nsRFA (version 0.3-0)

REGRDIAGNOSTICS: Diagnostics of regressions

Description

Diagnostics of the output of lm, that is used to fit linear models.

Usage

R2.lm (x)
 prt.lm (x)
 mantel.lm (x, Nperm = 1000)
 vif.lm (x)
 RMSE.lm (x) 
 MAE.lm (x)
 predinterval.lm (x, level = 0.95)
 jackknife1.lm (x)
 RMSEjk.lm (x)
 MAEjk.lm (x)

Arguments

x

object of class ``lm'' (output of `lm')

Nperm

number of permutations

level

significance level

Value

• R2.lm returns the coefficient of determination $R^2$ and the adjusted coefficient of determination $R^2_{adj}$ of the regression.

  prt.lm returns the probability $Pr(>|t|)$ of the significance test (Student t) of the independent variables. If the value is 0.06 for a regressor, its coefficient is not significantly different from 0 for a test with significance level of 5 mantel.lm returns the probability $P$ of the Mantel test on every variable conditionated to the others. It substitutes prt.lm when dealing with distance matrices. If $P$ is, for example, 0.92, the variable should be considered significant with significance level greater of 8 vif.lm returns the variance inflation factors (VIF) of the independent values of the regression. If $VIF > 5$ (or 10) there is a problem of multicollinearity.

  RMSE.lm returns the root mean squared error of the regression.

  MAE.lm returns the mean absolute error of the regression.

  predinterval.lm returns the prediction intervals at a specified level in correspondence to the fitted data.

  jackknife1.lm returns predicted values by a jackknife (cross-validation) procedure. The procedure (remove 1 observation, fit the model, estimate in the removed point) is repeated for all the points.

  RMSEjk.lm returns the root mean squared error of the cross-validation (performed with jackknife1.lm).

  MAEjk.lm returns the mean absolute error of the cross-validation (performed with jackknife1.lm).

References

Viglione A., Claps P., Laio F. (2006) Utilizzo di criteri di prossimit`a nell'analisi regionale del deflusso annuo, XXX Convegno di Idraulica e Costruzioni Idrauliche - IDRA 2006, Roma, 10-15 Settembre 2006.

Viglione A., Claps P., Laio F. (2006) Water resources assessment and management under water scarcity scenarios, chapter Meanannual runoff estimation in North-Western Italy. CDSU, Milan.

See Also

lm, summary.lm, predict.lm

Examples

data(hydroSIMN)

D <- annualflows["dato"][,]
cod <- annualflows["cod"][,]

#Dm <- tapply(D,cod,mean)
#datregr <- cbind(Dm,parameters)
datregr <- parameters
regr0 <- lm(Dm ~ .,datregr); summary(regr0)
regr1 <- lm(Dm ~ Am + Hm + Ybar,datregr); summary(regr1)

R2.lm(regr0)
R2.lm(regr1)

prt.lm(regr0)
prt.lm(regr1)

vif.lm(regr0)
vif.lm(regr1)

RMSE.lm(regr0)
RMSE.lm(regr1)

MAE.lm(regr0)
MAE.lm(regr1)

predinterval.lm(regr0)

jackknife1.lm(regr0)
jackknife1.lm(regr1)

RMSEjk.lm(regr0)
RMSEjk.lm(regr1)

MAEjk.lm(regr0)
MAEjk.lm(regr1)

# mantel test on distance matrices
#Y <- AD.dist(D,cod)             # it takes some time
#X <- data.frame(apply(datregr[,c("Hm","Ybar")],2,dist))
#dati <- cbind(as.numeric(Y),X)
#modello <- lm(Y ~ Hm + Ybar, dati)
#mantel.lm(modello, Nperm=100)