Geek Answers Handbook

Linear model with categorical variables in R

I am trying to set a linear model with some categorical variables

model <- lm(price ~ carat+cut+color+clarity)
summary(model)

Answer:

Call:
lm(formula = price ~ carat + cut + color + clarity)

Residuals:
     Min       1Q   Median       3Q      Max 
-11495.7   -688.5   -204.1    458.2   9305.3 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3696.818     47.948 -77.100  < 2e-16 ***
carat        8843.877     40.885 216.311  < 2e-16 ***
cut.L         755.474     68.378  11.049  < 2e-16 ***
cut.Q        -349.587     60.432  -5.785 7.74e-09 ***
cut.C         200.008     52.260   3.827 0.000131 ***
cut^4          12.748     42.642   0.299 0.764994    
color.L      1905.109     61.050  31.206  < 2e-16 ***
color.Q      -675.265     56.056 -12.046  < 2e-16 ***
color.C       197.903     51.932   3.811 0.000140 ***
color^4        71.054     46.940   1.514 0.130165    
color^5         2.867     44.586   0.064 0.948729    
color^6        50.531     40.771   1.239 0.215268    
clarity.L    4045.728    108.363  37.335  < 2e-16 ***
clarity.Q   -1545.178    102.668 -15.050  < 2e-16 ***
clarity.C     999.911     88.301  11.324  < 2e-16 ***
clarity^4    -665.130     66.212 -10.045  < 2e-16 ***
clarity^5     920.987     55.012  16.742  < 2e-16 ***
clarity^6    -712.168     52.346 -13.605  < 2e-16 ***
clarity^7    1008.604     45.842  22.002  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1167 on 4639 degrees of freedom
Multiple R-squared:  0.9162,    Adjusted R-squared:  0.9159 
F-statistic:  2817 on 18 and 4639 DF,  p-value: < 2.2e-16

But I don’t understand why the answers with ".L, .Q, ​​.C, ^ 4, ..." are something wrong, but I don’t know what is wrong, I already tried with the functional coefficient for each variable.

+4
source share
3 answers

, - , n-1, n - . ... . , , ( ), , , .

ggplot2 , , , , "" "" < "" < "". ()

> levels(diamonds$cut)
[1] "Fair"      "Good"      "Very Good" "Premium"   "Ideal"    
> levels(diamonds$clarity)
[1] "I1"   "SI2"  "SI1"  "VS2"  "VS1"  "VVS2" "VVS1" "IF"  
> levels(diamonds$color)
[1] "D" "E" "F" "G" "H" "I" "J"

, , , - as.numeric, .

> contrasts(diamonds$cut) <- contr.treatment(5) # Removes ordering
> model <- lm(price ~ carat+cut+as.numeric(color)+as.numeric(clarity), diamonds)
> summary(model)

Call:
lm(formula = price ~ carat + cut + as.numeric(color) + as.numeric(clarity), 
    data = diamonds)

Residuals:
     Min       1Q   Median       3Q      Max 
-19130.3   -696.1   -176.8    556.9   9599.8 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)         -5189.460     36.577 -141.88   <2e-16 ***
carat                8791.452     12.659  694.46   <2e-16 ***
cut2                  909.433     35.346   25.73   <2e-16 ***
cut3                 1129.518     32.772   34.47   <2e-16 ***
cut4                 1156.989     32.427   35.68   <2e-16 ***
cut5                 1264.128     32.160   39.31   <2e-16 ***
as.numeric(color)    -318.518      3.282  -97.05   <2e-16 ***
as.numeric(clarity)   522.198      3.521  148.31   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1227 on 53932 degrees of freedom
Multiple R-squared:  0.9054,    Adjusted R-squared:  0.9054 
F-statistic: 7.371e+04 on 7 and 53932 DF,  p-value: < 2.2e-16
+7

@Roland , , , ( ), , R. SO @SvenHohenstein: R , as.numeric, , , , - "" (, " " ) LHS- . , , 1000 cut2-5 cut1. "value" cut == 1 "(Intercept)". :

> cbind( levels(diamonds$cut), c(coef(model.cut)[grep('Intercept|cut', names(coef(model.cut)))] ))
            [,1]        [,2]               
(Intercept) "Fair"      "-5189.46034442502"
cut2        "Good"      "909.432743872746" 
cut3        "Very Good" "1129.51839934007" 
cut4        "Premium"   "1156.98898349819" 
cut5        "Ideal"     "1264.12800574865"

, ( ):

> with(diamonds, tapply(price, cut, mean))
     Fair      Good Very Good   Premium     Ideal 
 4358.758  3928.864  3981.760  4584.258  3457.542

, carat:

> with(diamonds, tapply(price, list(cut, cut2(carat, g=5) ), mean))
          [0.20,0.36) [0.36,0.54) [0.54,0.91) [0.91,1.14) [1.14,5.01]
Fair         802.4528    1193.162    2336.543    4001.972    8682.351
Good         574.7482    1101.406    2701.412    4872.072    9788.294
Very Good    597.9258    1151.537    2727.251    5464.223   10158.057
Premium      717.1096    1149.550    2537.446    5214.787   10131.999
Ideal        739.8972    1254.229    2624.180    6050.358   10317.725

, ... ? , 800 "" ?

contrasts(diamonds$cut, how.many=1) <- poly(1:5)
> model.cut2 <- lm(price ~ carat+cut, diamonds)
> model.cut2

Call:
lm(formula = price ~ carat + cut, data = diamonds)

Coefficients:
(Intercept)        carat         cut1  
    -2555.1       7838.5        815.8  

> contrasts(diamonds$cut)
                   1
Fair      -0.6324555
Good      -0.3162278
Very Good  0.0000000
Premium    0.3162278
Ideal      0.6324555

carat constant Fair versus Ideal (-0.6324555 -0.6324555) * 815.8 1031,91 ( ... )

, , , , , "". . poly -, "" . , , R poly(). 1, 0.

+3

A reasonable a priori approach that retains power here would be to evaluate linear, apartment and cubic contrasts. This allows for most plausible models and avoids testing these higher-order polynomials, which are allowed by a large number of levels, but which William Ockham would have felt bad if he had theoretically relied :-)

library(ggplot2)
df = diamonds[1:1000, ] # a chunk of data
contrasts(df$cut    , how.many=3) = contr.poly(nlevels(df$cut))
contrasts(df$color  , how.many=3) = contr.poly(nlevels(df$color))
contrasts(df$clarity, how.many=3) = contr.poly(nlevels(df$clarity))
model <- lm(price ~ carat+cut+color+clarity, data = df)
summary(model)


Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -692.74      30.99 -22.353  < 2e-16 ***
carat        4444.79      41.37 107.431  < 2e-16 ***
cut.L         286.35      22.31  12.835  < 2e-16 ***
cut.Q         -88.61      20.26  -4.374 1.35e-05 ***
cut.C         120.91      18.51   6.532 1.03e-10 ***
color.L      -660.17      24.93 -26.476  < 2e-16 ***
color.Q      -119.34      23.90  -4.993 7.03e-07 ***
color.C        37.18      20.90   1.779   0.0756 .  
clarity.L    1356.12      43.22  31.375  < 2e-16 ***
clarity.Q    -220.86      33.48  -6.596 6.87e-11 ***
clarity.C     375.47      31.10  12.073  < 2e-16 ***

Multiple R-squared:  0.929, Adjusted R-squared:  0.9283 
F-statistic:  1293 on 10 and 989 DF,  p-value: < 2.2e-16
0
source

More articles:


All Articles