Choice modelling an introduction

1
Choice modelling - an introduction
2
(No Transcript)
3
Class experiment

• Everybody loves Chocolate- fact
• Of the following choices
• White Chewy NoNuts
• Dark Chewy NoNuts
• White Soft NoNuts
• Dark Soft NoNuts
• White Chewy Nuts
• Dark Chewy Nuts
• White Soft Nuts
• Dark Soft Nuts
• Which one do you choose?

4
(No Transcript)
5
introduction

• When we wish to look at launching new products or
  change features of current products we would like
  to ascertain the impact this will have in the
  market place
• We need to be able to model the effect of each
  change on a range of similar products
  
• The way we do this is via choice modelling
• whereby each respondent examine a number of
  market scenarios and gets to choose which product
  they would purchase
  
• We need to be able to answer the marketing
  questions
  
• We need to be able to model this appropriately

6
Introduction

• There are 3 components to choice modelling
• Design of experiment
• Analysis of data
• Presentation of results
• Firstly an example

7
Multinomial logit

• We begin with a very simple example. In this
  example, each of ten subjects was presented with
  eight different chocolate candies and asked to
  choose one.
• The eight candies consist of the 23 combinations
  of dark or milk chocolate, soft or chewy centre,
  and nuts or no nuts. Each subject saw all eight
  candies and made one choice.
• There are m 8 attribute vectors in this
  example, one for each alternative. Let x
  
• Dark/Milk (1 Dark, 0 Milk),
• Soft/Chewy (1 Soft, 0 Chewy),
• Nuts/No Nuts (1 Nuts, 0 No Nuts).
• The eight attribute vectors are
• x1 (0 0 0) (Milk, Chewy, No Nuts)
• x2 (0 0 1) (Milk, Chewy, Nuts )
• x3 (0 1 0) (Milk, Soft, No Nuts)
• x4 (0 1 1) (Milk, Soft, Nuts )
• x5 (1 0 0) (Dark, Chewy, No Nuts)
• x6 (1 0 1) (Dark, Chewy, Nuts )
• x7 (1 1 0) (Dark, Soft, No Nuts)
• x8 (1 1 1) (Dark, Soft, Nuts )

8
Multinomial logit model

• Experimental choice data such as these are
  typically analyzed with a multinomial logit
  model.
  
• The Multinomial Logit Model
• The multinomial logit model assumes that the
  probability that an individual will choose one of
  the m alternatives, ci , from choice set C is
  
• where xi is a vector of alternative attributes
  and b is a vector of unknown parameters. U(c i)
  xi b is the utility for alternative ci, which is
  a linear function of the attributes.
• The probability that an individual will choose
  one of the m alternatives, ci, from choice set C
  is the exponential of the utility of the
  alternative divided by the sum of all of the
  exponentiated utilities.

9
Hypothetical calculations
10
Probability Choice as a function of utility
Note for pricing Data this is usually a negat
ive relationship
11
The input data

• 8 choices , 10 persons so 80 observations
• Typically, two variables are used to identify the
  choice sets, subject ID and choice set within
  subject (for larger studies we aggregate this
  over ID)
• The variable Subj is the subject number, and Set
  identifies the choice set within subject. The
  chosen alternative is indicated by c1, which
  means first choice.
• All second and subsequent choices are unobserved,
  so the unchosen alternatives are indicated by
  c2,
  

12
The data
13
Fitting the Multinomial Logit Model

• The data are now in the right form for analysis.
  In the SAS System, the multinomial logit model is
  fit with the SAS/STAT procedure PHREG
  (proportional hazards regression), with the
  tiesbreslow option.
• The likelihood function of the multinomial logit
  model has the same form as a survival analysis
  model fit by PROC
  
• PHREG. See Statistics 764 Survival Analysis notes
  Chapter 7
  

14
The code

• proc phreg datachocs outestbetas
• strata subj set
• model cc(2) dark soft nuts / tiesbreslow
• label dark Dark Chocolate soft Soft
  Centre nuts With Nuts
  
• run
• The data option specifies the input data set.
  The outest option requests an output data set
  called BETAS
  
• with the parameter estimates.
• The strata statement specifies that each
  combination of the variables Set and Subj forms a
  set from which a choice was made. Each term in
  the likelihood function is a stratum.
• There is one term or stratum per choice set per
  subject, and each is composed of information
  about the chosen and all the unchosen
  alternatives.

15
SAS output
16
Interpretation

• Model Fit Statistics and Testing Global Null
  Hypothesis BETA0, contain the overall fit of
  the model.
  
• The-2 LOG L statistic under With Covariates is
  28.727 and the Chi-Square statistic is 12.8618
  with 3 df (p0.0049),
  
• which is used to test the null hypothesis that
  the attributes do not influence choice.
  
• Note that 41.589 (-2 LOG L Without Covariates,
  which is -2 LOG L for a model with no explanatory
  variables) minus
  
• 28.727 (-2 LOG LWith Covariates, which is -2 LOG
  L for a model with all explanatory variables)
  equals 12.8618
  
• (Model Chi-Square, which is used to test the
  effects of the explanatory variables).
  

17
Probability of choice

• The parameter estimates are used next to
  construct the estimated probability that each
  alternative will be chosen.
  
• The DATA step program uses the following formula
  to create the choice probabilities.
  

18
Probabilities
19
Fabric Softener Example

• The study involves four fictitious fabric
  softener brand names Sploosh, Plumbbob, Platter,
  and Moosey.
  
• Each choice set consists of each of these four
  brands and a constant alternative Another.
  
• Each of the brands is available
• at three prices, 1.49, 1.99, and 2.49. Another
  is only offered at 1.99.
  
• There are 50 subjects, each of which will see the
  same choice sets.
  

20
Designing the experiment

• In order to do any choice model we need to
  construct an experimental design
  
• Using SAS
• We can use the MKTRUNS autocall macro to help us
  choose the number of choice sets. All of the
  autocall macros used in this report are
  documented starting on page 261. To use this
  macro, you specify the number of levels for each
  of the factors. With four brands each with three
  prices, you specify four 3s.
• title Choice of Fabric Softener
• mktruns( 3 3 3 3 )

21
Output
22
The design

• In this problem, the MKTRUNS macro reports ten
  different sizes with no violations Ideally, we
  would like to have a manageable number of choice
  sets for people to evaluate and a design that is
  both orthogonal and balanced.
• When violations are reported, orthogonal and
  balanced designs are not possible. While
  orthogonality and balance are not required, they
  are nice properties to have. With 4 three-level
  factors, the number of choice sets in all
  orthogonal and balanced designs must be divisible
  by 3 x 3 9.
• In this example we would go for 18 runs.

23
The design .

• In the next steps, an efficient experimental
  design is created. We will use an autocall macro
  MKTDES to create most of our designs.
  
• When you invoke the MKTDES macro for a simple
  problem, you only need to specify the factors,
  number of levels,
  
• and number of runs. The macro does the rest.
• For just main effects we simply type (note no
  second order effects are asked for here usually
  we ask for them)
  
• let n 18 / n choice sets /
• mktdes(factorsx1-x43, nn)
• proc print
• run

24
Design output
25
Design

• For now, notice that the macro found a perfect,
• orthogonal and balanced, 100 efficient design
  consisting of three-level factors, x1-x4. The
  levels are the
  
• integers 1 to 3.
• Note that we would need to randomise the order of
  these eventual this design to consumers.

26
Design ..
27
What consumers see
Etc
28
The Data
29
How the data needs to be formatted
Person 1 first 3 scenarios note this assumes
the price effect is the same for each brand us
ually its different.
30
The analysis

• proc phreg datacoded outestbetas
• title2 Discrete Choice Model
• model cc(2) Sploosh Plumbbob Platter Moosey
  Another Price / tiesbreslow
  
• strata subj set
• run

proc phreg datacoded outestbetas
title2 Discrete Choice Model
model cc(2) / tiesbreslow
strata subj set run
31
The analysis