Important 2: Logistic Regression and Multinominal Logit Models

Question 1

What is the Multinominal Logit Model?

Answer 1

is a choice model where the consumer chooces between j alternatives

–>Here as well as in the binary case we assume that the alternative which yields highest utility is chosen

Question 2

What is the Independence of Irrelevant Alternative (IIA) Property?

Multinominal Logit Models

Answer 2

Multinominal Logit Models suffer from the IIA, this property states

that the odds of choosing one alternative over another are constant regardless of whcih other alternatives are present

Question 3

Why is the IIA property not realistic in marketing?

Answer 3

• In many marketing applications this is not realistic especially if some alternatives are close substitutes
• If similarities across alternatives are incorrectly assumed , the estimated effects of marketing variables are incorrect

Question 4

How to deal with the Independence of Irrelevant Alternaitves

Answer 4

1. perform statistical test of IIA e.g. attraction model
2. use choice model that explicitly accounts for the fact that consumer choice behavior is affected by the composition of the choice set

–>Other models that eliminate the IIA assummptions are the Nested Multinominal Logit Model and the Multinominal Probit model

Question 5

What do Markov Chain model?

Answer 5

model behavior over time and consists of several observable (behavior, corresponding profits/losses) and unobservable (probabilities) factors

model how sequence of observations is related to transitioning among states

Question 6

Markov Chain models define set of customer states based on…

Answer 6

The idea is to define the set of customer states based on:

• observed customer properties, e.g. the purchase of a product
• estimation of transition probabilities between the different states
• corresponding profits and losses

Question 7

4 Probabilities of Markov Chain Models

Answer 7

1. Transition probability: probability of going from one hidden state to another
2. Emission probability: probability that observations are emitted from the hidden states ( prob observed outcome given particular state int he system
3. Prior probability: basic likelihood for hidden state (prob that a random customer has a preferecne for brand A or B)
4. Posterior probability: likelihood for hidden state given observation (prob that a customer prefers Brand A or brand B given that he buys brand A)

Question 8

What is the goal of Markov Chain Models?
Capture….

Answer 8

Our goal is to capture dynamics in customer behavior over time, for
example, to see how firm interventions influence this behavior

Question 9

For what do we use Logistic regression?

Answer 9

is used to predict binary or categorical outcomes (buy or not buy)

–>are binary choice models*

Question 10

What are the two variables in logistic regression?

Answer 10

depdent variable: which is the variable of interest that we want to predict or explain

predictor variable/independent variable: are the variables used to explain or predict the depdent variable, these can be categorical but can also be continous (numerous)

Question 11

How to infer prefercenes
(Markov Chain models)

Answer 11

Multiply every probabillity along the path (Viterbi Algorithm)
–>Machine learning system which identifies path with highest probability to be chosen
- finding most profitable preference combination
- If preference probabillities are close to each other advertising makes sense

Question 12

What is necessary to check in the data, when doing Logistic regression?

Answer 12

–>used for binary dependable variables

• check whether there are characters turn them into factor levels

–>if indepent variable is character just check if the second or last entry is also the best if there is a best, for example if (Bundle, No Bundle –>here Bundle 1 and no Bundle 2

Question 13

What is an interaction effect?
How is it incorporated in glm?

Answer 13

Interaction effect: refers to the combined effect of two or more predictor variables on the outcome

incorporated by: either Offer:Channel or by Offer*Channel —>always in reference to base in this case E-Mail

Question 14

What happens in logistics regression when there are multiple predictiors? What is the baseline?

Answer 14

glm(purchase ~ coupon + Channel +..)

for Channek: E-Mail, Mail, Park
automatically glm takes the first variable –>E-Mail as baseline
–>all other variables in Channel are compared to the baseline
–>the

Question 15

What is the meaning of the ods ratio?
5.6
How is this measure called?

Answer 15

Customer are 5.6 times more likely to purchase product when they receive a coupon (OfferBundle)

odds ratio is the association between variiables

Question 16

What is the Intercept (alternative-specific constant) in Multinominal Logit Models?

Answer 16

intercept: represents he baseline

if we have a model with intercept:
–>the intercepts capture the baseline probability of choosing the reference category when all other predictors variables are zero

example: (intercept): ec = 1.6 –>baseline log-odds of choosing “ec” over “hp” (reflevel) if all other predictor variables are zero

Question 17

What is the output of the Mlogit model?

Answer 17

1. frequencies of alternatives choice
2. Coefficients
   - predictor coefficient: indepent of reference for all
   - conditioned ceoffivient (income:ec) compared to reference level ( if income increase than the likelihood of choosing ec dercreases with respect to hp)
   - intercept prob of choosing ec over hp (baseline) if all other are zero

Question 18

How can the estimated probabilities of the mlogit model be tested?

Answer 18

1. take observed frequencies of the Mlogit output
2. Predict() the predicttec values for the dependable variable
3. in predict( need too but outcome = FALSE –>to ensure to get probabilities for each alternative

–>using apply() to get the mean values per column (2)

Question 19

How to compare two Mlogit models?
What is the h0?

Answer 19

using liklihood ratio test:
lrtest( model 1, model 2)

H0: model 1 (smaller) is better than model 2 (larger)

Question 20

What are the steps in estimating a Markov chains?

Answer 20

1. convert data into formal clickstream object (=refers to collection of user interactions or events that occur during a user´s session on a website or application
2. Using fitMarkovChain()
   fitMarkovChain(data, order =1 or 0
   0= prob of next stage independent of previous state
   1= prob of net stage depends only on the previous state

Question 21

What is the Output of the MarkovChain prediction and how to read the matrix?

Answer 21

Output Transition matrix:
read from Column (t) to row(t+1)

Question 22

How to calculate prob in t+1 using Markov Chian models?

Answer 22

= start “*” transition