Goal: Build practical intuition for multinomial logit (MNL): what it is, when to use it, how to prep data, how to estimate it using three approaches, and how to interpret results for managerial what-ifs.

Dataset: Fishing from mlogit (choice of fishing mode: beach, boat, charter, pier).
Approaches: nnet::multinom, VGAM::vglm, mlogit::mlogit.
Data prep: mlogit.data (shortcut), tidyverse pivot_longer, classic tidyverse gather/separate/spread.

1 1. What is Multinomial Logit (MNL)?

MNL models the probability that a decision-maker chooses one option out of several. In marketing, think: - Brand choice, channel choice, ad click, SKU selection, service mode (here: fishing mode).

Each option $j$ has a latent utility $U_{ij}$ for person $i$. With the logit form: \[ P(Y_i=j) \;=\; \frac{\exp(X_{ij}\beta)}{\sum_k \exp(X_{ik}\beta)}. \] - Coefficients are relative to a baseline alternative (we use beach).
- Variables can be alternative-specific (e.g., the price of the specific option) or individual-specific (e.g., income of the chooser).
- IIA assumption: odds between any pair of alternatives don’t depend on other options. Good for learning and often reasonable; for close substitutes, consider nested/mixed logit.

2 2. Setup

# Optionally install packages if missing
pkgs <- c("nnet","VGAM","mlogit","lmtest","pscl","tidyverse","knitr","kableExtra")
to_install <- setdiff(pkgs, rownames(installed.packages()))
if (length(to_install)) install.packages(to_install, repos = "https://cloud.r-project.org")

library(nnet)
library(VGAM)
library(mlogit)
library(lmtest)
library(pscl)
library(tidyverse)
library(knitr); library(kableExtra)

set.seed(123) # reproducibility for multinom
knitr::opts_chunk$set(comment = NA, fig.align = "center", fig.width = 7, fig.height = 4.5, message = FALSE, warning = FALSE)

# ---- tables-helper (define kbl_safe early) ----
if (!exists("kbl_safe")) {
  kbl_safe <- function(x, ...) {
    tb <- knitr::kable(x, ...)
    if (knitr::is_html_output()) {
      out <- tryCatch(kableExtra::kable_styling(tb), error = function(e) tb)
      return(out)
    }
    tb
  }
}

Data preview (wide format):

data("Fishing", package="mlogit")
str(Fishing)

'data.frame':   1182 obs. of  10 variables:
 $ mode         : Factor w/ 4 levels "beach","pier",..: 4 4 3 2 3 4 1 4 3 3 ...
 $ price.beach  : num  157.9 15.1 161.9 15.1 106.9 ...
 $ price.pier   : num  157.9 15.1 161.9 15.1 106.9 ...
 $ price.boat   : num  157.9 10.5 24.3 55.9 41.5 ...
 $ price.charter: num  182.9 34.5 59.3 84.9 71 ...
 $ catch.beach  : num  0.0678 0.1049 0.5333 0.0678 0.0678 ...
 $ catch.pier   : num  0.0503 0.0451 0.4522 0.0789 0.0503 ...
 $ catch.boat   : num  0.26 0.157 0.241 0.164 0.108 ...
 $ catch.charter: num  0.539 0.467 1.027 0.539 0.324 ...
 $ income       : num  7083 1250 3750 2083 4583 ...

kbl_safe(head(Fishing))

mode	price.beach	price.pier	price.boat	price.charter	catch.beach	catch.pier	catch.boat	catch.charter	income
charter	157.930	157.930	157.930	182.930	0.0678	0.0503	0.2601	0.5391	7083.332
charter	15.114	15.114	10.534	34.534	0.1049	0.0451	0.1574	0.4671	1250.000
boat	161.874	161.874	24.334	59.334	0.5333	0.4522	0.2413	1.0266	3750.000
pier	15.134	15.134	55.930	84.930	0.0678	0.0789	0.1643	0.5391	2083.333
boat	106.930	106.930	41.514	71.014	0.0678	0.0503	0.1082	0.3240	4583.332
charter	192.474	192.474	28.934	63.934	0.5333	0.4522	0.1665	0.3975	4583.332

Interpretation: - mode: chosen alternative (beach, boat, charter, pier) - price.*, catch.*: alternative-specific attributes - income: individual-specific attribute

3 3. Data Preparation (3 ways)

Goal: create long choice format = one row per (chooser, alternative) + a logical mode flag that equals TRUE for the chosen alternative.

3.1 3A. Shortcut: `mlogit.data`

fishing_mlogit <- mlogit.data(Fishing,
                              shape = "wide",
                              choice = "mode",
                              varying = 2:9,   # price.* and catch.*
                              sep = ".")

kbl_safe(head(as.data.frame(fishing_mlogit)[, c("chid","alt","mode","price","catch","income")]))

chid	alt	mode	price	catch	income
1	beach	FALSE	157.930	0.0678	7083.332
1	boat	FALSE	157.930	0.2601	7083.332
1	charter	TRUE	182.930	0.5391	7083.332
1	pier	FALSE	157.930	0.0503	7083.332
2	beach	FALSE	15.114	0.1049	1250.000
2	boat	FALSE	10.534	0.1574	1250.000

chid: chooser id; alt: alternative; mode: TRUE for the chosen row.
This is exactly the structure mlogit() expects.

3.2 3B. Tidyverse: `pivot_longer`

fishing_pivot <- Fishing %>%
  mutate(chid = row_number()) %>%
  pivot_longer(cols = starts_with(c("price","catch")),
               names_to = c(".value","alt"),
               names_sep = "\\.") %>%
  mutate(mode = (mode == alt))

kbl_safe(head(as.data.frame(fishing_pivot)[, c("chid","alt","mode","price","catch","income")]))

chid	alt	mode	price	catch	income
1	beach	FALSE	157.930	0.0678	7083.332
1	pier	FALSE	157.930	0.0503	7083.332
1	boat	FALSE	157.930	0.2601	7083.332
1	charter	TRUE	182.930	0.5391	7083.332
2	beach	FALSE	15.114	0.1049	1250.000
2	pier	FALSE	15.114	0.0451	1250.000

3.3 3C. Tidyverse (classic): `gather` / `separate` / `spread`

fishing_gather <- Fishing %>%
  mutate(chid = row_number()) %>%
  gather(key = "var_alt", value = "val",
         starts_with("price"), starts_with("catch")) %>%
  separate(var_alt, into = c("var","alt"), sep = "\\.") %>%
  spread(var, val) %>%
  mutate(mode = (mode == alt))

kbl_safe(head(as.data.frame(fishing_gather)[, c("chid","alt","mode","price","catch","income")]))

chid	alt	mode	price	catch	income
604	beach	TRUE	5.934	0.0678	416.6667
604	boat	FALSE	7.740	0.0014	416.6667
604	charter	FALSE	36.740	0.0029	416.6667
604	pier	FALSE	5.934	0.0789	416.6667
893	beach	TRUE	3.870	0.5333	416.6667
893	boat	FALSE	47.730	0.2413	416.6667

3.3.1 3C.1 Why this older tidyverse path? (what we did & why)

What we did
1. mutate(chid = row_number()) — label each chooser; tells the model which rows form a choice set.
2. gather(...) — melt alt-specific columns; exposes the hidden alternative dimension.
3. separate(var_alt, c("var","alt")) — split price.boat → var="price", alt="boat".
4. spread(var, val) — pivot var back into columns so each (chid, alt) row has price and catch columns.
5. mutate(mode = (mode == alt)) — one TRUE per chooser, marking the chosen alt.

Why we did it
- Make the alternative dimension explicit.
- Align with mlogit formula: alt-specific (price, catch) before |; individual-specific (income) after.
- Pedagogically clarifies what rows mean in a choice model.

Mini checks (run & inspect):

# See the stacked alternatives just after gather/separate
tmp_long <- Fishing %>% 
  mutate(chid = row_number()) %>%
  gather("var_alt","val", starts_with("price"), starts_with("catch")) %>%
  separate(var_alt, c("var","alt"), sep="\\.")
head(tmp_long)

# Exactly one chosen row per chooser?
fishing_gather %>%
  group_by(chid) %>%
  summarise(chosen_rows = sum(mode)) %>%
  count(chosen_rows)

3.4 3D. Sanity check: structures are equivalent

check1 <- all.equal(
  as.data.frame(fishing_mlogit)[,c("chid","alt","mode","price","catch","income")],
  as.data.frame(fishing_pivot)[,c("chid","alt","mode","price","catch","income")]
)
check2 <- all.equal(
  as.data.frame(fishing_mlogit)[,c("chid","alt","mode","price","catch","income")],
  as.data.frame(fishing_gather)[,c("chid","alt","mode","price","catch","income")]
)
check1; check2

[1] "Attributes: < Component \"class\": Lengths (2, 1) differ (string compare on first 1) >"
[2] "Component \"alt\": 'current' is not a factor"                                          
[3] "Component \"mode\": 2096 element mismatches"                                           
[4] "Component \"price\": Mean relative difference: 0.8301712"                              
[5] "Component \"catch\": Mean relative difference: 1.243696"

[1] "Attributes: < Component \"class\": Lengths (2, 1) differ (string compare on first 1) >"
[2] "Component \"chid\": Mean relative difference: 0.7143749"                               
[3] "Component \"alt\": 'current' is not a factor"                                          
[4] "Component \"mode\": 1720 element mismatches"                                           
[5] "Component \"price\": Mean relative difference: 0.9345275"                              
[6] "Component \"catch\": Mean relative difference: 1.222338"                               
[7] "Component \"income\": Mean relative difference: 0.6685676"

4 4. “Classification” View (Only the Chosen Row per Person)

This is familiar from ML classes, but less suited to what-ifs.

wide_df <- subset(fishing_mlogit, mode == TRUE)
wide_df$alt <- relevel(wide_df$alt, ref = "beach")  # baseline
table(wide_df$alt)


  beach    boat charter    pier 
    134     418     452     178

4.1 4A. `nnet::multinom`

m_nnet <- multinom(alt ~ price + catch + income, data = wide_df, trace = FALSE)
summary(m_nnet)

Call:
multinom(formula = alt ~ price + catch + income, data = wide_df, 
    trace = FALSE)

Coefficients:
        (Intercept)        price      catch        income
boat      0.9880772  0.003555725 -1.2997215  6.930617e-05
charter   0.1588430  0.022700714  1.4116330 -1.788990e-04
pier      1.0836892 -0.003027237 -0.9494361 -1.286185e-04

Std. Errors:
         (Intercept)       price        catch       income
boat    1.767921e-05 0.003155494 2.992347e-06 3.161360e-05
charter 1.364347e-05 0.003160311 9.419144e-06 3.691491e-05
pier    2.304065e-05 0.003965765 5.115583e-06 4.049548e-05

Residual Deviance: 2531.988 
AIC: 2555.988

Wald-style p-values (quick read; LR preferred):

coefs <- summary(m_nnet)$coefficients
ses   <- summary(m_nnet)$standard.errors
pvals <- 2*(1 - pnorm(abs(coefs/ses)))
kbl_safe(round(pvals, 3))

	price	income
boat	0.260	0.028
charter	0.000	0.000
pier	0.445	0.001

LR test vs null:

m0_nnet <- multinom(alt ~ 1, data = wide_df, trace = FALSE)
anova(m0_nnet, m_nnet, test = "Chisq")

In-sample classification snapshot (for intuition only):

pred_nnet_class <- predict(m_nnet, type = "class")
tab_nnet <- table(True = wide_df$alt, Pred = pred_nnet_class)
acc_nnet <- mean(pred_nnet_class == wide_df$alt)
tab_nnet; acc_nnet

         Pred
True      beach boat charter pier
  beach       0   96      38    0
  boat        0  314     102    2
  charter     0  138     314    0
  pier        0  129      46    3

[1] 0.5338409

4.2 4B. `VGAM::vglm`

m_vgam <- vglm(alt ~ price + catch + income,
               family = multinomial(refLevel = "beach"),
               data   = wide_df)
summary(m_vgam)


Call:
vglm(formula = alt ~ price + catch + income, family = multinomial(refLevel = "beach"), 
    data = wide_df)

Coefficients: 
                Estimate Std. Error z value Pr(>|z|)    
(Intercept):1  9.880e-01  2.231e-01   4.429 9.49e-06 ***
(Intercept):2  1.589e-01  2.367e-01   0.671 0.502172    
(Intercept):3  1.084e+00  2.584e-01   4.194 2.75e-05 ***
price:1        3.557e-03  3.343e-03   1.064 0.287253    
price:2        2.270e-02  3.333e-03   6.811 9.71e-12 ***
price:3       -3.026e-03  4.180e-03  -0.724 0.469130    
catch:1       -1.300e+00  3.406e-01  -3.816 0.000136 ***
catch:2        1.412e+00  2.760e-01   5.115 3.14e-07 ***
catch:3       -9.493e-01  4.023e-01  -2.360 0.018291 *  
income:1       6.931e-05  4.239e-05   1.635 0.102074    
income:2      -1.789e-04  4.891e-05  -3.658 0.000254 ***
income:3      -1.286e-04  5.514e-05  -2.332 0.019683 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Names of linear predictors: log(mu[,2]/mu[,1]), log(mu[,3]/mu[,1]), 
log(mu[,4]/mu[,1])

Residual deviance: 2531.988 on 3534 degrees of freedom

Log-likelihood: -1265.994 on 3534 degrees of freedom

Number of Fisher scoring iterations: 5 

No Hauck-Donner effect found in any of the estimates


Reference group is level  1  of the response

LR test vs null:

m0_vgam <- vglm(alt ~ 1, family = multinomial(refLevel = "beach"), data = wide_df)
VGAM::lrtest(m0_vgam, m_vgam)

Likelihood ratio test

Model 1: alt ~ 1
Model 2: alt ~ price + catch + income
   #Df  LogLik Df  Chisq Pr(>Chisq)    
1 3543 -1497.7                         
2 3534 -1266.0 -9 463.46  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interpretation note: Coefficients are log-odds vs baseline (beach). Negative price means higher price lowers odds of choosing that alternative vs beach; positive catch raises odds.

5 5. “Choice Model” View (One Row per `(chooser, alternative)`)

This is the econometric formulation used for market-share simulation and policy experiments.

m_mlogit <- mlogit(mode ~ price + catch | income,
                   data     = fishing_mlogit,
                   reflevel = "beach")
summary(m_mlogit)


Call:
mlogit(formula = mode ~ price + catch | income, data = fishing_mlogit, 
    reflevel = "beach", method = "nr")

Frequencies of alternatives:choice
  beach    boat charter    pier 
0.11337 0.35364 0.38240 0.15059 

nr method
7 iterations, 0h:0m:0s 
g'(-H)^-1g = 1.37E-05 
successive function values within tolerance limits 

Coefficients :
                       Estimate  Std. Error  z-value  Pr(>|z|)    
(Intercept):boat     5.2728e-01  2.2279e-01   2.3667 0.0179485 *  
(Intercept):charter  1.6944e+00  2.2405e-01   7.5624 3.952e-14 ***
(Intercept):pier     7.7796e-01  2.2049e-01   3.5283 0.0004183 ***
price               -2.5117e-02  1.7317e-03 -14.5042 < 2.2e-16 ***
catch                3.5778e-01  1.0977e-01   3.2593 0.0011170 ** 
income:boat          8.9440e-05  5.0067e-05   1.7864 0.0740345 .  
income:charter      -3.3292e-05  5.0341e-05  -0.6613 0.5084031    
income:pier         -1.2758e-04  5.0640e-05  -2.5193 0.0117582 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Log-Likelihood: -1215.1
McFadden R^2:  0.18868 
Likelihood ratio test : chisq = 565.17 (p.value = < 2.22e-16)

Left side: the choice indicator mode.
Before |: alt-specific variables (price, catch).
After |: individual-specific variables (income).
reflevel="beach" sets the baseline utility.

LR test vs null:

m0_mlogit <- mlogit(mode ~ 1 | 1, data = fishing_mlogit, reflevel = "beach")
lmtest::lrtest(m0_mlogit, m_mlogit)

Reading the output: For each non-baseline alternative (boat/charter/pier), you’ll see coefficients on price and catch. Signs should match intuition; magnitudes are in utility units (log-odds). Probability effects depend on the full choice set (softmax).

IIA caveat: MNL assumes IIA (relative odds unaffected by presence/absence of other options). For close substitutes, consider nested or mixed logit.

5.1 5.1 How to Interpret the Coefficients (all three approaches)

Across multinom, vglm, and mlogit, coefficients are in log-odds units relative to baseline (beach).

Log-odds change: $\Delta \log\text{-odds} = \beta \cdot \Delta x$
Odds ratio (OR): $\text{OR} = e^{\beta}$
% change in odds: $100\times(e^{\beta}-1)\%$

Examples:
- β_price_boat = -0.05 ⇒ +1 in boat price multiplies odds(boat vs beach) by exp(-0.05)≈0.95 (≈5% drop).
- β_catch_charter = +0.20 ⇒ +1 in catch multiplies odds(charter vs beach) by exp(0.20)≈1.22 (≈22% increase).

Intercepts (ASCs): baseline appeal relative to beach.
Significance: prefer LR vs null for overall signal; use per-coefficient p-values for details.
Units: rescale (e.g., price per $10) for easier storytelling.

# Optional: explicit odds ratios for mlogit fit
or_tab <- exp(summary(m_mlogit)$coefficients)
kbl_safe(round(or_tab, 3))

	x
(Intercept):boat	1.694
(Intercept):charter	5.443
(Intercept):pier	2.177
price	0.975
catch	1.430
income:boat	1.000
income:charter	1.000
income:pier	1.000

5.2 5.2 Why `mlogit` for marketing inference & what-ifs

When your goal is to identify significant drivers of choice and to run credible what-if simulations, mlogit beats simple multi-class classifiers:

Uses the full choice set (updates all alternatives when one attribute changes).
Respects variable roles (alt-specific vs individual-specific).
Doesn’t discard information (uses all rows, not just the chosen row).
Managerial interpretation (coefficients → odds → predicted shares).
Proper significance testing (evidence from the whole choice set).
Policy-ready & extensible (ASCs, robust SEs, nested/mixed logit).

5.2.1 Guard (ensures objects exist if students jump here)

# Packages
if (!requireNamespace("mlogit", quietly = TRUE)) install.packages("mlogit", repos = "https://cloud.r-project.org")
if (!requireNamespace("nnet", quietly = TRUE)) install.packages("nnet", repos = "https://cloud.r-project.org")

# Data
if (!exists("Fishing")) data("Fishing", package = "mlogit")

# Long choice data
if (!exists("fishing_mlogit")) {
  fishing_mlogit <- mlogit::mlogit.data(Fishing, shape = "wide", choice = "mode", varying = 2:9, sep = ".")
}
# Classification data
if (!exists("wide_df")) {
  wide_df <- subset(fishing_mlogit, mode == TRUE)
  wide_df$alt <- stats::relevel(wide_df$alt, ref = "beach")
}
# Models
if (!exists("m_nnet")) {
  m_nnet <- nnet::multinom(alt ~ price + catch + income, data = wide_df, trace = FALSE)
}
if (!exists("m_mlogit")) {
  m_mlogit <- mlogit::mlogit(mode ~ price + catch | income, data = fishing_mlogit, reflevel = "beach")
}

5.2.2 Quick contrast demo: why classification what-ifs can mislead

# Baseline class shares from multinom (classification view)
p_class0 <- predict(m_nnet, type = "probs")
share_class0 <- colMeans(p_class0)

# Attempt a classification what-if: +20 boat price (only affects chosen 'boat' rows here)
wide_df_whatif <- wide_df
wide_df_whatif$price[wide_df_whatif$alt == "boat"] <- wide_df_whatif$price[wide_df_whatif$alt == "boat"] + 20

p_class1 <- predict(m_nnet, newdata = wide_df_whatif, type = "probs")
share_class1 <- colMeans(p_class1)

kbl_safe(round(rbind(Classifier_Base = share_class0,
                     Classifier_BoatUp = share_class1), 3))

	beach	boat	charter	pier
Classifier_Base	0.113	0.354	0.382	0.151
Classifier_BoatUp	0.108	0.345	0.407	0.140

Proper choice-model what-if (updates everyone):

p0_mlogit <- predict(m_mlogit, newdata = fishing_mlogit)
share0_mlogit <- colMeans(p0_mlogit)

whatif_mlogit <- fishing_mlogit
whatif_mlogit$price[whatif_mlogit$alt == "boat"] <- whatif_mlogit$price[whatif_mlogit$alt == "boat"] + 20

p1_mlogit <- predict(m_mlogit, newdata = whatif_mlogit)
share1_mlogit <- colMeans(p1_mlogit)

kbl_safe(round(rbind(mlogit_Base  = share0_mlogit,
                     mlogit_BoatUp = share1_mlogit), 3))

	beach	boat	charter	pier
mlogit_Base	0.113	0.354	0.382	0.151
mlogit_BoatUp	0.123	0.259	0.454	0.164

Marketing takeaway: mlogit is the right tool because it uses the full competitive set, keeps alt-specific vs individual-specific effects straight, and turns significance into credible share-shift predictions under price/feature changes.

6 6. Prediction & What-If Simulation

Effect of raising boat price by 20 on predicted market shares.

# Baseline market shares
p0 <- predict(m_mlogit, newdata = fishing_mlogit)        # rows = obs, cols = alts
share0 <- colMeans(p0)

# Counterfactual: increase boat price by +20
whatif <- fishing_mlogit
whatif$price[whatif$alt == "boat"] <- whatif$price[whatif$alt == "boat"] + 20
p1 <- predict(m_mlogit, newdata = whatif)
share1 <- colMeans(p1)

# Compare
shares <- rbind(Baseline = share0, BoatPriceUp = share1)
kbl_safe(round(shares, 3))

	beach	boat	charter	pier
Baseline	0.113	0.354	0.382	0.151
BoatPriceUp	0.123	0.259	0.454	0.164

Bar plot:

barplot(t(shares), beside = TRUE, legend = TRUE,
        ylab = "Market Share",
        main = "What-if: Boat Price +20")

What-if: Boat Price +20 (Predicted Market Shares)

Reading: Own effect (boat share falls). Cross effects (which alts gain?) indicate substitution patterns.

7 7. Extensions & Exercises

Heterogeneity: interact income with price/catch:

m_mlogit_ix <- mlogit(mode ~ price + catch + price:income + catch:income | income,
                      data = fishing_mlogit, reflevel = "beach")
summary(m_mlogit_ix)

ASCs: add alternative-specific constants to capture baseline appeal.
Model comparison: AIC/BIC; out-of-sample validation by splitting choosers.
IIA discussion: when to consider nested or mixed logit.

8 8. Summary (Talking Points)

MNL models one-of-many choices.
Choice-model view supports scenario analysis and share predictions.
Interpret through odds ratios; use AMEs/elasticities for probability-level stories.
IIA is an assumption—know when to move beyond MNL.

9 Appendix: Interpretation Tools (AMEs & Elasticities)

# Average Marginal Effects (AME): nudge a variable and average Δprobabilities
ame <- function(model, data, var, delta = 1, target_alt = NULL) {
  p0 <- predict(model, newdata = data)
  d1 <- data
  if (!is.null(target_alt)) {
    d1[[var]][d1$alt == target_alt] <- d1[[var]][d1$alt == target_alt] + delta
  } else {
    d1[[var]] <- d1[[var]] + delta
  }
  p1 <- predict(model, newdata = d1)
  colMeans(p1 - p0)
}

# Examples:
ame_price_boat <- ame(m_mlogit, fishing_mlogit, var = "price", delta = 1, target_alt = "boat")
ame_income_all <- ame(m_mlogit, fishing_mlogit, var = "income", delta = 1, target_alt = NULL)
kbl_safe(round(ame_price_boat, 4))

	x
beach	0.0006
boat	-0.0050
charter	0.0037
pier	0.0007

kbl_safe(round(ame_income_all, 4))

	x
beach	0
boat	0
charter	0
pier	0

# Elasticities: %Δshare / %Δprice for an alt-specific price
elasticities <- function(model, data, target_alt, pct = 0.01) {
  base_s <- colMeans(predict(model, newdata = data))

  d_up <- data
  idx  <- d_up$alt == target_alt
  d_up$price[idx] <- d_up$price[idx] * (1 + pct)

  s_up <- colMeans(predict(model, newdata = d_up))
  ((s_up - base_s) / base_s) / pct
}

elas_boat <- elasticities(m_mlogit, fishing_mlogit, target_alt = "boat", pct = 0.01)
kbl_safe(round(elas_boat, 3))

	x
beach	0.292
boat	-0.609
charter	0.376
pier	0.255

10 9. Reproducibility

sessionInfo()

R version 4.4.2 (2024-10-31)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Australia/Melbourne
tzcode source: internal

attached base packages:
[1] splines   stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] kableExtra_1.4.0 knitr_1.49       lubridate_1.9.4  forcats_1.0.0   
 [5] stringr_1.5.1    dplyr_1.1.4      purrr_1.0.4      readr_2.1.5     
 [9] tidyr_1.3.1      tibble_3.2.1     ggplot2_3.5.2    tidyverse_2.0.0 
[13] pscl_1.5.9       lmtest_0.9-40    zoo_1.8-13       mlogit_1.1-3    
[17] dfidx_0.1-0      VGAM_1.1-13      nnet_7.3-20     

loaded via a namespace (and not attached):
 [1] sass_0.4.9        generics_0.1.3    xml2_1.3.8        stringi_1.8.4    
 [5] lattice_0.22-6    hms_1.1.3         digest_0.6.37     magrittr_2.0.3   
 [9] timechange_0.3.0  evaluate_1.0.3    grid_4.4.2        fastmap_1.2.0    
[13] jsonlite_1.9.0    Formula_1.2-5     viridisLite_0.4.2 scales_1.3.0     
[17] textshaping_1.0.0 jquerylib_0.1.4   Rdpack_2.6.2      cli_3.6.4        
[21] rlang_1.1.5       rbibutils_2.3     munsell_0.5.1     withr_3.0.2      
[25] cachem_1.1.0      yaml_2.3.10       tools_4.4.2       tzdb_0.5.0       
[29] colorspace_2.1-1  vctrs_0.6.5       R6_2.6.1          lifecycle_1.0.4  
[33] MASS_7.3-64       pkgconfig_2.0.3   pillar_1.10.1     bslib_0.9.0      
[37] gtable_0.3.6      glue_1.8.0        systemfonts_1.2.3 statmod_1.5.0    
[41] xfun_0.52         tidyselect_1.2.1  rstudioapi_0.17.1 htmltools_0.5.8.1
[45] svglite_2.2.1     rmarkdown_2.29    compiler_4.4.2

Multinomial Logit for Marketing: Hands-On Demo

Instructor

2 October 2025

1 1. What is Multinomial Logit (MNL)?

2 2. Setup

3 3. Data Preparation (3 ways)

3.1 3A. Shortcut: `mlogit.data`

3.2 3B. Tidyverse: `pivot_longer`

3.3 3C. Tidyverse (classic): `gather` / `separate` / `spread`

3.3.1 3C.1 Why this older tidyverse path? (what we did & why)

3.4 3D. Sanity check: structures are equivalent

4 4. “Classification” View (Only the Chosen Row per Person)

4.1 4A. `nnet::multinom`

4.2 4B. `VGAM::vglm`

5 5. “Choice Model” View (One Row per `(chooser, alternative)`)

5.1 5.1 How to Interpret the Coefficients (all three approaches)

5.2 5.2 Why `mlogit` for marketing inference & what-ifs

5.2.1 Guard (ensures objects exist if students jump here)

5.2.2 Quick contrast demo: why classification what-ifs can mislead

6 6. Prediction & What-If Simulation

7 7. Extensions & Exercises

8 8. Summary (Talking Points)

9 Appendix: Interpretation Tools (AMEs & Elasticities)

10 9. Reproducibility

Multinomial Logit for Marketing: Hands-On Demo

Instructor

2 October 2025

1 1. What is Multinomial Logit (MNL)?

2 2. Setup

3 3. Data Preparation (3 ways)

3.1 3A. Shortcut: mlogit.data

3.2 3B. Tidyverse: pivot_longer

3.3 3C. Tidyverse (classic): gather / separate / spread

3.3.1 3C.1 Why this older tidyverse path? (what we did & why)

3.4 3D. Sanity check: structures are equivalent

4 4. “Classification” View (Only the Chosen Row per Person)

4.1 4A. nnet::multinom

4.2 4B. VGAM::vglm

5 5. “Choice Model” View (One Row per (chooser, alternative))

5.1 5.1 How to Interpret the Coefficients (all three approaches)

5.2 5.2 Why mlogit for marketing inference & what-ifs

5.2.1 Guard (ensures objects exist if students jump here)

5.2.2 Quick contrast demo: why classification what-ifs can mislead

6 6. Prediction & What-If Simulation

7 7. Extensions & Exercises

8 8. Summary (Talking Points)

9 Appendix: Interpretation Tools (AMEs & Elasticities)

10 9. Reproducibility

3.1 3A. Shortcut: `mlogit.data`

3.2 3B. Tidyverse: `pivot_longer`

3.3 3C. Tidyverse (classic): `gather` / `separate` / `spread`

4.1 4A. `nnet::multinom`

4.2 4B. `VGAM::vglm`

5 5. “Choice Model” View (One Row per `(chooser, alternative)`)

5.2 5.2 Why `mlogit` for marketing inference & what-ifs