[英]regarding the I( ) term in linear regression modeling in R using lm
I once saw a linear model fitting written as follows: 我曾经看到线性模型拟合写成如下:
lm(formula = Ozone ~ Solar.R + Wind + Temp + I(Wind^2) + I(Temp^2) +
I(Wind * Temp) + I(Wind * Temp^2) + I(Temp * Wind^2) + I(Temp^2 *
Wind^2), data = airquality)
I am not sure what does I( )
mean here? 我不确定
I( )
在这里是什么意思? Or for example, what does I(Wind * Temp^2)
here. 或者例如,
I(Wind * Temp^2)
在这里是什么I(Wind * Temp^2)
。 can I write it as Wind:Temp^2
? 我可以将其写为
Wind:Temp^2
吗?
The I()
notation in the formula syntax in R means 'as is' ie I(a+b)
simply means add the variable a+b as a predictor in the lm model. R中的公式语法中的
I()
表示“按原样”,即I(a+b)
仅表示在lm模型中添加变量a + b作为预测变量。 In your case I(Wind * Temp^2)
means include as a predictor variable the product of Wind and Temp squared. 在您的情况下,
I(Wind * Temp^2)
意味着将Wind和Temp平方的乘积包括在内作为预测变量。 The I()
function is used so that there is no confusion with the operators of the formula syntax. 使用
I()
函数是为了避免与公式语法的运算符混淆。
For more info page 2 here explains it in full detail. 有关更多信息,请在此处第2页进行详细说明。
Hope this is clear! 希望这很清楚!
UPDATE I just want to add Hong Ooi's very good comment on this: 更新我只想在此添加Hong Ooi的非常好的评论:
I(Wind * Temp^2)
is not the same as Wind:Temp^2 I(Wind * Temp^2)
与 Wind:Temp ^ 2不同
The ^n
operator in formula syntax means 'include these variables and all interactions up to n way' . 公式语法中的
^n
运算符表示“包括这些变量和所有交互,直至n方式” 。 For example Y ~ (X + Z + W)^2
is equivalent to Y ~ X + Z + W + X:Z + X:W + Z:W
例如
Y ~ (X + Z + W)^2
等效于Y ~ X + Z + W + X:Z + X:W + Z:W
So, in our case Wind:Temp^2
means just Wind:Temp
因此,在我们的示例中,
Wind:Temp^2
意味着Wind:Temp
Small illustration: 小插图:
Y <- runif(100)
X1 <- runif(100)
X2 <- runif(100)
df <- data.frame(Y,X1,X2)
> b <- lm( Y ~ X1:X2^2,data=df)
> summary(b)
Call:
lm(formula = Y ~ X1:X2^2, data = df)
Residuals:
Min 1Q Median 3Q Max
-0.4802 -0.2490 -0.0173 0.2345 0.5066
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.45126 0.04794 9.413 2.28e-15 ***
X1:X2 0.08991 0.13414 0.670 0.504
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2965 on 98 degrees of freedom
Multiple R-squared: 0.004563, Adjusted R-squared: -0.005594
F-statistic: 0.4493 on 1 and 98 DF, p-value: 0.5043
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