Going beyond the Simple MNL model

class: center, middle, inverse, title-slide

.title[
# Going beyond the Simple MNL model
]
.subtitle[
## Using latent Gold and R packages to build more advanced choice models
]
.author[
### Going beyond the Simple MNL model.Rmd
]
.date[
### 2025-01-28
]

---

#  Multinomial logit choice models

+ Advantages
    + Simple utility function  - linear in its parameters
    + Readily available software
        + CBCHB, LatentGold, SPSS, Stata, SAS
        + R: Bayesm , ChoiceModelR , Mlogit , Apollo, RSGHB …
    + Can be applied to almost any choice modeling context
    + Easy to implement in a simulator
    + Disadvantages
    + Only strict linear-in-its-parameters utility functions
    + Assumes proportional substitution - IIA

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#  Going beyond the MNL choice model

+ Wouldn’t it be nice to be able to fit some of the more advanced models seen at Sawtooth without writing your own programs:
    + Model diminishing returns in a utility function?
    + Fit a nested logit model?
    + Fit a volume model
    + A MaxDiff model with a scalar to model the best choices differently than the worst choices.

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#  Build more complex models using R

+ R Basics
    + Using RSGHB
        + Simple MNL model
    + Using Latent Gold to produce the RSGHB program
    + More advanced models
        + Diminishing returns on additional features in a simple MNL model
        + The nested logit model
        + The Joint/Discrete volumetric model

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#  R Basics

+ R editors
    + R itself
    + Rstudio
    + Visual Studio Code
    + R packages
    + Tidyverse ,
    + RSGHB, Bayesm , ChoiceModelR , mlogit
    + Requirements
    + Input data
    + Transform data

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#  MNL model

+ Utility function
    + V in = b i0 + b 1 X in1 + b 2 X in2 + … b K X inK
    + V in =
    + where
        + n is the respondent;
        + i is the alternative;
        + k is the number of variables; and
        + b 0 is an intercept
    + V in = b in0 + b i1 X in1 + b i2 X in2 + … b iK X inK
    + A respondent’s utility function…

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#  MNL model

+ MNL formula
            + Where i is the respondent;
            + k is the number of variables; and b 0 is an intercept

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#  MNL model likelihood

+ Likelihood formula
    +  
        + Where y in = 1 if respondent n chose alternative i ; 0 = otherwise
        + C n is the choice set respondent i sees
        + J is the number of alternatives in C n
    + Log Likelihood

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#  What we are going to do

+ Go over some Model and R basics
    + Model
        + Utility functions
        + The MNL model
            + What is a MNL model likelihood function
    + R basics
        + Some experience in R programming desirable
        + Input and output of data sets
        + Creating new and coded variables for RSGHB
        + R functions
        + Output intermediate and final data/results

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#  What we are going to do

+ RSGHB basics
    + Data input
    + Data coding
    + Likelihood function
    + Output results

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#  Model and R Basics

+ R Basics
    + Read and write datasets
    + Creating new variables
    + Executing function
    + MNL basics
    + Utility functions
    + MNL model likelihood function
        + Aggregate
        + RUM - HB
        + Latent class – LG choice model

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#  Using Latent Gold to produce a RSGHB program

+ Jay shows LG syntax approach
    + Demo RUM LG syntax using Flynn MaxDiff data

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#  Diminishing Returns in a MNL Utility Function

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#  The Nested Logit Model

+ Tom intro NL
    + Jay demos syntax for NL
    + Demo RSGHB run using NL

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#  The Joint/Discrete volumetric model