Fit a Linear Cross-Price Demand Model

Usage

fit_cp_linear(
  data,
  type = c("fixed", "mixed"),
  x_var = "x",
  y_var = "y",
  id_var = "id",
  group_var = "group",
  target_var = "target",
  filter_target = TRUE,
  target_level = "alt",
  formula = NULL,
  log10x = FALSE,
  group_effects = FALSE,
  random_slope = FALSE,
  return_all = TRUE,
  ...
)

fit_cp_linear.default(
  data,
  formula = NULL,
  log10x = FALSE,
  return_all = FALSE,
  ...
)

fit_cp_linear.mixed(
  data,
  formula = NULL,
  log10x = FALSE,
  return_all = FALSE,
  ...
)

Arguments

data: A data frame containing columns for price, consumption, and optionally target indicator, subject identifier, and group.
type: The type of model: "fixed" for standard linear or "mixed" for mixed effects.
x_var: Character string; name of the price column. Default is "x". Renamed to "x" internally.
y_var: Character string; name of the consumption column. Default is "y". Renamed to "y" internally.
id_var: Character string; name of the subject identifier column. Default is "id". Required for mixed models; renamed to "id" internally.
group_var: Character string; name of the group column. Default is "group". Renamed to "group" internally when present.
target_var: Character string; name of the target indicator column. Default is "target". Renamed to "target" internally when present.
filter_target: Logical; if TRUE (default), filters to rows where the target column equals target_level.
target_level: Character string; value of the target column to retain when filter_target = TRUE. Default is "alt".
formula: Optional formula override. If NULL, a formula will be constructed based on other parameters. If non-NULL and any *_var argument differs from its default, an error is thrown because the formula references canonical column names that no longer exist before renaming; rename columns before calling, or omit the formula argument.
log10x: Logical; if TRUE and formula is NULL, uses log10(x) instead of x in the formula. Default is FALSE.
group_effects: Logical or character; if TRUE, includes group as a factor with interactions. Can also be "intercept" for group intercepts only or "interaction" for full interactions. Default is FALSE.
random_slope: Logical; for mixed models, if TRUE, includes random slopes for x. Default is FALSE.
return_all: Logical; if TRUE, returns additional model metadata.
...: Additional arguments passed to underlying modeling functions.

Value

Fitted linear model.

Examples

# \donttest{
data(etm)
## Fixed-effects linear cross-price model
fit_fixed <- fit_cp_linear(etm, type = "fixed", group_effects = TRUE)
summary(fit_fixed)
#> Linear Cross-Price Demand Model Summary
#> =======================================
#> 
#> Formula: y ~ x * group 
#> Method: lm 
#> 
#> Coefficients:
#>                         Estimate Std. Error t value Pr(>|t|)  
#> (Intercept)             0.400000   1.590686  0.2515  0.80168  
#> x                       0.016667   0.052731  0.3161  0.75223  
#> groupCombustibles       4.594527   2.249569  2.0424  0.04224 *
#> groupE-Cigarettes       1.586070   2.249569  0.7051  0.48148  
#> groupNon-Combustibles   3.572637   2.249569  1.5881  0.11362  
#> x:groupCombustibles     0.073276   0.074572  0.9826  0.32682  
#> x:groupE-Cigarettes     0.010981   0.074572  0.1473  0.88306  
#> x:groupNon-Combustibles 0.075906   0.074572  1.0179  0.30979  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> R-squared: 0.09809   Adjusted R-squared: 0.07087 

## Mixed-effects linear cross-price model
fit_mixed <- fit_cp_linear(etm, type = "mixed", group_effects = TRUE)
summary(fit_mixed)
#> Mixed-Effects Linear Cross-Price Demand Model Summary
#> ====================================================
#> 
#> Formula: y ~ x * group + (1 | id) 
#> Method: lmer 
#> 
#> Fixed Effects:
#>                         Estimate Std. Error t value
#> (Intercept)             0.400000   2.045999  0.1955
#> x                       0.016667   0.044684  0.3730
#> groupCombustibles       4.594527   1.906295  2.4102
#> groupE-Cigarettes       1.586070   1.906295  0.8320
#> groupNon-Combustibles   3.572637   1.906295  1.8741
#> x:groupCombustibles     0.073276   0.063193  1.1596
#> x:groupE-Cigarettes     0.010981   0.063193  0.1738
#> x:groupNon-Combustibles 0.075906   0.063193  1.2012
#> 
#> Random Effects:
#>     Group        Term Variance  Std.Dev       NA
#>        id (Intercept)     <NA> 23.69132 4.867373
#>  Residual        <NA>     <NA> 56.18664 7.495775
#> 
#> Model Fit:
#> R2 (marginal): 0.09372   [Fixed effects only]
#> R2 (conditional): 0.3625   [Fixed + random effects]
#> AIC: 1692 
#> BIC: 1727 
#> 
#> Note: R2 values for mixed models are approximate.
# }