The {gvlma} package

{gvlma}

• The {gvlma} package is a comprehensive, automatic testing suite for many of the assumptions of general linear models.
• It does both statistical tests and diagnostic plots using an extremely simple implementation for powerful results.

The package is an implementation of a paper by Pena & Slate called Global Validation of Linear Model Assumptions and allows you to quickly check for:

• Linearity - the Global Stat tests for the null hypothesis that our model is a linear combination of its predictors.

• Homoscedasticity - the respective stat tests for the null that the residial variance is relatively constant over the range of values.

• Normality - skewness and kurtosis tests help you understand if the residuals fits a normal distribution.

• If the null is rejected you probably need to transform your data in some way (like a log transform). This can also be assessed by looking at the normal probability plot it generates.

gvlma( )

The gvlma( ) function in the {gvlma} package, performs a global validation of linear model assumptions as well separate evaluations of skewness, kurtosis, and heteroscedasticity.

# Global test of model assumptions

gvmodel <- gvlma(fit) 
summary(gvmodel)

Example

This examples uses the cheddar data set, available in the {faraway} R package.

library("gvlma")

# model <- lm(y ~ x, data)
  
summary(gvlma(model))

## 
## Call:
## lm(formula = taste ~ Acetic + H2S + Lactic, data = cheddar)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.390  -6.612  -1.009   4.908  25.449 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -28.8768    19.7354  -1.463  0.15540   
## Acetic        0.3277     4.4598   0.073  0.94198   
## H2S           3.9118     1.2484   3.133  0.00425 **
## Lactic       19.6705     8.6291   2.280  0.03108 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.13 on 26 degrees of freedom
## Multiple R-squared:  0.6518, Adjusted R-squared:  0.6116 
## F-statistic: 16.22 on 3 and 26 DF,  p-value: 3.81e-06
## 
## 
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance =  0.05 
## 
## Call:
##  gvlma(x = model) 
## 
##                      Value p-value                Decision
## Global Stat        1.33099  0.8561 Assumptions acceptable.
## Skewness           1.12180  0.2895 Assumptions acceptable.
## Kurtosis           0.02119  0.8843 Assumptions acceptable.
## Link Function      0.02906  0.8646 Assumptions acceptable.
## Heteroscedasticity 0.15894  0.6901 Assumptions acceptable.

Diagnostic Plots for {gvlma}

• The diagnostic plots also let you understand the relation between your data and these assumptions visually.
• Other useful capabilities are the link function test which is used for understanding whether the underlying data is categorical or continuous.

  plot(gvlma(model),which=1)