The {logitr} package requires that data be structured in a
data.frame and arranged in a “long” format [@Wickham2014] where each row contains data on a
single alternative from a choice observation. The choice observations do
not have to be symmetric, meaning they can have a “ragged” structure
where different choice observations have different numbers of
alternatives. The data must also include variables for each of the
following:
1 is chosen, 0
is not chosen). Only one alternative should have a 1 per
choice observation.obsID variable would be
1, 1, 2, 2, 3, 3.The {logitr} package contains several example data sets that
illustrate this data structure. For example, the yogurt
contains observations of yogurt purchases by a panel of 100 households
[@Jain1994]. Choice is identified by the
choice column, the observation ID is identified by the
obsID column, and the columns price,
feat, and brand can be used as model
covariates:
library("logitr")
head(yogurt)
#> id obsID alt choice price feat brand
#> 1 1 1 1 0 8.1 0 dannon
#> 2 1 1 2 0 6.1 0 hiland
#> 3 1 1 3 1 7.9 0 weight
#> 4 1 1 4 0 10.8 0 yoplait
#> 5 1 2 1 1 9.8 0 dannon
#> 6 1 2 2 0 6.4 0 hilandThis data set also includes an alt variable that
determines the alternatives included in the choice set of each
observation and an id variable that determines the
individual as the data have a panel structure containing multiple choice
observations from each individual.
Variables are modeled as either continuous or discrete based on their
data type. Numeric variables are by default estimated with a
single “slope” coefficient. For example, consider a data frame that
contains a price variable with the levels $10, $15, and
$20. Adding price to the pars argument in the
main logitr() function would result in a single
price coefficient for the “slope” of the change in
price.
In contrast, categorical variables (i.e. character or
factor type variables) are by default estimated with a
coefficient for all but the first level, which serves as the reference
level. The default reference level is determined alphabetically, but it
can also be set by modifying the factor levels for that variable. For
example, the default reference level for the brand variable
is "dannon" as it is alphabetically first. To set
"weight" as the reference level, the factor levels can be
modified using the factor() function:
If you wish to make dummy-coded variables yourself to use them in a
model, I recommend using the dummy_cols() function from the
{fastDummies}
package. For example, in the code below, I create dummy-coded columns
for the brand variable and then use those variables as
covariates in a model:
yogurt2 <- fastDummies::dummy_cols(yogurt2, "brand")The yogurt2 data frame now has new dummy-coded columns
for brand:
head(yogurt2)
#> # A tibble: 6 × 11
#> id obsID alt choice price feat brand brand_weight brand_hiland
#> <dbl> <int> <int> <dbl> <dbl> <dbl> <fct> <int> <int>
#> 1 1 1 1 0 8.1 0 dannon 0 0
#> 2 1 1 2 0 6.10 0 hiland 0 1
#> 3 1 1 3 1 7.90 0 weight 1 0
#> 4 1 1 4 0 10.8 0 yoplait 0 0
#> 5 1 2 1 1 9.80 0 dannon 0 0
#> 6 1 2 2 0 6.40 0 hiland 0 1
#> # ℹ 2 more variables: brand_yoplait <int>, brand_dannon <int>Now I can use those columns as covariates:
mnl_pref_dummies <- logitr(
data = yogurt2,
outcome = 'choice',
obsID = 'obsID',
pars = c(
'price', 'feat', 'brand_yoplait', 'brand_dannon', 'brand_weight'
)
)
summary(mnl_pref_dummies)
#> =================================================
#>
#> Model estimated on: Fri Nov 01 19:41:38 2024
#>
#> Using logitr version: 1.1.2
#>
#> Call:
#> logitr(data = yogurt2, outcome = "choice", obsID = "obsID", pars = c("price",
#> "feat", "brand_yoplait", "brand_dannon", "brand_weight"))
#>
#> Frequencies of alternatives:
#> 1 2 3 4
#> 0.402156 0.029436 0.229270 0.339138
#>
#> Exit Status: 3, Optimization stopped because ftol_rel or ftol_abs was reached.
#>
#> Model Type: Multinomial Logit
#> Model Space: Preference
#> Model Run: 1 of 1
#> Iterations: 18
#> Elapsed Time: 0h:0m:0.02s
#> Algorithm: NLOPT_LD_LBFGS
#> Weights Used?: FALSE
#> Robust? FALSE
#>
#> Model Coefficients:
#> Estimate Std. Error z-value Pr(>|z|)
#> price -0.366581 0.024366 -15.045 < 2.2e-16 ***
#> feat 0.491412 0.120063 4.093 4.259e-05 ***
#> brand_yoplait 4.450197 0.187118 23.783 < 2.2e-16 ***
#> brand_dannon 3.715575 0.145419 25.551 < 2.2e-16 ***
#> brand_weight 3.074399 0.145384 21.147 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Log-Likelihood: -2656.8878788
#> Null Log-Likelihood: -3343.7419990
#> AIC: 5323.7757575
#> BIC: 5352.7168000
#> McFadden R2: 0.2054148
#> Adj McFadden R2: 0.2039195
#> Number of Observations: 2412.0000000