of their mean factor scores

Rationale behind CPM

  1. In daily life, consumers distinguish between products on


    more primary needs/strategic benefits (halo effect)


  2. Ratings on more specific attributes/benefits are related


    to positions on strategic-benefit dimensions (these dimensions are eliciting)

  3. Therefore, exploratory factor analysis will reveal these
    strategic-benefit dimensions

Use for marketing management

  • Compare product perceptions in terms of
    general dimensions
  • Predict effect of changes in product’s attribute
    scores on strategic dimensions
    – each dimension is weighted sum of attributes
  • Identify potential opportunities

Issues in CPM

Data collection

  • different scales can be used
  • ask respondents to only evaluate those products that
    they are familiar with
  • warning: consumers tend to give inflated ratings to
    product concepts (NPD)
  • Ynte’s lecture: difference between unrestricted versus
    restricted (context) evaluations

Extended data matrix

  • (L10 22-24)Correlation between attribute determined by two
    sources of covariation: consumers and products
    -the dominance of consumer heterogeneity can be prevented by preprocessing (centering or standardizing)
    -Perceptions are generally assumed to be homogenous across
    consumers (in contrast to preferences)  No modeling of
    (inter)individual differences.

Covariances vs correlations

  • Correlation matrix: each attribute has equal impact on the results


  • Covariance matrix: Attributes with more variance have a larger impact on the results

  • when attributes are not in the same scale, it's better to analyze with correlation matrix
  • the correlation matrix is calculated based on standardized data

Compositional VS Decompositional

  • Advantages of CPM
    +strong face validity
    +data easy to collect
    +easy to interpret
    +one can choose actionable attributes
  • Disadvantages of CPM
    – depends on pre-specified set of attributes
    – dimensions are linear combinations of attributes
    – attributes that are important for preference/choice, but
    independent of other attributes tend to be overlooked
    – arbitrary scaling of dimensions

Cluster

Hierarchical clustering procedures

  • agglomerative
  • divisive

Cluster distance

  • single linkage
  • complete linkage
  • average linkage
  • ward's method
  • centroid method

How many homogeneous groups?

  • A priori idea
  • Absolute value of agglomeration coefficient
  • Screetest criterion based on agglomeration coefficient
  • Measures of tradeoff between withincluster homogeneity and number of clusters
    -Variance between clusters versus variance within clusters, choose the greatest one
    – Pseudo F-value does not follow theoretical F-distribution
  • Interpretability/usefulness of clusters

Disadvantage of hierarchical cluster analysis

  • joins and divisions are irreversible → successive solutions may depend on minor details the data
  • with equal dissimilarities (ties) in the data, successive solutions even depend on (arbitrary) order of respondents in the dataset!

Nonhierarchical cluster analysis

  • start out with K random/selected cluster means (centroids)

  • in each of a series of iterative steps (optimizing):


  • we stop with the iterative steps, when there is no improvement in the cluster solution anymore

  • criterion: sum of squared deviances from cluster mean

Disadvantages of nonhierarchical methods

  • different seeds tend to give different solutions
  • random seeds tend to give inferior solutions
  • computationally more intensive

Validity

Internal validity

  • convergent validity: compare results from different (reasonable) dissimilarity measures
  • convergent validity: compare results from different clustering procedures
  • cross-validation: compare results from one half of the sample to results from another half of the sample)
  • simulation using random data: do we get more homogenous clusters with our actual data?

External validity

  • compare results with expected clustering (theoretical classification ⇒ taxonomy)
  • check expected relations (= ?? validity)
  • does the clustering yield useful market segments? (criteria?)

1) Is the data suited for exploratory factor analysis?

  • Number of observations
  • Interval-scaled scores (?); Independent observations
    (?); Normally distributed scores (?)
  • Sufficient association between attributes/variables
    (multicollinearity)
    • Sufficient number of large correlations
    • Low partial correlations
    • Bartlett’s test of sphericity
    • KMO and MSA