Get mode from a histogram

[Rodrigo Badilla]

Hi all

Edit: I find a solution, below i post it, but lamentably I can not get the scalar:

I am trying to get the mode from a histogram:

sysuse auto, clear

hist mpg,  freq addlabels
   

My goal its get the value=25.

I find the solution but I could not get the scalar:
graph save Graph "mpg.gph", replace

clear
graph use mpg
serset use
sum

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
    __000000 |         8        9.25    8.293715          1         25
    __000001 |         9           0           0          0          0
    __000002 |         9    24.88889    9.609859         12    39.1875

. ret li

scalars:
                  r(N) =  9
              r(sum_w) =  9
               r(mean) =  24.88888888888889
                r(Var) =  92.34939236111111
                 r(sd) =  9.609859122854566
                r(min) =  12
                r(max) =  39.1875
                r(sum) =  224

[Nick Cox]

That’s not the mode; that is the frequency of most frequent bin, itself sensitive to bin width and origin.

See hsmode from SSC for a systematic way to estimate the mode.

[William Lisowski]

If indeed what you want is the frequency of the most frequent bin, given that the bin widths are arbitrary (at least in your example), then the following might be a start.

. sysuse auto, clear
(1978 Automobile Data)

. hist mpg,  freq addlabels
(bin=8, start=12, width=3.625)

. serset use

. list, clean

       __000000   __000001   __000002  
  1.         10          0    13.8125  
  2.         25          0    17.4375  
  3.         13          0    21.0625  
  4.         15          0    24.6875  
  5.          6          0    28.3125  
  6.          1          0    31.9375  
  7.          3          0    35.5625  
  8.          1          0    39.1875  
  9.          .          0         12  

.

This suggests to me that the most frequent bin is the second one, with 25 observations, (__000000) and the bin is centered on 17.4375 (__000002) with a width of 3.6250 calculated as the difference between any pair of adjacent centers.

[Rodrigo Badilla]

Thanks Nick Cox and William Lisowski for you reply. I agree "mode" is wrong, the most frequent bin its the correct.

[Rodrigo Badilla]

Finally I could get the most frequent bin as local macro:

sysuse auto, clear

hist mpg, freq addlabels

serset  use
sum __000000
local maximo `r(max)'
di "`maximo'"
25

[Nick Cox]

The frequency of the modal bin is necessarily sensitive to bin width and even bin start. Why is of it of interest? Genuinely puzzled.

Regardless of that, twoway__histogram_gen is arguably a better way to get what you want, which has received its own proper puff

SJ-5-2 gr0014 . . . . . . . Stata tip 20: Generating histogram bin variables
. . . . . . . . . . . . . . . . . . . . . . . . . . . . D. A. Harrison
Q2/05 SJ 5(2):280--281 (no commands)
tip illustrating the use of twoway__histogram_gen for
creation of complex histograms and other graphs or tables

https://www.stata-journal.com/articl...article=gr0014

To pursue the problem of artefacts, I pushed harder at some defensible choices for mpg in the auto data, which ranges from 12 to 41.

25 is just one of several answers. To take it literally would be to put more weight on the defaults of histogram than I guess even its designers would want anyone to do.

FWIW I note that modes from the Stata Journal has different goals here, but

search sg113, entry

if you want to see what it does.

sysuse auto, clear 

gen result = .  
gen start = . 
gen width = . 

local i = 1 

tempvar h x 
quietly foreach s in 10 11 12 { 
    foreach w in 1 2 3 4 5 { 
        twoway__histogram_gen mpg, freq gen(`h' `x' `replace') w(`w') start(`s')
        replace width = `w' in `i' 
        replace start = `s' in `i'
        su `h', meanonly 
        replace result = r(max) in `i' 
        local replace , replace 
        local ++i 
    }
}

* tabplot is from the Stata Journal 
tabplot start width [fw=result], showval yreverse subtitle(which result would you like for modal frequency?)

[Rodrigo Badilla]

Thanks Nick Cox I am clear with your point... I will check twoway__histogram_gen.