00gvlma.package: Global Validation of Linear Model Assumptions
In gvlma: Global Validation of Linear Models Assumptions

Description Details Author(s) References See Also Examples

Perform a single global test to assess the linear model assumptions, as well as perform specific directional tests designed to detect skewness, kurtosis, a nonlinear link function, and heteroscedasticity.

Package:	gvlma
Type:	Package
Version:	1.0
Date:	2006-06-07
License:	GPL

The function gvlma will take either a linear models object or a formula and data set for a linear model (single response) and compute the global and directional tests for assessing modeling assumptions as described in the reference listed below. The function deletion.gvlma will compute the deletion (“leave-one-out”) global statistics described in that paper.

Slate, EH slate@stat.fsu.edu and Pena, EA pena@stat.sc.edu

Maintainer: Slate, EH <slate@stat.fsu.edu>

Pena, EA and Slate, EH (2006). “Global validation of linear model assumptions,” J.\ Amer.\ Statist.\ Assoc., 101(473):341-354.

gvlma

x1 <- rnorm(100,0,2)
x2 <- runif(100)
y <- 3*x1 -x2 + rnorm(100)
gvmodel <- gvlma(lm(y ~ x1 + x2))
plot(gvmodel)
summary(gvmodel)
gvmodel.del <- deletion.gvlma(gvmodel)
summary(gvmodel.del)
plot(gvmodel.del)

Call:
lm(formula = y ~ x1 + x2)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2430 -0.5947 -0.0501  0.6627  2.3840 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.40184    0.20326  -1.977   0.0509 .  
x1           3.02981    0.04923  61.542   <2e-16 ***
x2          -0.61964    0.33910  -1.827   0.0707 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.046 on 97 degrees of freedom
Multiple R-squared:  0.9751,	Adjusted R-squared:  0.9746 
F-statistic:  1901 on 2 and 97 DF,  p-value: < 2.2e-16


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

Call:
 gvlma(x = lm(y ~ x1 + x2)) 

                    Value p-value                Decision
Global Stat        4.4505 0.34846 Assumptions acceptable.
Skewness           0.6999 0.40281 Assumptions acceptable.
Kurtosis           0.1643 0.68525 Assumptions acceptable.
Link Function      0.6240 0.42955 Assumptions acceptable.
Heteroscedasticity 2.9622 0.08523 Assumptions acceptable.

Global test deletion statistics.

Linear Model:
 lm(formula = y ~ x1 + x2) 

gvlma call:
 gvlma(x = lm(y ~ x1 + x2)) 


Summary values:
                        Min.      1st Qu.       Median        Mean     3rd Qu.
DeltaGlobalStat -55.13812735  -4.29743479 -0.415264818  0.01579949  4.53133259
GStatpvalue       0.22375003   0.32488757  0.350690777  0.35126889  0.37206440
DeltaStat1      -99.40074375 -12.57023710 -0.239045913  0.76004135 12.43848715
Stat1pvalue       0.23491978   0.37501740  0.403373338  0.40710100  0.43405872
DeltaStat2      -31.39714967 -24.85880705 -6.287119001  7.43880489 27.83753757
Stat2pvalue       0.52968148   0.64678748  0.694789167  0.68001037  0.72533099
DeltaStat3      -96.99610755  -8.43063865  0.005084153  1.05027751  9.26559133
Stat3pvalue       0.28034338   0.40894839  0.429537933  0.43294435  0.44969227
DeltaStat4      -58.48521676  -6.10437473  0.296048299 -0.78964742  4.49077528
Stat4pvalue       0.05083204   0.07852139  0.084769545  0.08869596  0.09536893
                       Max.
DeltaGlobalStat  27.7908716
GStatpvalue       0.7363908
DeltaStat1      101.5690121
Stat1pvalue       0.9483623
DeltaStat2      140.4446952
Stat2pvalue       0.7370900
DeltaStat3       86.7545144
Stat3pvalue       0.8910986
DeltaStat4       28.7476032
Stat4pvalue       0.2674531


Unusual observations for Global Stat:
   Delta Global Stat (%)  Global Stat p-value
18             -55.13813            0.7363908
21             -26.86029            0.5160837


Unusual observations for Directional Stat1:
   Delta Directional Stat1 (%)  Directional Stat1 p-value
15                   101.56901                  0.2349198
18                   -99.40074                  0.9483623


Unusual observations for Directional Stat2:
[1] Delta Directional Stat2 (%)  Directional Stat2 p-value 
<0 rows> (or 0-length row.names)


Unusual observations for Directional Stat3:
   Delta Directional Stat3 (%)  Directional Stat3 p-value
21                   -96.99611                  0.8910986
24                    82.23167                  0.2862447
27                    86.75451                  0.2803434


Unusual observations for Directional Stat4:
   Delta Directional Stat4 (%)  Directional Stat4 p-value
15                   -36.25814                  0.1694073
18                   -58.48522                  0.2674531