Why I get more coefficients than I had features using multinom() in R?

Question

I have a data set containing about 20 samples and 4 features. enter image description here I wanted to create a model using multinom(). But this function returns about 50 coefficients with strange names.

>model <- multinom(types ~ LD1+LD2+LD3+LD4, t)    
> colnames(coef(model))    
    [1] "(Intercept)"           "LD1-0.924675250911259" "LD1-0.996017404791012" "LD1-11.0091236817909"  "LD1-11.0470069995094"  "LD1-11.1382649674021"  "LD1-11.1449776356607" 
         [8] "LD1-1.11507632119743"  "LD1-11.4100167287132"  "LD1-1.15405541868851"  "LD1-1.42692764536373"  "LD11.45075731787807"   "LD1-1.562329638922"    "LD1-2.03752025992806" 
        [15] "LD132.7387270807495"   "LD133.0932516010117"   "LD135.0760659080006"   "LD1-3.57028123573125"  "LD1-5.22424301205266"  "LD1-5.95754635904308"  "LD1-6.39430959506567" 
        [22] "LD1-6.8622462443044"   "LD1-7.03073614006179"  "LD1-8.00430359650879"  "LD1-8.17057054273565"  "LD1-9.02013723266161"  "LD20.0761110897194115" "LD20.83307548406597"  
        [29] "LD210.9301821277818"   "LD21.2118957034112"    "LD2-1.7139684831726"   "LD2-1.85478166588227"  "LD2-2.11785431701449"  "LD2-2.19678883756181"  "LD2-2.43688626054258" 
        [36] "LD22.71656669882489"   "LD23.17377132687911"   "LD23.25781591451936"   "LD2-3.4433493942635"   "LD2-3.5203090034966"   "LD2-3.71418994994738"  "LD2-3.8380001046407"  
        [43] "LD2-3.87686665511689"  "LD2-3.9100454768453"   "LD2-3.95942532853135"  "LD2-4.04744180009915"  "LD2-4.12030177266551"  "LD24.17412372599923"   "LD24.75169238888003"  
        [50] "LD2-4.91414969791761"  "LD29.19759557325694" 

Why is it so and what does it mean?

Answer 1

A multinomial model is an extension of a logistic regression that predicts the probability of each level of your response. So if you have 11 levels, you'll get 10 prediction equations, each with 1 coefficient per predictor. (One level of the response is the baseline.)

In this case, though, you might have another problem. R is treating your LD1 and LD2 predictors as factors even though they appear to be numeric. So you should check that you've imported your data correctly.