usa_a <- structure(
 list(
  states = c("Alabama", "Alaska", "Arizona", "Arkansas", "California"),
  Murder = c(13.2, 10, 8.1, 8.8, 9),
  Assault = c(236L, 263L, 294L, 190L, 276L),
  UrbanPop = c(58L, 48L, 80L, 50L, 91L),
  Rape = c(21.2, 44.5, 31, 19.5, 40.6),
  log = c(TRUE, TRUE, TRUE, TRUE, TRUE),
  fracs = c(113.953488372093, 74.4186046511628,
            109.302325581395, 53.4883720930233,
            55.8139534883721),
  mix_bag = c("Mazda RX4", "Mazda RX4 Wag", "Datsun 710",
              "Hornet 4 Drive", "Hornet Sportabout")
             ),
  .Names = c("states", "Murder", "Assault", "UrbanPop",
             "Rape", "log", "fracs", "mix_bag"),
  row.names = c("Alabama", "Alaska", "Arizona", "Arkansas",
              "California"),
  class = "data.frame")

usa_a <- usa_a %>% mutate_all(as.character)
str(usa_a)
$ states  : chr "Alabama"
$ Murder  : chr "13.2"
$ Assault : chr "236"
$ UrbanPop: chr "58"
$ Rape    : chr "21.2"
$ log     : chr "TRUE"
$ fracs   : chr "113.953488372093"
$ mix_bag : chr "Mazda RX4"

rgx.pats <- list(
  numeric = "^(\d){1,}(\.(\d){1,})?",
  logical = "^(TRUE|FALSE)$",
  character = "(?!^[(\d){1,}(\.(\d){1,})?|(TRUE|FALSE)]+$)^.+$"
)

class_idx <- mapply(function(x){
    a <- lapply(names(rgx.pats), function(i){
        if(all(stringi::stri_detect_regex(x, rgx.pats[[i]]))){
            i
        }else{
            FALSE
        }
    })
}, usa_a) %>% {
    d <- as.data.frame(.)
    dd <- sapply(colnames(d), function(i){
        which(!mapply(is.logical,d[[i]]))
    })
    as.data.frame(mapply(function(j, y){
        d[j,y]
    }, dd, names(dd)))
}

class_idx
    states  Murder Assault UrbanPop    Rape     log   fracs   mix_bag
1 character numeric numeric  numeric numeric logical numeric character