Generate dummy variables from all possible combinations of variables

Question

I’ve 5 conditions that can be present (=1) or not (=0):

set.seed(101)
df <- data.frame(
alfa = sample(c(0, 1), 30, replace = TRUE),
beta = sample(c(0, 1), 30, replace = TRUE),
gamma = sample(c(0, 1), 30, replace = TRUE),
delta = sample(c(0, 1), 30, replace = TRUE),
epsilon = sample(c(0, 1), 30, replace = TRUE)
)

I want to generate a set of dummy variables from all the possible combinations (2⁵) of the presence of these conditions. Specifically, I would like to verify the concomitant presence of the following conditions:

1) alfa + beta;
2) alfa + gamma;
3) alfa + delta;
4) alfa + epsilon;
5) alfa + beta + gamma;
[...]
27) alfa + beta + gamma + delta + epsilon;

Generate matrix of all possible combinations

v <- as.matrix(expand.grid(rep(list(c(FALSE, TRUE)), ncol(df))))

All the combinations:

 head(v)
      Var1  Var2  Var3  Var4  Var5
[1,]  TRUE FALSE FALSE FALSE FALSE
[2,] FALSE  TRUE FALSE FALSE FALSE
[3,]  TRUE  TRUE FALSE FALSE FALSE
[4,] FALSE FALSE  TRUE FALSE FALSE
[5,]  TRUE FALSE  TRUE FALSE FALSE
[6,] FALSE  TRUE  TRUE FALSE FALSE

Convert the matrix into a list of column indexes

indexes <- lapply(seq_len(nrow(v)), function(x) v[x, ])
names(indexes) <- apply(v, 1, function(x) paste(names(df)[x], collapse="."))

Unfortunately I got stuck here.
I need to generate 27 dummy variables (32-5) according to the above mentioned combinations.

EDT: I solved the problem with this dirty way:

# my df
set.seed(101)
df <- data.frame(
alfa = sample(c(0, 1), 30, replace = TRUE),
beta = sample(c(0, 1), 30, replace = TRUE),
gamma = sample(c(0, 1), 30, replace = TRUE),
delta = sample(c(0, 1), 30, replace = TRUE),
epsilon = sample(c(0, 1), 30, replace = TRUE)
)

# count the numebr of coesistent conditions:
df$n <- rowSums(df[1:5], na.rm = TRUE)

# Dirty way to compute multiple combinations:
df$alfa.beta <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 0 & df$delta == 0 & df$epsilon == 0 , 1, 0)
df$alfa.gamma <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 1 & df$delta == 0 & df$epsilon == 0 , 1, 0)
df$beta.gamma <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 1 & df$delta == 0 & df$epsilon == 0 , 1, 0)
df$alfa.beta.gamma <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 1 & df$delta == 0 & df$epsilon == 0 , 1, 0)
df$alfa.delta <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 0 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$beta.delta <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 0 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$alfa.beta.delta <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 0 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$gamma.delta <- ifelse (df$alfa == 0 & df$beta == 0 & df$gamma == 1 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$alfa.gamma.delta <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 1 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$beta.gamma.delta <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 1 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$alfa.beta.gamma.delta <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 1 & df$delta == 1 & df$epsilon == 0 , 1, 0)
df$alfa.epsilon <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 0 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$beta.epsilon <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 0 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$alfa.beta.epsilon <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 0 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$gamma.epsilon <- ifelse (df$alfa == 0 & df$beta == 0 & df$gamma == 1 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$alfa.gamma.epsilon <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 1 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$beta.gamma.epsilon <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 1 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$alfa.beta.gamma.epsilon <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 1 & df$delta == 0 & df$epsilon == 1 , 1, 0)
df$delta.epsilon <- ifelse (df$alfa == 0 & df$beta == 0 & df$gamma == 0 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$alfa.delta.epsilon <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 0 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$beta.delta.epsilon <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 0 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$alfa.beta.delta.epsilon <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 0 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$gamma.delta.epsilon <- ifelse (df$alfa == 0 & df$beta == 0 & df$gamma == 1 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$alfa.gamma.delta.epsilon <- ifelse (df$alfa == 1 & df$beta == 0 & df$gamma == 1 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$beta.gamma.delta.epsilon <- ifelse (df$alfa == 0 & df$beta == 1 & df$gamma == 1 & df$delta == 1 & df$epsilon == 1 , 1, 0)
df$alfa.beta.gamma.delta.epsilon <- ifelse (df$alfa == 1 & df$beta == 1 & df$gamma == 1 & df$delta == 1 & df$epsilon == 1 , 1, 0)

? I am not sure what your question is. I thought that the `expand.grid()` step already is the answer to your problem. So, if not. What is your problem/question? — petermeissner, Jun 15 '19 at 20:39
@petermeissner I need to generate additional 27 dummy variables according to the above mentioned combinations. I updated the question accordingly. — Borexino, Jun 15 '19 at 20:47

Joris C. · Answer 1 · 2019-06-16T12:17:56.830

Perhaps you can achieve what you are after by using stats::model.matrix and the ^ operator in the model formula to return all (higher-order) variable interactions:

library(stats)

df <- data.frame(
    alfa = sample(c(TRUE, FALSE), 30, replace = TRUE),
    beta = sample(c(TRUE, FALSE), 30, replace = TRUE),
    gamma = sample(c(TRUE, FALSE), 30, replace = TRUE),
    delta = sample(c(TRUE, FALSE), 30, replace = TRUE),
    epsilon = sample(c(TRUE, FALSE), 30, replace = TRUE)
)

df_dummy <- model.matrix(~ .^5, data = df)

colnames(df_dummy)
#>  [1] "(Intercept)"                                      
#>  [2] "alfaTRUE"                                         
#>  [3] "betaTRUE"                                         
#>  [4] "gammaTRUE"                                        
#>  [5] "deltaTRUE"                                        
#>  [6] "epsilonTRUE"                                      
#>  [7] "alfaTRUE:betaTRUE"                                
#>  [8] "alfaTRUE:gammaTRUE"                               
#>  [9] "alfaTRUE:deltaTRUE"                               
#> [10] "alfaTRUE:epsilonTRUE"                             
#> [11] "betaTRUE:gammaTRUE"                               
#> [12] "betaTRUE:deltaTRUE"                               
#> [13] "betaTRUE:epsilonTRUE"                             
#> [14] "gammaTRUE:deltaTRUE"                              
#> [15] "gammaTRUE:epsilonTRUE"                            
#> [16] "deltaTRUE:epsilonTRUE"                            
#> [17] "alfaTRUE:betaTRUE:gammaTRUE"                      
#> [18] "alfaTRUE:betaTRUE:deltaTRUE"                      
#> [19] "alfaTRUE:betaTRUE:epsilonTRUE"                    
#> [20] "alfaTRUE:gammaTRUE:deltaTRUE"                     
#> [21] "alfaTRUE:gammaTRUE:epsilonTRUE"                   
#> [22] "alfaTRUE:deltaTRUE:epsilonTRUE"                   
#> [23] "betaTRUE:gammaTRUE:deltaTRUE"                     
#> [24] "betaTRUE:gammaTRUE:epsilonTRUE"                   
#> [25] "betaTRUE:deltaTRUE:epsilonTRUE"                   
#> [26] "gammaTRUE:deltaTRUE:epsilonTRUE"                  
#> [27] "alfaTRUE:betaTRUE:gammaTRUE:deltaTRUE"            
#> [28] "alfaTRUE:betaTRUE:gammaTRUE:epsilonTRUE"          
#> [29] "alfaTRUE:betaTRUE:deltaTRUE:epsilonTRUE"          
#> [30] "alfaTRUE:gammaTRUE:deltaTRUE:epsilonTRUE"         
#> [31] "betaTRUE:gammaTRUE:deltaTRUE:epsilonTRUE"         
#> [32] "alfaTRUE:betaTRUE:gammaTRUE:deltaTRUE:epsilonTRUE"

^{Created on 2019-06-16 by the reprex package (v0.3.0)}

The expanded data.frame df_dummy returns one-hot encoded columns for all 31 possible interaction combinations (in addition to an intercept). To lose the intercept replace the model formula by ~ .^5 + 0 or ~.^5 - 1. Note that this easily extends to more variables by replacing the 5 by the number of columns in df.

Edit: the above code will not give you the exclusive presence of a variable combination (similar to the manual encoding in your edited question). To achieve this you could try instead:

df_dummy <- model.matrix(~ .^5 - .^4 - 1, data = df)

colnames(df_dummy)
#>  [1] "alfaFALSE:betaFALSE:gammaFALSE:deltaFALSE:epsilonFALSE"
#>  [2] "alfaTRUE:betaFALSE:gammaFALSE:deltaFALSE:epsilonFALSE" 
#>  [3] "alfaFALSE:betaTRUE:gammaFALSE:deltaFALSE:epsilonFALSE" 
#>  [4] "alfaTRUE:betaTRUE:gammaFALSE:deltaFALSE:epsilonFALSE"  
#>  [5] "alfaFALSE:betaFALSE:gammaTRUE:deltaFALSE:epsilonFALSE" 
#>  [6] "alfaTRUE:betaFALSE:gammaTRUE:deltaFALSE:epsilonFALSE"  
#>  [7] "alfaFALSE:betaTRUE:gammaTRUE:deltaFALSE:epsilonFALSE"  
#>  [8] "alfaTRUE:betaTRUE:gammaTRUE:deltaFALSE:epsilonFALSE"   
#>  [9] "alfaFALSE:betaFALSE:gammaFALSE:deltaTRUE:epsilonFALSE" 
#> [10] "alfaTRUE:betaFALSE:gammaFALSE:deltaTRUE:epsilonFALSE"  
#> [11] "alfaFALSE:betaTRUE:gammaFALSE:deltaTRUE:epsilonFALSE"  
#> [12] "alfaTRUE:betaTRUE:gammaFALSE:deltaTRUE:epsilonFALSE"   
#> [13] "alfaFALSE:betaFALSE:gammaTRUE:deltaTRUE:epsilonFALSE"  
#> [14] "alfaTRUE:betaFALSE:gammaTRUE:deltaTRUE:epsilonFALSE"   
#> [15] "alfaFALSE:betaTRUE:gammaTRUE:deltaTRUE:epsilonFALSE"   
#> [16] "alfaTRUE:betaTRUE:gammaTRUE:deltaTRUE:epsilonFALSE"    
#> [17] "alfaFALSE:betaFALSE:gammaFALSE:deltaFALSE:epsilonTRUE" 
#> [18] "alfaTRUE:betaFALSE:gammaFALSE:deltaFALSE:epsilonTRUE"  
#> [19] "alfaFALSE:betaTRUE:gammaFALSE:deltaFALSE:epsilonTRUE"  
#> [20] "alfaTRUE:betaTRUE:gammaFALSE:deltaFALSE:epsilonTRUE"   
#> [21] "alfaFALSE:betaFALSE:gammaTRUE:deltaFALSE:epsilonTRUE"  
#> [22] "alfaTRUE:betaFALSE:gammaTRUE:deltaFALSE:epsilonTRUE"   
#> [23] "alfaFALSE:betaTRUE:gammaTRUE:deltaFALSE:epsilonTRUE"   
#> [24] "alfaTRUE:betaTRUE:gammaTRUE:deltaFALSE:epsilonTRUE"    
#> [25] "alfaFALSE:betaFALSE:gammaFALSE:deltaTRUE:epsilonTRUE"  
#> [26] "alfaTRUE:betaFALSE:gammaFALSE:deltaTRUE:epsilonTRUE"   
#> [27] "alfaFALSE:betaTRUE:gammaFALSE:deltaTRUE:epsilonTRUE"   
#> [28] "alfaTRUE:betaTRUE:gammaFALSE:deltaTRUE:epsilonTRUE"    
#> [29] "alfaFALSE:betaFALSE:gammaTRUE:deltaTRUE:epsilonTRUE"   
#> [30] "alfaTRUE:betaFALSE:gammaTRUE:deltaTRUE:epsilonTRUE"    
#> [31] "alfaFALSE:betaTRUE:gammaTRUE:deltaTRUE:epsilonTRUE"    
#> [32] "alfaTRUE:betaTRUE:gammaTRUE:deltaTRUE:epsilonTRUE"