Deletion and Other Diagnostic Methods for "ivreg" Objects

Source: R/ivregDiagnostics.R

Methods for computing deletion and other regression diagnostics for 2SLS regression. It's generally more efficient to compute the deletion diagnostics via the influence method and then to extract the various specific diagnostics with the methods for "influence.ivreg" objects. Other diagnostics for linear models, such as added-variable plots (avPlots) and component-plus-residual plots (crPlots), also work, as do effect plots (e.g., predictorEffects) with residuals (see the examples below). The pointwise confidence envelope for the qqPlot method assumes an independent random sample from the t distribution with degrees of freedom equal to the residual degrees of freedom for the model and so are approximate, because the studentized residuals aren't independent.

For additional information, see the vignette Diagnostics for 2SLS Regression.

# S3 method for class 'ivreg'
influence(
  model,
  sigma. = n <= 1000,
  type = c("stage2", "both", "maximum"),
  applyfun = NULL,
  ncores = NULL,
  ...
)

# S3 method for class 'ivreg'
rstudent(model, ...)

# S3 method for class 'ivreg'
cooks.distance(model, ...)

# S3 method for class 'influence.ivreg'
dfbeta(model, ...)

# S3 method for class 'ivreg'
dfbeta(model, ...)

# S3 method for class 'ivreg'
hatvalues(model, type = c("stage2", "both", "maximum", "stage1"), ...)

# S3 method for class 'influence.ivreg'
rstudent(model, ...)

# S3 method for class 'influence.ivreg'
hatvalues(model, ...)

# S3 method for class 'influence.ivreg'
cooks.distance(model, ...)

# S3 method for class 'influence.ivreg'
qqPlot(
  x,
  ylab = paste("Studentized Residuals(", deparse(substitute(x)), ")", sep = ""),
  distribution = c("t", "norm"),
  ...
)

# S3 method for class 'ivreg'
influencePlot(model, ...)

# S3 method for class 'influence.ivreg'
influencePlot(model, ...)

# S3 method for class 'ivreg'
infIndexPlot(model, ...)

# S3 method for class 'influence.ivreg'
infIndexPlot(model, ...)

# S3 method for class 'influence.ivreg'
model.matrix(object, ...)

# S3 method for class 'ivreg'
avPlots(model, terms, ...)

# S3 method for class 'ivreg'
avPlot(model, ...)

# S3 method for class 'ivreg'
mcPlots(model, terms, ...)

# S3 method for class 'ivreg'
mcPlot(model, ...)

# S3 method for class 'ivreg'
Boot(
  object,
  f = coef,
  labels = names(f(object)),
  R = 999,
  method = "case",
  ncores = 1,
  ...
)

# S3 method for class 'ivreg'
crPlots(model, terms, ...)

# S3 method for class 'ivreg'
crPlot(model, ...)

# S3 method for class 'ivreg'
ceresPlots(model, terms, ...)

# S3 method for class 'ivreg'
ceresPlot(model, ...)

# S3 method for class 'ivreg'
plot(x, ...)

# S3 method for class 'ivreg'
qqPlot(x, distribution = c("t", "norm"), ...)

# S3 method for class 'ivreg'
outlierTest(model, ...)

# S3 method for class 'ivreg'
spreadLevelPlot(x, main = "Spread-Level Plot", ...)

# S3 method for class 'ivreg'
ncvTest(model, ...)

# S3 method for class 'ivreg'
deviance(object, ...)

# S3 method for class 'rivreg'
influence(model, ...)

Arguments

model, x, object

A "ivreg" or "influence.ivreg" object.

sigma.

If TRUE (the default for 1000 or fewer cases), the deleted value of the residual standard deviation is computed for each case; if FALSE, the overall residual standard deviation is used to compute other deletion diagnostics.

type

If "stage2" (the default), hatvalues are for the second stage regression; if "both", the hatvalues are the geometric mean of the casewise hatvalues for the two stages; if "maximum", the hatvalues are the larger of the casewise hatvalues for the two stages. In computing the geometric mean or casewise maximum hatvalues, the hatvalues for each stage are first divided by their average (number of coefficients in stage regression/number of cases); the geometric mean or casewise maximum values are then multiplied by the average hatvalue from the second stage.

applyfun

Optional loop replacement function that should work like lapply with arguments function(X, FUN, ...). The default is to use a loop unless the ncores argument is specified (see below).

ncores

Numeric, number of cores to be used in parallel computations. If set to an integer the applyfun is set to use either parLapply (on Windows) or mclapply (otherwise) with the desired number of cores.

...

arguments to be passed down.

ylab

The vertical axis label.

distribution

"t" (the default) or "norm".

terms

Terms for which added-variable plots are to be constructed; the default, if the argument isn't specified, is the "regressors" component of the model formula.

f, labels, R

see Boot.

method

only "case" (case resampling) is supported: see Boot.

main

Main title for the graph.

Value

In the case of influence.ivreg, an object of class "influence.ivreg" with the following components:

coefficients

the estimated regression coefficients

model

the model matrix

dfbeta

influence on coefficients

sigma

deleted values of the residual standard deviation

dffits

overall influence on the regression coefficients

cookd

Cook's distances

hatvalues

hatvalues

rstudent

Studentized residuals

df.residual

residual degrees of freedom

In the case of other methods, such as rstudent.ivreg or rstudent.influence.ivreg, the corresponding diagnostic statistics. Many other methods (e.g., crPlot.ivreg, avPlot.ivreg, Effect.ivreg) draw graphs.

Examples

kmenta.eq1 <- ivreg(Q ~ P + D | D + F + A, data = Kmenta)
summary(kmenta.eq1)
#> 
#> Call:
#> ivreg(formula = Q ~ P + D | D + F + A, data = Kmenta)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -3.4305 -1.2432 -0.1895  1.5762  2.4920 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) 94.63330    7.92084  11.947 1.08e-09 ***
#> P           -0.24356    0.09648  -2.524   0.0218 *  
#> D            0.31399    0.04694   6.689 3.81e-06 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.966 on 17 degrees of freedom
#> Multiple R-Squared: 0.7548,	Adjusted R-squared: 0.726 
#> Wald test: 23.81 on 2 and 17 DF,  p-value: 1.178e-05 
#> 
car::avPlots(kmenta.eq1)
#> Error in avPlot.lm(model, term, main = "", ...): P is not a column of the model matrix.
car::mcPlots(kmenta.eq1)

car::crPlots(kmenta.eq1)

car::ceresPlots(kmenta.eq1)

car::influencePlot(kmenta.eq1)

#>      StudRes        Hat      CookD
#> 1 -1.7359357 0.09079703 0.06956671
#> 2 -1.3686682 0.26453459 0.21973049
#> 3 -2.0995532 0.13849570 0.17147564
#> 4 -0.2010944 0.39711512 0.01508349
#> 5 -0.4505155 0.46498004 0.05257374
car::influenceIndexPlot(kmenta.eq1)

car::qqPlot(kmenta.eq1)

#> 1937 1929 
#>   16    8 
car::spreadLevelPlot(kmenta.eq1)

#> 
#> Suggested power transformation:  -2.44685 
plot(effects::predictorEffects(kmenta.eq1, residuals = TRUE))

set.seed <- 12321 # for reproducibility
confint(car::Boot(kmenta.eq1, R = 250)) # 250 reps for brevity
#> Bootstrap bca confidence intervals
#> 
#>                  2.5 %       97.5 %
#> (Intercept) 74.1021451 107.77780398
#> P           -0.4454188   0.02161098
#> D            0.1902243   0.40024278
car::outlierTest(kmenta.eq1)
#> No Studentized residuals with Bonferroni p < 0.05
#> Largest |rstudent|:
#>       rstudent unadjusted p-value Bonferroni p
#> 1937 -2.099553           0.051985           NA
car::ncvTest(kmenta.eq1)
#> Non-constant Variance Score Test 
#> Variance formula: ~ fitted.values 
#> Chisquare = 0.2390325, Df = 1, p = 0.62491