線性模型假設的綜合驗證

• gvlma()

gvlma包中的gvlma()函數，對線性模型假設進行綜合驗證（經過/不經過），同時還能作偏斜度、峯度、異方差性的評價

> library(gvlma)
> gvmodel <- gvlma(fit)
> summary(gvmodel)

Call:
lm(formula = Murder ~ Population + Illiteracy + Income + Frost, 
    data = states)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.7960 -1.6495 -0.0811  1.4815  7.6210 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1.235e+00  3.866e+00   0.319   0.7510    
Population  2.237e-04  9.052e-05   2.471   0.0173 *  
Illiteracy  4.143e+00  8.744e-01   4.738 2.19e-05 ***
Income      6.442e-05  6.837e-04   0.094   0.9253    
Frost       5.813e-04  1.005e-02   0.058   0.9541    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.535 on 45 degrees of freedom
Multiple R-squared:  0.567,	Adjusted R-squared:  0.5285 
F-statistic: 14.73 on 4 and 45 DF,  p-value: 9.133e-08


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value p-value                Decision
Global Stat        2.7728  0.5965 Assumptions acceptable.  #Global Stat
Skewness           1.5374  0.2150 Assumptions acceptable.
Kurtosis           0.6376  0.4246 Assumptions acceptable.
Link Function      0.1154  0.7341 Assumptions acceptable.
Heteroscedasticity 0.4824  0.4873 Assumptions acceptable.

從輸出項Global Stat 中的文字欄能夠看出數據知足OLS迴歸模型全部的統計假設（p =0.597）。若Decision下的文字代表違反了假設條件（好比 p < 0.05），你能夠使用迴歸診斷改進的方法來判斷哪些假設沒有被知足