零截距模型的 lm() 中的 R 平方 [英] R-squared in lm() for zero-intercept model

问题描述

我在 R 中运行了一个 lm()，这是总结的结果:

多个 R 平方:0.8918，调整后的 R 平方:0.8917F 统计量:9416 和 10283 DF，p 值:<2.2e-16

而且它似乎是一个很好的模型，但是如果我手动计算 R^2，我会得到这个:

model=lm(S~0+C+HA+L1+L2,data=train)预测=预测(模型，火车)rss <- sum((model$fitted.values-train$S)^2)tss <- sum((train$S - mean(train$S)) ^ 2)1 - RSS/TSS##[1] 0.247238rSquared(train$S,(train$S-model$fitted.values))## [,1]## [1,] 0.247238

怎么了?

str(train[,c('S','Campionato','HA','L1','L2')])tbl_df"、tbl"和data.frame"类:10292 obs.共 5 个变量:$ S : 编号 19 18 9 12 12 8 21 24 9 8 ...$ C : 因子 w/6 个级别 "D","E","F","I",..: 4 4 4 4 4 4 4 4 4 4 ...$ HA : 因子 w/2 个级别 "A","H": 1 2 1 1 2 1 2 2 1 2 ...$ L1 : 数量 0.99 1.41 1.46 1.43 1.12 1.08 1.4 1.45 0.85 1.44 ...$ L2 : num 1.31 0.63 1.16 1.15 1.29 1.31 0.7 0.65 1.35 0.59 ...

解决方案

您正在运行一个没有截距(公式右侧的 ~0)的模型.对于这些类型的模型，R^2 的计算是有问题的，会产生误导性的值.这篇文章解释得很好:https://stats.stackexchange.com/a/26205/99681>

I run an lm() in R and this is the results of the summary:

Multiple R-squared:  0.8918,    Adjusted R-squared:  0.8917 
F-statistic:  9416 on 9 and 10283 DF,  p-value: < 2.2e-16

and it seems that it is a good model, but if I calculate the R^2 manually I obtain this:

model=lm(S~0+C+HA+L1+L2,data=train)
pred=predict(model,train)
rss <- sum((model$fitted.values - train$S) ^ 2)
tss <- sum((train$S - mean(train$S)) ^ 2)
1 - rss/tss
##[1] 0.247238
rSquared(train$S,(train$S-model$fitted.values))
##          [,1]
## [1,] 0.247238

What's wrong?

str(train[,c('S','Campionato','HA','L1','L2')])
Classes ‘tbl_df’, ‘tbl’ and 'data.frame':   10292 obs. of  5 variables:
 $ S         : num  19 18 9 12 12 8 21 24 9 8 ...
 $ C         : Factor w/ 6 levels "D","E","F","I",..: 4 4 4 4 4 4 4 4 4 4 ...
 $ HA        : Factor w/ 2 levels "A","H": 1 2 1 1 2 1 2 2 1 2 ...
 $ L1        : num  0.99 1.41 1.46 1.43 1.12 1.08 1.4 1.45 0.85 1.44 ...
 $ L2        : num  1.31 0.63 1.16 1.15 1.29 1.31 0.7 0.65 1.35 0.59 ...

解决方案

You are running a model without the intercept (the ~0 on the right hand side of your formula). For these kinds of models the calculation of R^2 is problematic and will produce misleading values. This post explains it very well: https://stats.stackexchange.com/a/26205/99681

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