User Defined Function

Here is the mode function I use with an additional line to choose a single mode in the event there are actually multiple modes:

my_mode <- function(x) {
  ux <- unique(x)
  tab <- tabulate(match(x, ux))
  mode <- ux[tab == max(tab)]
  ifelse(length(mode) > 1, sample(mode, 1), mode)
}

# single mode
cat_col_1 <- c(1, 1, 2, NA)
cat_col_1
#> [1]  1  1  2 NA
cat_col_1[is.na(cat_col_1)] <- my_mode(cat_col_1)
cat_col_1
#> [1] 1 1 2 1

# random sample among multimodal
cat_col_2 <- c(1, 1, 2, 2, NA)
cat_col_2
#> [1]  1  1  2  2 NA
cat_col_2[is.na(cat_col_2)] <- my_mode(cat_col_2)
cat_col_2
#> [1] 1 1 2 2 2

DescTools::Mode()

But other folks have written mode functions. One possibility is in the DescTools package and is named Mode().

Because it returns multiple modes in the event there are more than one, you would need to decide what to do in that event.

Here is an example to randomly sample with replacement, the necessary number of modes to replace the missing values.

# single mode
cat_col_3 <- c(1, 1, 2, NA)
cat_col_3
#> [1]  1  1  2 NA
cat_col_3_modes <- DescTools::Mode(cat_col_3, na.rm = TRUE)
cat_col_3_nmiss <- sum(is.na(cat_col_3))
cat_col_3[is.na(cat_col_3)] <- sample(cat_col_3_modes, cat_col_3_nmiss, TRUE)
cat_col_3
#> [1] 1 1 2 1

# random sample among multimodal
cat_col_4 <- c(1, 1, 2, 2, NA, NA)
cat_col_4
#> [1]  1  1  2  2 NA NA
cat_col_4_modes <- DescTools::Mode(cat_col_4, na.rm = TRUE)
cat_col_4_nmiss <- sum(is.na(cat_col_4))
cat_col_4[is.na(cat_col_4)] <- sample(cat_col_4_modes, cat_col_4_nmiss, TRUE)
cat_col_4
#> [1] 1 1 2 2 2 1

^{Created on 2021-04-16 by the reprex package (v1.0.0)}

def fillna(col):
    col.fillna(col.value_counts().index[0], inplace=True)
    return col
df=df.apply(lambda col:fillna(col))